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Most discrete event system models are based on defining the alphabet set or the set of events as a fundamental concept. This paper takes an alternative view of treating the state space as the fundamental concept. We approach the problem of controlling discrete event systems by using predicates and predicate transformers. Predicates have the advantage that they can concisely characterize an infinite state space. The notion of controllability of a predicate is defined, and the supervisory predicate control problem introduced in this paper is solved. A closed form expression for the weakest controllable predicate is obtained. The problem of controlling discrete event systems under incomplete state observation is also considered arid observability of predicates is defined. Techniques for finding external solutions of boolean equations is used to derive minimally restrictive supervisors.

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace. The Koopman operator is an infinite-dimensional linear operator that evolves observable functions of the state-space of a dynamical system [Koopman 1931, PNAS]. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems [Williams et al. 2015, JNLS]. Choosing nonlinear observable functions to form an invariant subspace where it is possible to obtain linear models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis using a new algorithm to determine terms in a dynamical system by sparse regression of the data in a nonlinear function space [Brunton et al. 2015, arxiv]; we show how this algorithm is related to DMD. Finally, we demonstrate how to design optimal control laws for nonlinear systems using techniques from linear optimal control on Koopman invariant subspaces.

A simple algorithm is described to target any desired operation point for simple one-dimensional and two-dimensional dynamical systems. What makes the algorithm unique is the fact that it targets any desired point, not merely a stable/unstable fixed point of the dynamics. It is shown how the method may be applied to the logistic map and the H\'enon map. Generalisations to the case of n-dimensional dynamical systems are discussed.

A methodology for solving two-point boundary value problems in phase space for Hamiltonian systems is presented. Using Hamilton-Jacobi theory in conjunction with the canonical transformation induced by the phase flow, we show that the generating functions for this transformation solve any two-point boundary value problem in phase space. Properties of the generating functions are exposed, we especially emphasize multiple solutions, singularities, relations with the state transition matrix and symmetries. Then, we show that using Hamilton's principal function we are also able to solve two-point boundary value problems, nevertheless both methodologies have fundamental differences that we explore. Finally, we present some applications of this theory. Using the generating functions for the phase flow canonical transformation we are able to solve the optimal control problem (without an initial guess), to study phase space structures in Hamiltonian dynamical systems (periodic orbits, equilibrium points) and classical targeting problems (this last topic finds its applications in the design of spacecraft formation trajectories, reconfiguration, formation keeping, etc...).

A methodology for solving two-point boundary value problems in phase space for Hamiltonian systems is presented. Using Hamilton-Jacobi theory in conjunction with the canonical transformation induced by the phase flow, we show that the generating functions for this transformation solve any two-point boundary value problem in phase space. Properties of the generating functions are exposed, we especially emphasize multiple solutions, singularities, relations with the state transition matrix and symmetries. Then, we show that using Hamilton's principal function we are also able to solve two-point boundary value problems, nevertheless both methodologies have fundamental differences that we explore. Finally, we present some applications of this theory. Using the generating functions for the phase flow canonical transformation we are able to solve the optimal control problem (without an initial guess), to study phase space structures in Hamiltonian dynamical systems (periodic orbits, equilibrium points) and classical targeting problems (this last topic finds its applications in the design of spacecraft formation trajectories, reconfiguration, formation keeping, etc...).

A methodology for solving two-point boundary value problems in phase space for Hamiltonian systems is presented. Using Hamilton-Jacobi theory in conjunction with the canonical transformation induced by the phase flow, we show that the generating functions for this transformation solve any two-point boundary value problem in phase space. Properties of the generating functions are exposed, we especially emphasize multiple solutions, singularities, relations with the state transition matrix and symmetries. Then, we show that using Hamilton's principal function we are also able to solve two-point boundary value problems, nevertheless both methodologies have fundamental differences that we explore. Finally, we present some applications of this theory. Using the generating functions for the phase flow canonical transformation we are able to solve the optimal control problem (without an initial guess), to study phase space structures in Hamiltonian dynamical systems (periodic orbits, equilibrium points) and classical targeting problems (this last topic finds its applications in the design of spacecraft formation trajectories, reconfiguration, formation keeping, etc...).

This final report summarizes work on a three-year project devoted to dynamic friction and on control of systems with frictional forces. Detailed theoretical and numerical studies of static and dynamic friction and various phenomena of dynamic friction (stick-slip motion, self-excited oscillations, frictional damping, etc.) are described. Included in the report is also a study of methods of statistical homogenization, devised to develop new micromechanics-based models of contact and friction. The question of optimal control with distributed dynamical systems of viscoelastic bodies with frictional forces is also described. A final component of this study focuses on the mathematical and numerical analysis of elastohydrodynamic lubrication problems and is included in the final chapter. The studies presented in this report provide both a theoretical and numerical basis for modeling contact and friction. These models are shown to produce results in very good qualitative and quantitative agreement with experimental results. Keywords: Friction, Damping, Structural dynamics, Elastohydrodynamic lubrication.

Identification and control of non-linear dynamical systems is a very complex task which requires new methods of approaching. This research addresses the problem of emulation and control via the use of distributed parallel processing, namely artificial neural networks. Four models for describing non-linear MIMO dynamical systems are presented. Based on these models a combined feedforward and recurrent neural networks are structured to emulate the dynamical system. Further, a procedure to emulate multiple systems is suggested. A method for finding a minimal realization of a network is introduced. The minimization greatly reduces the complexity of the network without degrading the operating performance of the network. This work also examines the application of artificial neural networks for adaptive control. The multiple system approach is used to find an adaptive neural network controller for non-linear MIMO time-varying system in a direct model reference control scheme. The controller network is trained using a procedure called back-propagation through the plant, which was extended in this work. The application of neural networks is demonstrated on a longitudinal model of the F/A-18A fighter aircraft both with the undamaged aircraft and with a damage mechanism as a time-varying MIMO dynamical system.

Effective heat transport systems in aerospace are based on multiphase loop heat pipes (LHPs). For a precise thermal control of the electronics, electrical heaters are additionally used to control the operating temperature of the LHP. This work focusses on the dynamical modeling and model-based control design for LHP-based heat transport systems. The results of this work can be used for the optimization of current control parameters and the efficient control design for future LHP applications.

Effective heat transport systems in aerospace are based on multiphase loop heat pipes (LHPs). For a precise thermal control of the electronics, electrical heaters are additionally used to control the operating temperature of the LHP. This work focusses on the dynamical modeling and model-based control design for LHP-based heat transport systems. The results of this work can be used for the optimization of current control parameters and the efficient control design for future LHP applications.

Effective heat transport systems in aerospace are based on multiphase loop heat pipes (LHPs). For a precise thermal control of the electronics, electrical heaters are additionally used to control the operating temperature of the LHP. This work focusses on the dynamical modeling and model-based control design for LHP-based heat transport systems. The results of this work can be used for the optimization of current control parameters and the efficient control design for future LHP applications.

Effective heat transport systems in aerospace are based on multiphase loop heat pipes (LHPs). For a precise thermal control of the electronics, electrical heaters are additionally used to control the operating temperature of the LHP. This work focusses on the dynamical modeling and model-based control design for LHP-based heat transport systems. The results of this work can be used for the optimization of current control parameters and the efficient control design for future LHP applications.

Progress is reported on modeling of toxic pathways for dioxin and trichloroethylene, reduced order modeling in nonlinear coupled fluid/acoustics problems, electromagnetic interrogation of dispersive media and modeling of nonlinear hysteresis in materials.

Progress is reported on modeling of toxic pathways for dioxin and trichloroethylene, reduced order modeling in nonlinear coupled fluid/acoustics problems, electromagnetic interrogation of dispersive media and modeling of nonlinear hysteresis in materials.

A unified theory is given of dynamically modified decay and decoherence of field-driven multilevel multipartite entangled states that are weakly coupled to zero-temperature baths or undergo random phase fluctuations. The theory allows for arbitrary local differences in their coupling to the environment. Due to such differences, the optimal driving-field modulation to ensure maximal fidelity is found to substantially differ from conventional ``Bang-Bang'' or $\pi$-phase flips of the single-qubit evolution.

Dissertation supervisor, Daniel J. Collins

A number of results have been obtained for problems of stochastic control and stochastic differential games. Stochastic linear-quadratic, continuous time, stochastic control problems are solved for systems with noise processes that are arbitrary fractional Brownian motions or more generally square integrable continuous processes. Linear-quadratic control problems for stochastic partial differential equations with fractional Brownian motions having the Hurst parameter in the interval (1/2,1), which includes the long range dependent processes, are solved. A direct method for solving stochastic control problems is given that does not require the solution of Hamilton-Jacobi-Bellman equations or the solution of backward stochastic differential equations. Both of these latter methods present serious difficulties for solutions. A stochastic control problem is explicitly solved for a system that evolves in the two-sphere which is useful for applications. Linear exponential quadratic Gaussian control problems for both continuous and discrete time systems are solved in a simple direct way. Linear exponential-quadratic control problems for stochastic partial differential equations are explicitly solved. Discrete time linear quadratic control problems for systems with correlated noise are explicitly solved. Linear-quadratic stochastic differential games are explicitly solved for systems with arbitrary noise. Stochastic differential games for stochastic partial differential equations with fractional Brownian motions are explicitly solved. Ergodic control problems for linear exponential quadratic control for stochastic partial differential equations with fractional brownian motions are explicitly solved. Stochastic differential games that evolve in spheres are explicitly solved. Various aspects of stochastic adaptive control are described. Some linear quadratic control problems with state dependent noise are explicitly solved.

This thesis develops an approach to addressing the coupled navigation and control problem for wheeled mobile robots. Instead of using a top-down decoupled approach that does not respect low-level constraints, or a bottom-up approach that cannot guarantee satisfaction of high-level goals, our approach is middle-out. We develop local feedback control policies that respect the low-level constraints. The approach then uses a collection of these policies with existing formal discrete planning methods to either produce a hybrid feedback control policy that guarantees high-level goals are satisfied, or in the worst case, verifies that the high-level specification is not realizable. Our approach enables existing formal symbolic planning methods to be applied to highly constrained systems. We extend the sequential composition of local feedback control policies to wheeled mobile robots in a way that enables the automated synthesis of hybrid control policies. The thesis defines four basic composability requirements that guide our design of local policies. We develop two families of generic feedback policies that induce low-level behaviors in a way that enables their formal composition. The thesis also develops a novel approach for guaranteeing that a given control policy is collision free. By design, the policies respect multiple interacting constraints including large non-circular body shapes, nonholonomic constraints, and input bounds. Given a collection of the local policies and a task specification, our approach uses existing symbolic planning methods to automatically synthesize a switching strategy among the policies. Executing the switching strategy induces continuous motion that satisfies the high-level behavioral specification. This thesis demonstrates the approach on real mobile robots.

This thesis develops an approach to addressing the coupled navigation and control problem for wheeled mobile robots. Instead of using a top-down decoupled approach that does not respect low-level constraints, or a bottom-up approach that cannot guarantee satisfaction of high-level goals, our approach is middle-out. We develop local feedback control policies that respect the low-level constraints. The approach then uses a collection of these policies with existing formal discrete planning methods to either produce a hybrid feedback control policy that guarantees high-level goals are satisfied, or in the worst case, verifies that the high-level specification is not realizable. Our approach enables existing formal symbolic planning methods to be applied to highly constrained systems. We extend the sequential composition of local feedback control policies to wheeled mobile robots in a way that enables the automated synthesis of hybrid control policies. The thesis defines four basic composability requirements that guide our design of local policies. We develop two families of generic feedback policies that induce low-level behaviors in a way that enables their formal composition. The thesis also develops a novel approach for guaranteeing that a given control policy is collision free. By design, the policies respect multiple interacting constraints including large non-circular body shapes, nonholonomic constraints, and input bounds. Given a collection of the local policies and a task specification, our approach uses existing symbolic planning methods to automatically synthesize a switching strategy among the policies. Executing the switching strategy induces continuous motion that satisfies the high-level behavioral specification. This thesis demonstrates the approach on real mobile robots.

The objectives of this work are 1) to develop a robust stability theory for hybrid dynamical systems, both in continuous time and discrete time, including a complete theory on the existence of smooth Lyapunov functions (which are the major workhorse for the analysis of non-hybrid dynamical systems) for hybrid systems; 2) to exploit this theory in developing tools for the design of robust feedback control algorithms for hybrid dynamical systems; and 3) to apply the developed control concepts to problems relevant to the Army's mission, ie.g., autonomous vehicles and network centric control.

Studies of spatiotemporal dynamical behavior in chemical systems were carried out. We have built on our expertise in addressable excitable media to develop and characterize particle-like waves that autonomously navigate and traverse obstacle-filled landscapes. Experimental investigations have been combined with theoretical and computational analyses in each project. The results of our studies are generally applicable, and our advances in designing and controlling spatiotemporal dynamical systems will be beneficial to the Department of Defense.

Studies of spatiotemporal dynamical behavior in chemical systems were carried out. We have built on our expertise in addressable excitable media to develop and characterize particle-like waves that autonomously navigate and traverse obstacle-filled landscapes. Experimental investigations have been combined with theoretical and computational analyses in each project. The results of our studies are generally applicable, and our advances in designing and controlling spatiotemporal dynamical systems will be beneficial to the Department of Defense.

Research results include: (1) Developed empirical performance criteria for characterizing stabilities and robustness of the maglev control experimental system and completed a preliminary implementation of the performance characterization algorithms; (2) Developed and experimented with a phase-space search algorithm for synthesizing control actions; (3) Presented part of the above results in an article, 'Phas-Space Nonlinear Control Tool-box: The Maglev Experience' at HS'97: Fifth International Hybrid Systems Workshop, Notre Dame, IN, Sept. 11-13,1997

This dissertation addresses issues in the control of nonlinear instabilities in high-performance engineering systems. Specifically, the author considers nonlinear control systems near the limits of their operating envelope. These are highly nonlinear situations occurring in the high-performance operation of a wide variety of systems. Such systems tend to exhibit nonlinear stabilities in terms of a jump to a new low-performance operating point, oscillatory behavior, chaotic behavior, or system collapse in the absence of appropriate control action. Such situations necessitate the study of controlling nonlinear phenomena such as bifurcations and chaos. A new approach to the control of chaotic dynamical systems is introduced, namely, control of routes to chaos. The theme is to design feedback control laws that ensure a sufficient degree of stability for a primary bifurcation in the routes to chaos. A thermal convection loop is used as a vehicle to illustrate the idea. Moreover, as the period doubling cascade is one of the most famous routes to chaos, the stabilization of period doubling bifurcations for general n-dimensional discrete-time nonlinear systems is investigated. The technique presented here affords considerable flexibility in terms of achievable behavior of the nonlinear system over a range of parameter values. One contribution is the modeling, analysis, and control of voltage collapse in electric power systems. A new mechanism of voltage collapse is suggested based on the framework of catastrophic bifurcations. Bifurcation control laws are designed to control these nonlinear phenomena at the inception of voltage collapse. The control laws are shown to result in improved performance of the system for a greater range of parameter values. Another important application considered is the stall phenomenon in axial flow compressors. A combination of bifurcation analysis and nonlinear control is used to study the dynamics and active control of rotating stall.

This project aims to develop new concepts, theory, and algorithms for control and signal processing using ideas inspired by molecular systems biology. Cell biology provides a wide repertoire of systems that are strongly fault-tolerant, nonlinear, feedback-rich, and truly hybrid, while making effective use of highly heterogeneous sensing and actuation channels. Advances in genomic/proteomics and molecular systems biology research are continually adding detailed knowledge of such systems' architecture and operation, thus offering, in principle, a powerful source of inspiration for innovative solutions to problems of control and communication, sensor and actuator design, and systems integration.

Efforts continue on methods for estimation and control in distributed systems. Numerical work has also begun on these techniques. A complete treatment for the problem of estimating coefficients and boundary parameters in hyperbolic systems such as those that arise in geophysical inverse problems is given. (Author)

The research supported by the grant developed an approach for robust control system design and a compatible theory for modeling, identification and approximation of dynamical systems. It dealt with the case of linear systems, lumped as well as distributed parameter systems. Case studies highlighted the use of the techniques, and computer software was prepared. An analogous framework for robust control analysis of nonlinear systems was advanced. In particular, robustness measures were developed and a methodology for computing induced norms was derived. The research also focused on implementation issues of sampled data control systems, the effects of persistent excitations in control systems, and numerical aspects of spectral factorization.

The research supported by the grant developed an approach for robust control system design and a compatible theory for modeling, identification and approximation of dynamical systems. It dealt with the case of linear systems, lumped as well as distributed parameter systems. Case studies highlighted the use of the techniques, and computer software was prepared. An analogous framework for robust control analysis of nonlinear systems was advanced. In particular, robustness measures were developed and a methodology for computing induced norms was derived. The research also focused on implementation issues of sampled data control systems, the effects of persistent excitations in control systems, and numerical aspects of spectral factorization.

The research supported by the grant developed an approach for robust control system design and a compatible theory for modeling, identification and approximation of dynamical systems. It dealt with the case of linear systems, lumped as well as distributed parameter systems. Case studies highlighted the use of the techniques, and computer software was prepared. An analogous framework for robust control analysis of nonlinear systems was advanced. In particular, robustness measures were developed and a methodology for computing induced norms was derived. The research also focused on implementation issues of sampled data control systems, the effects of persistent excitations in control systems, and numerical aspects of spectral factorization.

The goal of this research is to develop high-performance computational tools for designing control systems for a class of complex physical systems. (1) Developed a verification algorithm for verifying control laws using phase-space geometric modeling of dynamical systems. The algorithm evolves a hierarchically-refined bound of system nonlinear dynamics and can address practical concerns such as sensor, actuator, and modeling uncertainties in a systematic manner. We have applied the algorithm to the maglev control system prototype and compared the results against the physical measurements. (2) Constructed a physical experiment to study distributed acoustic sensing. The experiment comprises an enclosed chamber measured 1.7m x 0.846m x 0.201m, and an 8-channel A/D and D/A system with 6 microphones and a speaker. (3) Started to investigate control system design and optimization for distributed parameter physical systems (systems modeled by partial differential equations). (4) Will present the control verification paper at the IFAC International Symposium on Artificial Intelligence in Real-Time Control, Grand Canyon, AZ in October. Have presented an invited tutorial at AAAI National Conference in Madison, Wisconsin, July 1998. Jeff May and Feng Zhao, "Verification of control laws using phase-space geometric modeling of dynamical systems." IFAC AIRTC-98. Feng Zhao and Chris Bailey-Kellogg, "Intelligent Simulation." AAAI-98 Tutorial Forum.

The goal of this research is to develop high-performance computational tools for designing control systems for a class of complex physical systems. (1) Developed a verification algorithm for verifying control laws using phase-space geometric modeling of dynamical systems. The algorithm evolves a hierarchically-refined bound of system nonlinear dynamics and can address practical concerns such as sensor, actuator, and modeling uncertainties in a systematic manner. We have applied the algorithm to the maglev control system prototype and compared the results against the physical measurements. (2) Constructed a physical experiment to study distributed acoustic sensing. The experiment comprises an enclosed chamber measured 1.7m x 0.846m x 0.201m, and an 8-channel A/D and D/A system with 6 microphones and a speaker. (3) Started to investigate control system design and optimization for distributed parameter physical systems (systems modeled by partial differential equations). (4) Will present the control verification paper at the IFAC International Symposium on Artificial Intelligence in Real-Time Control, Grand Canyon, AZ in October. Have presented an invited tutorial at AAAI National Conference in Madison, Wisconsin, July 1998. Jeff May and Feng Zhao, "Verification of control laws using phase-space geometric modeling of dynamical systems." IFAC AIRTC-98. Feng Zhao and Chris Bailey-Kellogg, "Intelligent Simulation." AAAI-98 Tutorial Forum.

I investigate experimentally and theoretically the application of control techniques in systems that display temporal instabilities, including chaos, on very short timescales. My study includes two distinct systems: a fast chaotic electronic circuit called the diode resonator, and a compound-cavity semiconductor laser system that exhibits an instability called low-frequency fluctuations. Control of fast unstable systems presents several experimental challenges. It is also a topic of broad interest, since it requires the development of new control techniques, and addresses technologically important devices such as the semiconductor laser. The diode resonator is a well-understood system, and when modified for 10 MHz operation serves as a good testbed for the application of novel control techniques. I develop a new high-speed time-delay feedback control technique that is based on the comparison of the present value of a system variable with a series of its past values. The principles of operation of this technique are studied in both time and frequency domains, as well as possible methods for its implementation. I develop a detailed analog electronic implementation that addresses the experimental needs of rapid processing and faithful reproduction of the feedback signal. This control system successfully stabilizes unstable periodic orbits in the diode resonator, the fastest experimental instability controlled to date. This technique also increases significantly the regions of parameter space in which control is effective, in comparison with previous methods. The improvement is gained by incorporating more information from further in the system's past.

This work involves investigations in reaction diffusion equations with Neumann boundary conditions, numerical approximations of the attractor for abstract evolutionary equations which include the Navier Stokes equation, and in computational methods for control and identification of processes governed by distributed parameter systems. Contents: Inverse problems for hyperbolic systems with unknown boundary parameters; Parameter identification in continuum models, Modeling of flexible surfaces: A preliminary study; The linear regulator problem for parabolic systems; Computational methods for estimation of parameters in hyperbolic systems; Estimation of temporally and spatially varying coefficients in models for insect dispersal; Spline-based estimation techniques for parameters in elliptic distributed systems; A spline-based parameter and state estimation technique for static models of elastic surfaces; Estimation techniques for transport equations; Large diffusivity and asymptotic behavior in parabolic systems; and Varying boundary conditions with large diffusivity.

In this article we develop, step by step, the framework for universal dynamical control of two-level systems (TLS) or qubits experiencing amplitude- or phase-noise (AN or PN) due to coupling to a thermal bath. A comprehensive arsenal of modulation schemes is introduced and applied to either AN or PN, resulting in completely analogous formulae for the decoherence rates, thus underscoring the unified nature of this universal formalism. We then address the extension of this formalism to multipartite decoherence control, where symmetries are exploited to overcome decoherence.

Chemical model systems were studied to develop insights into the behavior and control of spatiotemporal dynamical systems. Noise supported wave propagation has been characterized as well as power-law relations that are characteristic of avalanche behavior. Studies were also carried out of periodically driven excitable media, spatial symmetry breaking, and the evolution of three-dimensional scroll waves. Theoretical studies were carried out on exclusive product selectivity and self-segregation in systems with competitive autocatalysis as well as coherent structure analysis of spatiotemporal chaos. Topographic organization of Hebbian neural connections, uncertain destination dynamics in coupled Lorenz systems, and normal modes for chemical reactions from time series analysis were also studied.

Two very important and fundamental topics in the theory of dynamical systems are observability and identifiability. There has been limited work on the observability and identifiability of nonlinear dynamical systems. This problem is addressed by viewing the observation process as a nonlinear mapping of the initial states (and parameters) to the output measurements. The problem of observability and identifiability is then reduced to finding conditions under which the nonlinear mapping is one-to-one. (Author)

Feedback control of bifurcation and chaos in nonlinear dynamical system is discussed. Open problems in bifurcation control are noted. The past two decades have witnessed a steadily increasing appreciation of nonlinear dynamics across a broad range of disciplines. Applications of bifurcation and chaos have appeared in many areas of science, engineering, and the social sciences. The main purpose of this article is to discuss the role which nonlinear dynamics has played in the cross-disciplinary field of automatic control. The article also discusses in some detail the analysis and control of period-doubling bifurcations, and application to control of the associated route to chaos. Thoughts on some open problems are given, emphasizing the needed interplay between nonlinear dynamics and control theory.

Identification and control of non-linear dynamical systems is a very complex task which requires new methods of approaching. This research addresses the problem of emulation and control via the use of distributed parallel processing, namely artificial neural networks. Four models for describing non- linear MIMO dynamical system are presented. Based on these models a combined feedforward and recurrent neural networks are structured to emulate the dynamical system. Further, a procedure to emulate multiple systems in a single network is suggested. A method for finding a minimal realization of a network is introduced. The minimization greatly reduces the complexity of the network without degrading the operating performance of the network. This work also examines the application of artificial neural networks for adaptive control. The multiple-system approach is used to find an adaptive neural network controller for non-linear MIMO time-varying system in a direct model reference control scheme. The controller network is trained using a procedure called bock- propagation through the plant, which was extended in this work. The application of neural networks is demonstrated on a longitudinal model of the F/A-18A fighter aircraft both with the undamaged aircraft and with a the mechanism as a time-varying MIMO dynamical system. Neural networks, Identification, Adaptive control, Non-Linear systems, Tim-Varying dynamical systems.

The main goal of this report is to summarize the progress achieved under the program during the past three years. Since most of the technical results appeared, or soon will appear, in over 100 archival journals and conference publications, we shall only summarize results and remark on their significance and interrelationship. As part of this research program, we proposed the development of a general analysis and control design framework for large-scale nonlinear dynamical systems. In particular, we concentrate on hybrid control, hierarchical control, impulsive dynamical systems, non-negative dynamical systems, compartmental systems, large-scale systems, nonlinear switching control, and adaptive control. Application areas include large flexible interconnected space structures, vibration control of aerospace structures, spacecraft stabilization, biological systems, physiological systems, and pharmacological systems.

This report lists all the research results that have been achieved during the funding period for robot trajectory planning problems and testbed: (i) research goals and milestones, (ii) hardware/software design, integration, and validation, (iii) bio-inspired trajectory planning algorithm, (iv) robot localization and obstacle detection, (v) simulation validation and hardware demonstration. All the research objectives have been accomplished.

This project aims to develop new concepts, theory, and algorithms for control and signal processing using ideas inspired by molecular systems biology. Cell biology provides a wide repertoire of systems that are strongly fault-tolerant, nonlinear, feedback-rich, and truly hybrid, while making effective use of highly heterogeneous sensing and actuation channels. Advances in genomic/proteomics and molecular systems biology research are continually adding detailed knowledge of such systems' architecture and operation, thus offering, in principle, a powerful source of inspiration for innovative solutions to problems of control and communication, sensor and actuator design, and systems integration.

We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of the process matrix acting on a system. This equation is applicable to non-Markovian and/or strong coupling regimes. We propose two distinct applications for this dynamical equation. We first demonstrate identification of quantum Hamiltonians generating dynamics of closed or open systems via performing process tomography. In particular, we argue how one can efficiently estimate certain classes of sparse Hamiltonians by performing partial tomography schemes. In addition, we introduce a novel optimal control theoretic setting for manipulating quantum dynamics of Hamiltonian systems, specifically for the task of decoherence suppression.

Essential book to know how the data drive the decisions

A Markovian model for a quantum automata, i.e. an open quantum dynamical discrete-time system with input and output channels and a feedback, is described. A dynamical theory of quantum discrete-time adaptive measurements and multi-stage quantum statistical decisions is developed and applied to the optimal feedback control problem for the quantum dynamical objects. Quantum analogies of Stratonovich non-stationary filtering, and Bellman quantum dynamical programming in the discrete time are derived. A Gaussian Langevin model of the quantum one-dimensional linear Markovian dynamical system matched with a quantum linear transmission line as an input-output quantum noisy channel is studied. The optimal quantum multi-stage decision rule consisting of a classical linear optimal control strategy and the quantum optimal filtering of the noise is found. The latter contains the optimal quantum coherent measurement on the output of the line and the recursive processing by the Kalman filter. A time-continuous limit of the above model is considered, and the quantum nondemolition measurement, time-continuous filtering and the optimal dynamical programming are found in this limit. All the results are illustrated by an example of the optimal control problem for a quantum open oscillator matched to a quantum transmission line.

In this paper state estimation and feedback tracking control methods for nonlinear systems are presented. The methods, which are based on the state-dependent Riccati equation, allow the construction of nonlinear estimators and nonlinear feedback tracking controls for a wide class of systems. Our emphasis will be on development of computational methods that are easily implementable as well as efficient. Simulation results of the performance of the nonlinear estimator and tracking control are included. In addition, comparisons with the linear estimator and linear tracking control found through the linearized system are also made.

The primary objective of this research is to develop new tools of analysis and control strategies for mechanical systems which can be modeled as a set of differential equations with time-periodic coefficients. These systems include helicopter rotor blades (in forward flight), asymmetric rotor bearing systems high speed reciprocating engines, etc. Analysis is essential for basic understanding of such systems and it is the first step before one can attempt to design or develop an active control technology. In this research techniques have been developed to construct dynamically equivalent time invariant forms of time periodic systems, utilizing the Lyapunov-Floquet (L-F) transformation. These time-invariant forms permit one to employ classical control methods readily available for time-invariant systems. An efficient symbolic technique to compute stability boundaries explicitly in terms of system parameters has been developed. Unlike the traditional averaging and perturbation methods, this approach does not require the time varying parameters to be small. Further, it has been shown that transient response of periodic linear systems with either deterministic or stochastic external excitation can also be efficiently computed using the L-F transformation technique. Control of several rotating time-periodic systems has been studied, utilizing the time-invariant forms constructed via the L-F transformation. For the time-invariant systems classical state-feedback and observer based controllers can be designed and the time-varying controller can be obtain by back transformation. Control of lumped model systems as well as elastic beam models and systems with periodic discontinuities have been considered.

In this paper we investigate the limits of control for mixed-state quantum systems. The constraint of unitary evolution for non-dissipative quantum systems imposes kinematical bounds on the optimization of arbitrary observables. We summarize our previous results on kinematical bounds and show that these bounds are dynamically realizable for completely controllable systems. Moreover, we establish improved bounds for certain partially controllable systems. Finally, the question of dynamical realizability of the bounds for arbitary partially controllable systems is shown to depend on the accessible sets of the associated control system on the unitary group U(N) and the results of a few control computations are discussed briefly.