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The research supported by AFOSR Grant 76-2923 has led to some significant results which can be used in the design of optimal controllers when disturbances are present. Sufficient conditions which a minmax control must satisfy were developed for systems with disturbances in the state equation or in the measurement of the initial state. From these conditions, constructive techniques were developed which can be used to generate minmax controllers. The second major area of the research was controllability problems. Criteria for determining the controllability properties of constrained systems were derived. The criteria involve finite dimensional optimization problems and are amenable to computer implementation. (Author)

This paper presents an optimal control method for a class of distributed-parameter systems governed by first order, quasilinear hyperbolic partial differential equations that arise in many physical systems. Such systems are characterized by time delays since information is transported from one state to another by wave propagation. A general closed-loop hyperbolic transport model is controlled by a boundary control embedded in a periodic boundary condition. The boundary control is subject to a nonlinear differential equation constraint that models actuator dynamics of the system. The hyperbolic equation is thus coupled with the ordinary differential equation via the boundary condition. Optimality of this coupled system is investigated using variational principles to seek an adjoint formulation of the optimal control problem. The results are then applied to implement a model predictive control design for a wind tunnel to eliminate a transport delay effect that causes a poor Mach number regulation.

A method is devised for numerically solving a class of finite-horizon optimal control problems subject to cascade linear discrete-time dynamics. It is assumed that the linear state and input inequality constraints, and the quadratic measure of performance, are all separable with respect to the spatial dimension of the underlying cascade of sub-systems, as well as the temporal dimension of the dynamics. By virtue of this structure, the computation cost of an interior-point method for an equivalent quadratic programming formulation of the optimal control problem can be made to scale linearly with the number of sub-systems. However, the complexity of this approach grows cubically with the time horizon. As such, computational advantage becomes apparent in situations where the number of sub-systems is relatively large. In any case, the method is amenable to distributed computation with low communication overhead and only immediate upstream neighbour sharing of partial model data among processing agents. An example is presented to illustrate an application of the main results to model data for the cascade dynamics of an automated irrigation channel.

The paper is concerned with optimal control of backward stochastic differential equation (BSDE) driven by Teugel's martingales and an independent multi-dimensional Brownian motion, where Teugel's martingales are a family of pairwise strongly orthonormal martingales associated with L\'{e}vy processes (see Nualart and Schoutens \cite{NuSc}). We derive the necessary and sufficient conditions for the existence of the optimal control by means of convex variation methods and duality techniques. As an application, the optimal control problem of linear backward stochastic differential equation with a quadratic cost criteria (called backward linear-quadratic problem, or BLQ problem for short) is discussed and characterized by stochastic Hamilton system.

Continuous motorization and urbanization around the globe leads to an expansion of population in major cities. Therefore, ever-growing pressure imposed on the existing mass transit systems calls for a better technology, Intelligent Transportation Systems (ITS), to solve many new and demanding management issues. Many studies in the extant ITS literature attempted to address these issues within which various research methodologies were adopted. However, there is very few paper summarized what does optimal control theory (OCT), one of the sharpest tools to tackle management issues in engineering, do in solving these issues. It{\textquoteright}s both important and interesting to answer the following two questions. (1) How does OCT contribute to ITS research objectives? (2) What are the research gaps and possible future research directions? We searched 11 top transportation and control journals and reviewed 41 research articles in ITS area in which OCT was used as the main research methodology. We categorized the articles by four different ways to address our research questions. We can conclude from the review that OCT is widely used to address various aspects of management issues in ITS within which a large portion of the studies aimed to reduce traffic congestion. We also critically discussed these studies and pointed out some possible future research directions towards which OCT can be used.

This paper presents a novel method for controlling teams of unmanned aerial vehicles using Stochastic Optimal Control (SOC) theory. The approach consists of a centralized high-level planner that computes optimal state trajectories as velocity sequences, and a platform-specific low-level controller which ensures that these velocity sequences are met. The planning task is expressed as a centralized path-integral control problem, for which optimal control computation corresponds to a probabilistic inference problem that can be solved by efficient sampling methods. Through simulation we show that our SOC approach (a) has significant benefits compared to deterministic control and other SOC methods in multimodal problems with noise-dependent optimal solutions, (b) is capable of controlling a large number of platforms in real-time, and (c) yields collective emergent behaviour in the form of flight formations. Finally, we show that our approach works for real platforms, by controlling a team of three quadrotors in outdoor conditions.

This paper presents the topology and machine learning-based intelligent control of a single-stage grid-connected high-power photovoltaic (PV) system for quality power export to the grid and optimal net energy utilization. A nineteen-level bi-modular inverter is proposed for efficient single-stage PV power conversion. The proposed integrated intelligent machine learning-based control serves for power conversion control as well as supervisory control for hourly PV energy estimation and load demand control for optimal energy consumption. The objectives of power control are extracting maximum power from PV sources and exporting power to the grid at unity power factor. While the objectives for supervisory control are local load demand control for exporting power at higher export prices. The proposed system is implemented using MATLAB/Simulink to validate the efficiency of power conversion, effectiveness of machine learning for energy estimation, and load relay control for optimal energy pricing. The results proved efficient tracking of maximum power, unity power factor at grid terminals, and load relay control for PV energy availability and export cost function.

This paper presents a new model-reference adaptive control method based on a bi-objective optimal control formulation for systems with input uncertainty. A parallel predictor model is constructed to relate the predictor error to the estimation error of the control effectiveness matrix. In this work, we develop an optimal control modification adaptive control approach that seeks to minimize a bi-objective linear quadratic cost function of both the tracking error norm and predictor error norm simultaneously. The resulting adaptive laws for the parametric uncertainty and control effectiveness uncertainty are dependent on both the tracking error and predictor error, while the adaptive laws for the feedback gain and command feedforward gain are only dependent on the tracking error. The optimal control modification term provides robustness to the adaptive laws naturally from the optimal control framework. Simulations demonstrate the effectiveness of the proposed adaptive control approach.

Optimal control of bilinear systems has been a well-studied subject in the area of mathematical control. However, techniques for solving emerging optimal control problems involving an ensemble of structurally identical bilinear systems are underdeveloped. In this work, we develop an iterative method to effectively and systematically solve these challenging optimal ensemble control problems, in which the bilinear ensemble system is represented as a time-varying linear ensemble system at each iteration and the optimal ensemble control law is then obtained by the singular value expansion of the input-to-state operator that describes the dynamics of the linear ensemble system. We examine the convergence of the developed iterative procedure and pose optimality conditions for the convergent solution. We also provide examples of practical control designs in magnetic resonance to demonstrate the applicability and robustness of the developed iterative method.

This final technical report contains a summary and highlights of the research funded by AFOSR under Grant F49620-924-0261, titled 'Computational Methods for Control and Optimal Design of Aerospace Systems (FY 91 AASERT)', for tbe period 1 June 1992 to 31 May 1995. This AASERT grant supported two graduate students to work on the following topics; (1) the development of shape optimization algorithms for flow tailoring with applications to the design of forebody simulators, and (2) control of fluid/structure interactions. A new sensitivity equation method was developed and integrated into an optimization package for optimal design and flow tailoring. This method was transitioned into software packages at several industrial and government sites. In addition, this research produced a new understanding of the role that dissipation plays in optimization based design, and produced a new framework to analyze convergence of algorithms based on approximations of sensitivity equations. The report contains a summary of these results and a list of papers produced during this period. (AN)

Traditionally, power system scheduling and control are separately implemented. To bridge the gap between these two activities, online adjustment of the optimal schedule is necessary. Because such adjustment degrades energy efficiency and dynamic response, it is desirable to integrate the two functions seamlessly. One possible solution is to optimize the control references directly. In this paper, a fully-distributed, multi-agent based control solution is presented to reduce the fuel consumption of shipboard power systems. Every generator has an associated agent that only communicates with its neighboring agents. With a properly-designed communication network, the solution can guarantee convergence, even during losses of the communication channel. This fully-distributed design can significantly improve the reliability and survivability of the system, especially during battle conditions. The improved subgradient based optimization solution can address both equality and inequality constraints and can provide performance comparable to that of centralized solutions. Simulation studies demonstrate the effectiveness of the proposed solution.

Optical jitter can result in the beam pointing inaccuracy and poor optical system performance. With a correlated measurement of the disturbance, improved control performance can be achieved. In this research, an adaptive optimal sensing strategy for optical systems is proposed. When an array of reference sensors is available, an optimal set of reference sensors that are coupled to modes of interests can be selected. The weighted reference signal from the optimal sensor set is then used in an adaptive control design algorithm. An adaptive generalized predictive control design algorithm combined with the proposed adaptive optimal sensing strategy achieves better performance than the control system using only one of the reference sensors. The overall algorithm is also advantageous in the presence of time-varying or uncertain disturbances. The proposed technique is applied to an experimental test bed in which multiple accelerometer sensors measure the structural vibration of optical elements. Reduction of the structural vibration of optical components is attained using a fast steering mirror which results in a reduction of the corresponding jitter.

In this paper, we study a class of fractional optimal control problems. A necessary condition for the existence of an optimal control is provided in the literature. It is commonly given as the existence of a solution of a fractional Pontryagin's system and the proof is based on the introduction of a Lagrange multiplier. Assuming an additional condition on these problems, we suggest a new presentation of this result with a proof using only classical mathematical tools adapted to the fractional case: calculus of variations, Gronwall's Lemma, Cauchy-Lipschitz Theorem and stability under perturbations of differential equations. In this paper, we furthermore provide a way in order to transit from a classical optimal control problem to its fractional version via the Stanislavsky's formalism. We also solve a strict fractional example allowing to test numerical schemes. Finally, we state a fractional Noether's theorem giving the existence of an explicit constant of motion for fractional Pontryagin's systems admitting a symmetry.

In this paper, we study a class of fractional optimal control problems. A necessary condition for the existence of an optimal control is provided in the literature. It is commonly given as the existence of a solution of a fractional Pontryagin's system and the proof is based on the introduction of a Lagrange multiplier. Assuming an additional condition on these problems, we suggest a new presentation of this result with a proof using only classical mathematical tools adapted to the fractional case: calculus of variations, Gronwall's Lemma, Cauchy-Lipschitz Theorem and stability under perturbations of differential equations. In this paper, we furthermore provide a way in order to transit from a classical optimal control problem to its fractional version via the Stanislavsky's formalism. We also solve a strict fractional example allowing to test numerical schemes. Finally, we state a fractional Noether's theorem giving the existence of an explicit constant of motion for fractional Pontryagin's systems admitting a symmetry.

Optimal control applications for electrothermal multijet systems for attitude control and station keeping of 24-hour synchronous satellite

A study was made, leading to development and analysis of a technique allowing the control moment gyro (CMG) momentum vectors to avoid adverse orientations and thus to provide optimal control for the Apollo Telescope Mount. The technique was formulated in terms of a feedback scheme using a check factor, K, formed as the product of the dot products of the three CMG momentum unit vectors. The parameter K approaches unity for all adverse orientations and was used to initiate a single correction maneuver to rotate the CMG momenta away from a pending adverse orientation and to reduce K to an acceptable value. A digital computer program for ATM simulations was modified to incorporate this correction maneuver and performance was evaluated in simulated cases. Antiparallelism was used as the primary example for the evaluation of the feedback optimization technique.

Recently a new optimal control modification has been introduced that can achieve robust adaptation with a large adaptive gain without incurring high-frequency oscillations as with the standard model-reference adaptive control. This modification is based on an optimal control formulation to minimize the L2 norm of the tracking error. The optimal control modification adaptive law results in a stable adaptation in the presence of a large adaptive gain. This study examines the optimal control modification adaptive law in the context of a system with a time scale separation resulting from a fast plant with a slow actuator. A singular perturbation analysis is performed to derive a modification to the adaptive law by transforming the original system into a reduced-order system in slow time. A model matching conditions in the transformed time coordinate results in an increase in the actuator command that effectively compensate for the slow actuator dynamics. Simulations demonstrate effectiveness of the method.

The need to maintain optimal energy efficiency is critical during the drilling operations performed on future and current planetary rover missions (see figure). Specifically, this innovation seeks to solve the following problem. Given a spring-loaded percussive drill driven by a voice-coil motor, one needs to determine the optimal input voltage waveform (periodic function) and the optimal hammering period that minimizes the dissipated energy, while ensuring that the hammer-to-rock impacts are made with sufficient (user-defined) impact velocity (or impact energy). To solve this problem, it was first observed that when voice-coil-actuated percussive drills are driven at high power, it is of paramount importance to ensure that the electrical current of the device remains in phase with the velocity of the hammer. Otherwise, negative work is performed and the drill experiences a loss of performance (i.e., reduced impact energy) and an increase in Joule heating (i.e., reduction in energy efficiency). This observation has motivated many drilling products to incorporate the standard bang-bang control approach for driving their percussive drills. However, the bang-bang control approach is significantly less efficient than the optimal energy-efficient control approach solved herein. To obtain this solution, the standard tools of classical optimal control theory were applied. It is worth noting that these tools inherently require the solution of a two-point boundary value problem (TPBVP), i.e., a system of differential equations where half the equations have unknown boundary conditions. Typically, the TPBVP is impossible to solve analytically for high-dimensional dynamic systems. However, for the case of the spring-loaded vibro-impactor, this approach yields the exact optimal control solution as the sum of four analytic functions whose coefficients are determined using a simple, easy-to-implement algorithm. Once the optimal control waveform is determined, it can be used optimally in the context of both open-loop and closed-loop control modes (using standard realtime control hardware).

The optimal control of two-level systems by time-dependent laser fields is studied using a variational theory. We obtain, for the first time, general analytical expressions for the optimal pulse shapes leading to global maximization or minimization of different physical quantities. We present solutions which reproduce and improve previous numerical results.

We consider optimizing average queueing delay and average power consumption in a nonpreemptive multi-class M/G/1 queue with dynamic power control that affects instantaneous service rates. Four problems are studied: (1) satisfying per-class average delay constraints; (2) minimizing a separable convex function of average delays subject to per-class delay constraints; (3) minimizing average power consumption subject to per-class delay constraints; (4) minimizing a separable convex function of average delays subject to an average power constraint. Combining an achievable region approach in queueing systems and the Lyapunov optimization theory suitable for optimizing dynamic systems with time average constraints, we propose a unified framework to solve the above problems. The solutions are variants of dynamic $c\mu$ rules, and implement weighted priority policies in every busy period, where weights are determined by past queueing delays in all job classes. Our solutions require limited statistical knowledge of arrivals and service times, and no statistical knowledge is needed in the first problem. Overall, we provide a new set of tools for stochastic optimization and control over multi-class queueing systems with time average constraints.

We consider optimizing average queueing delay and average power consumption in a nonpreemptive multi-class M/G/1 queue with dynamic power control that affects instantaneous service rates. Four problems are studied: (1) satisfying per-class average delay constraints; (2) minimizing a separable convex function of average delays subject to per-class delay constraints; (3) minimizing average power consumption subject to per-class delay constraints; (4) minimizing a separable convex function of average delays subject to an average power constraint. Combining an achievable region approach in queueing systems and the Lyapunov optimization theory suitable for optimizing dynamic systems with time average constraints, we propose a unified framework to solve the above problems. The solutions are variants of dynamic $c\mu$ rules, and implement weighted priority policies in every busy period, where weights are determined by past queueing delays in all job classes. Our solutions require limited statistical knowledge of arrivals and service times, and no statistical knowledge is needed in the first problem. Overall, we provide a new set of tools for stochastic optimization and control over multi-class queueing systems with time average constraints.

Part I of this paper deals with the problem of designing a feedback control for a linear infinite dimensional system in such a way that a given quadratic cost functional is minimized. The essential feature of this work is that: (a) it allows for unbounded control and observation, i.e. boundary control, point observation, input/output delays; and (b) the general theory is presented in such a way that it applies to both parabolic and hyperbolic partial differential equations as well as retarded and neutral functional differential equations. Part II develops a state space approach for retarded systems with delays in both input and output. A particular emphasis is placed on the development of the duality theory by means of two different state concepts. The resulting evolution equations fit into the framework of Part I. (Author)

The efficient numerical treatment of optimal control problems governed by elliptic partial differential equations (PDEs) and systems of elliptic PDEs, where the control is finite dimensional is discussed. Distributed control as well as boundary control cases are discussed. The main characteristic of the new methods is that they are designed to solve the full optimization problem directly, rather than accelerating a descent method by an efficient multigrid solver for the equations involved. The methods use the adjoint state in order to achieve efficient smoother and a robust coarsening strategy. The main idea is the treatment of the control variables on appropriate scales, i.e., control variables that correspond to smooth functions are solved for on coarse grids depending on the smoothness of these functions. Solution of the control problems is achieved with the cost of solving the constraint equations about two to three times (by a multigrid solver). Numerical examples demonstrate the effectiveness of the method proposed in distributed control case, pointwise control and boundary control problems.

The problem of resource allocation of nonlinear networked control systems is investigated, where, unlike the well discussed case of triggering for stability, the objective is optimal triggering. An approximate dynamic programming approach is developed for solving problems with fixed final times initially and then it is extended to infinite horizon problems. Different cases including Zero-Order-Hold, Generalized Zero-Order-Hold, and stochastic networks are investigated. Afterwards, the developments are extended to the case of problems with unknown dynamics and a model-free scheme is presented for learning the (approximate) optimal solution. After detailed analyses of convergence, optimality, and stability of the results, the performance of the method is demonstrated through different numerical examples.

We consider the optimal control of quantum systems interacting non-linearly with an electromagnetic field. We propose new monotonically convergent algorithms to solve the optimal equations. The monotonic behavior of the algorithm is ensured by a non-standard choice of the cost which is not quadratic in the field. These algorithms can be constructed for pure and mixed-state quantum systems. The efficiency of the method is shown numerically on molecular orientation with a non-linearity of order 3 in the field. Discretizing the amplitude and the phase of the Fourier transform of the optimal field, we show that the optimal solution can be well-approximated by pulses that could be implemented experimentally.

In this two-part paper, we identify a broad class of decentralized output-feedback LQG systems for which the optimal control strategies have a simple intuitive estimation structure and can be computed efficiently. Roughly, we consider the class of systems for which the coupling of dynamics among subsystems and the inter-controller communication is characterized by the same directed graph. Furthermore, this graph is assumed to be a multitree, that is, its transitive reduction can have at most one directed path connecting each pair of nodes. In this first part, we derive sufficient statistics that may be used to aggregate each controller's growing available information. Each controller must estimate the states of the subsystems that it affects (its descendants) as well as the subsystems that it observes (its ancestors). The optimal control action for a controller is a linear function of the estimate it computes as well as the estimates computed by all of its ancestors. Moreover, these state estimates may be updated recursively, much like a Kalman filter.

The bounded-real and positive-real lemmas solve two important linear-quadratic optimal control problems related to the concepts of non-expansive and passive systems, respectively. The lemmas assume controllability, yet a non-expansive or passive system can be uncontrollable. In this paper, we solve these optimal control problems without assuming controllability. We obtain necessary and sufficient conditions for a system to be non-expansive (passive) which augment the bounded-real (positive-real) condition with new conditions relating to the uncontrollable modes of the system. A characterisation of the set of solutions to the linear matrix inequalities in the bounded-real and positive-real lemmas is obtained.

In this paper, we prove a theorem on the rate of convergence for the optimal cost computed using PS methods. It is a first proved convergence rate in the literature of PS optimal control. In addition to the high-order convergence rate, two theorems are proved for the existence and convergence of the approximate solutions. This paper contains several essential differences from existing papers on PS optimal control as well as some other direct computational methods. The proofs do not use necessary conditions of optimal control. Furthermore, we do not make coercivity type of assumptions. As a result, the theory does not require the local uniqueness of optimal solutions. In addition, a restrictive assumption on the cluster points of discrete solutions made in existing convergence theorems are removed.

- In this paper we introduce a new method to solve fixed-delay optimal control problems which exploits numerical homotopy procedures. It is known that solving this kind of problems via indirect methods is complex and computationally demanding because their implementation is faced with two difficulties: the extremal equations are of mixed type, and besides, the shooting method has to be carefully initialized. Here, starting from the solution of the non-delayed version of the optimal control problem, the delay is introduced by numerical homotopy methods. Convergence results, which ensure the effectiveness of the whole procedure, are provided. The numerical efficiency is illustrated on an example.

This paper first describes a class of uncertain stochastic control systems with Markovian switching, and derives an It\^o-Liu formula for Markov-modulated processes. And we characterize an optimal control law, which satisfies the generalized Hamilton-Jacobi-Bellman (HJB) equation with Markovian switching. Then, by using the generalized HJB equation, we deduce the optimal consumption and portfolio policies under uncertain stochastic financial markets with Markovian switching. Finally, for constant relative risk-aversion (CRRA) felicity functions, we explicitly obtain the optimal consumption and portfolio policies. Moreover, we also make an economic analysis through numerical examples.

In this paper the notion of normalized nonspecificity is introduced. The nonspecifity measures the uncertainty of the estimated parameters that reflect impairment in a controlled system. Based on this notion, a quantity called a reconfiguration coverage is calculated. It represents the likelihood of success of a control reconfiguration action. This coverage links the overall system reliability to the achievable and required control, as well as diagnostic performance. The coverage, when calculated on-line, is used for managing the redundancy in the system.

In this work we study the asymptotic behavior of the solutions of a class of abstract parabolic time optimal control problems when the generators converge, in an appropriate sense, to a given strictly negative operator. Our main application to PDEs systems concerns the behavior of optimal time and of the associated optimal controls for parabolic equations with highly oscillating coefficients, as we encounter in homogenization theory. Our main results assert that, provided that the target is a closed ball centered at the origin and of positive radius, the solutions of the time optimal control problems for the systems with oscillating coefficients converge, in the usual norms, to the solution of the corresponding problem for the homogenized system. In order to prove our main theorem, we provide several new results, which could be of a broader interest, on time and norm optimal control problems.

We generalize the classical theory on algebraic Riccati equations and optimization to infinite-dimensional well-posed linear systems, thus completing the work of George Weiss, Olof Staffans and others. We show that the optimal control is given by the stabilizing solution of an integral Riccati equation. If the input operator is not maximally unbounded, then this integral Riccati equation is equivalent to the algebraic Riccati equation. Using the integral Riccati equation, we show that for (nonsingular) minimization problems the optimal state-feedback loop is always well-posed. In particular, the optimal state-feedback operator is admissible also for the original semigroup, not only for the closed-loop semigroup (as has been known in some cases); moreover, both settings are well-posed with respect to an external input. This leads to the positive solution of several central, previously open questions on exponential, output and dynamic (aka. "internal") stabilization and on coprime factorization of transfer functions. Our theory covers all quadratic (possibly indefinite) cost functions, but the optimal state feedback need not be well-posed (admissible) unless the cost function is uniformly positive or the system is sufficiently regular.

To operate a microgrid system in islanded mode, it is essential to analyze the economic feasibility and performance of the system. The proposed system integrates two or more renewable energy sources, providing a promising solution for meeting energy needs sustainably. Conducting a techno-economic analysis of such microgrid systems is critical to maximizing the efficient utilization of renewable energy sources. The simulations for these microgrid systems are performed using HOMER Pro software, where various economic parameters—such as cost of energy (COE), electricity production, net present cost (NPC), carbon emissions, fuel consumption, and payback period—are evaluated for the proposed systems. Additionally, the system's performance is analyzed using PSIM software, which incorporates optimal switching control. The results are further validated using a prototype hardware setup. The findings indicate that the PV/hydro system with NPC: 705,658 Rs and payback period: 9.65 years is the most suitable option for meeting the electricity demand in rural areas. Also, through optimal switching control applied to the micro grid converter the output voltage achieved is seven levels and harmonic distortion is 3.7% for voltage and 1.7% for the current.

This paper considers the problem of obtaining an optimal control law, which is constrained to be a linear feedback of the available measurements, for both continuous and discrete time linear systems subjected to additive white process noise and measurement noise. Necessary conditions are obtained for minimizing a quadratic performance function for both finite and infinite terminal time cases. The feedback gains are constrained to be time invariant for the infinite terminal time cases. For all the cases considered, algorithms are derived for generating sequences of feedback gain matrices which successively improve the performance function. A continuous time numerical example is included for the purpose of demonstration. Optimal control, Output feedback, Stochastic control, Star category 10.

The intent of the study detailed in this paper is to demonstrate the benefits of inverter var control on a fast timescale to mitigate rapid and large voltage fluctuations due to the high penetration of photovoltaic generation and the resulting reverse power flow. Our approach is to formulate the volt/var control as a radial optimal power flow (OPF) problem to minimize line losses and energy consumption, subject to constraints on voltage magnitudes. An efficient solution to the radial OPF problem is presented and used to study the structure of optimal inverter var injection and the net benefits, taking into account the additional cost of inverter losses when operating at non-unity power factor. This paper will illustrate how, depending on the circuit topology and its loading condition, the inverter's optimal reactive power injection is not necessarily monotone with respect to their real power output. The results are demonstrated on a distribution feeder on the Southern California Edison system that has a very light load and a 5 MW photovoltaic (PV) system installed away from the substation.

In this paper, a unified approach to sequence-based control and estimation of linear networked systems with multiple sensors is proposed. Time delays and data losses in the controller-actuator-channel are compensated by sending sequences of control inputs. The sequence-based design paradigm is further extended to the sensor-controller-channels without increasing the load of the network. In this context, we present a recursive solution based on the Hypothesizing Distributed Kalman Filter (HKF) that is included in the overall sequence-based controller design.

The recent works on quadrotor have focused on more and more challenging tasks on increasingly complex systems. Systems are often augmented with slung loads, inverted pendulums or arms, and accomplish complex tasks such as going through a window, grasping, throwing or catching. Usually, controllers are designed to accomplish a specific task on a specific system using analytic solutions, so each application needs long preparations. On the other hand, the direct multiple shooting approach is able to solve complex problems without any analytic development, by using on-the-shelf optimization solver. In this paper, we show that this approach is able to solve a wide range of problems relevant to quadrotor systems, from on-line trajectory generation for quadrotors, to going through a window for a quadrotor-and-pendulum system, through manipulation tasks for a aerial manipulator.

The objective of this work is to study time-minimum and energy-minimum global optimal control for dissipative open quantum systems whose dynamics is governed by the Lindblad equation. The controls appear only in the Hamiltonian. Using recent results regarding the decoupling of such dissipative dynamics into intra- and inter-unitary orbits, we transform the control system into a bi-linear control system on the Bloch ball (the unitary sphere together with its interior). We then design a numerical algorithm to construct an optimal path to achieve a desired point given initial states close to the origin (the singular point) of the Bloch ball. This is done both for the minimum-time and minimum -energy control problems.

A control problem with a system modeled as a nondeterministic finite state machine is considered. Several agents seek to optimize the behavior of the system under a minimax criterion, with each agent having different information about the system state. The nondeterministic model of uncertainty, combined with the minimax criterion, lead to equivalence relations on the past input/output histories of each agent which generate rather simple sufficient statistics for the optimal control laws. This sheds light on the basic nature of decentralized control and permits complete solution of a particular class of problems. (Author)

This paper considers the optimal control structure for multi-shop (Part I: Parallel, Part II: Series) systems, where the input to the shop system is random and the shop output is determined by the number of workers in the shop. The number of workers available to the system is held constant, while control is exercised in discrete time by adjusting the allocation of workers to the various shops in the system. There is a cost for transferring workers. Additionally, there is a cost of holding backlog in the system. The control objective is to minimize the sum of these costs over an infinite horizon. It is shown that for some regions of the system's state space the optimal control policies are known exactly without resorting to computational methods. For other regions it is shown that the problem can be decomposed into subproblems of reduced complexity. Finally, an inertia (hysteresis) property is established which reduces the number of policy combinations which must be considered in some dases, and completely eliminates the necessity to determine policy in other cases. The net result is a substantial reduction in the computer storage and computational effort required to solve for the optimal control policy.

This thesis documents the research effort to develop, integrate and implement the system hardware and the software necessary to validate the Air Force Institute of Technology's theoretical advances in small unmanned aerial systems (SUAS) cooperative control. The end state objective of the research effort was to flight test an autonomous control algorithm on a communication relay unmanned aerial vehicle (UAV) that was actively relaying data to and from a rover UAV. The relay UAV is one part of a SUAS designed to utilize cooperative control to extend the effective line-of-sight operating range for a rover UAV. An algorithm is integrated into ground control software that takes telemetry data (the current position of the ground station, rover UAV, and relay UAV) to determine where to navigate the relay aircraft for optimal communication signal strength. The ground station operator flies the rover aircraft in the extended line-of-sight operational envelope just as she/he would in the normal line-of-sight operations. The relay UAV is autonomously routed to the optimal communications relay position. The research yielded a SUAS based on the Ardupilot Mega 2.0. Flight testing demonstrated the SUAS's ability to generate the correct navigation data autonomously; however, the navigation data was not successfully activated as current waypoints on the relay UAV?s autopilot. Software in the loop testing was utilized to verify a solution to activate the navigation data but flight testing was not conducted to verify the simulation results.

Control problems for singularly perturbed systems with unconstrained control have been given considerable attention and major results have been obtained. For these problems the concept of time scale decomposition has been developed providing a separation of slow and fast dynamics and a reduction in problem order. (Author)

This paper studies the problem of optimal control of quasilinear partial differential systems. A maximum principle necessary condition is derived and shown to be sufficient when the Hamiltonian and boundary conditions satisfy a convexity condition. The derivation is made using Stokes theorem and a generalized version of Green's theorem. Management science applications are suggested to problems of cattle ranching, perishable inventories, manpower planning, and advertising. (Author)

We present variational theory for optimal control over a finite time interval in quantum systems with relaxation. The corresponding Euler-Lagrange equations determining the optimal control field are derived. In our theory the optimal control field fulfills a high order differential equation, which we solve analytically for some limiting cases. We determine quantitatively how relaxation effects limit the control of the system. The theory is applied to open two level quantum systems. An approximate analytical solution for the level occupations in terms of the applied fields is presented. Different other applications are discussed.

The research being performed under AFOSR Grant 76-2923 is concerned with optimally controlling a system to a specified target when disturbances or uncertainties enter the system. Two general problems in this area are being investigated. One problem is that of determining if there exists a control that assures that the system reaches a specified target set for all possible disturbances. If such a control exists, then the next problem is to determine a control which guarantees that the target is reached and it also optimal in the sense of minimizing a specified measure of the system's performance. Our research effort has been directed toward obtaining methods for answering the questions raised by these problems and thereby aiding in the design of controllers for uncertain systems. (Author)

Optimal control of switched systems is challenging due to the discrete nature of the switching control input. The embedding-based approach addresses this challenge by solving a corresponding relaxed optimal control problem with only continuous inputs, and then projecting the relaxed solution back to obtain the optimal switching solution of the original problem. This paper presents a novel idea that views the embedding-based approach as a change of topology over the optimization space, resulting in a general procedure to construct a switched optimal control algorithm with guaranteed convergence to a local optimizer. Our result provides a unified topology based framework for the analysis and design of various embedding-based algorithms in solving the switched optimal control problem and includes many existing methods as special cases.

Optimal control of switched systems is challenging due to the discrete nature of the switching control input. The embedding-based approach addresses this challenge by solving a corresponding relaxed optimal control problem with only continuous inputs, and then projecting the relaxed solution back to obtain the optimal switching solution of the original problem. This paper presents a novel idea that views the embedding-based approach as a change of topology over the optimization space, resulting in a general procedure to construct a switched optimal control algorithm with guaranteed convergence to a local optimizer. Our result provides a unified topology based framework for the analysis and design of various embedding-based algorithms in solving the switched optimal control problem and includes many existing methods as special cases.

In this paper we study strongly robust optimal control problems under volatility uncertainty. In the $G$-framework we adapt the stochastic maximum principle to find necessary and sufficient conditions for the existence of a strongly robust optimal control.

We present an efficient strategy for controlling a vast range of non-integrable quantum many body one-dimensional systems that can be merged with state-of-the-art tensor network simulation methods like the density Matrix Renormalization Group. To demonstrate its potential, we employ it to solve a major issue in current optical-lattice physics with ultra-cold atoms: we show how to reduce by about two orders of magnitudes the time needed to bring a superfluid gas into a Mott insulator state, while suppressing defects by more than one order of magnitude as compared to current experiments [1]. Finally, we show that the optimal pulse is robust against atom number fluctuations.