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Multibody dynamics simulations are currently widely accepted as valuable means for dynamic performance analysis of mechanical systems. The evolution of theoretical and computational aspects of the multibody dynamics discipline make it conducive these days for other types of applications, in addition to pure simulations. One very important such application is design optimization. A very important first step towards design optimization is sensitivity analysis of multibody system dynamics. Dynamic sensitivities are often calculated by means of finite differences. Depending of the number of parameters involved, this procedure can be computationally expensive. Moreover, in many cases, the results suffer from low accuracy when real perturbations are used. The main contribution to the state-of-the-art brought by this study is the development of the adjoint sensitivity approach of multibody systems in the context of the penalty formulation. The theory developed is demonstrated on one academic case study, a five-bar mechanism, and on one real-life system, a 14-DOF vehicle model. The five-bar mechanism is used to illustrate the sensitivity approach derived in this paper. The full vehicle model is used to demonstrate the capability of the new approach developed to perform sensitivity analysis and gradient-based optimization for large and complex multibody systems with respect to multiple design parameters.

Several concepts on the measure of observability, reachability, and robustness are defined and illustrated for both linear and nonlinear control systems. Defined by using computational dynamic optimization, these concepts are applicable to a wide spectrum of problems. Some questions addressed include the observability based on user-information, the determination of strong observability vs. weak observability, partial observability of complex systems, the computation of $L^2$-gain for nonlinear control systems, and the measure of reachability in the presence of state constraints. Examples on dynamic systems defined by both ordinary and partial differential equations are shown.

This is the final report of F49620-95-1-0131 which ended on 12/31/97. Our motivation for the work reported here is the need for effective design, analysis, and optimization techniques for large, complex, stochastic Discrete Event Dynamic Systems (D, EDS). DEDS are typified by communication networks, manufacturing, computer, C41, traffic and other systems governed by human-made rules and clearly important in all aspects of modern technology. The two major research thrusts of this effort are: New approaches to optimization specifically aimed at the problem of large search spaces that lack analytical structure. New ways to simulate DEDS in concurrent or parallel fashion that will speed up our ability to design and analyze their performance and that are naturally matched to emerging parallel computing capabilities and software paradigms such as object-oriented programming.

This paper introduces an improved particle swarm optimization (iPSO) algorithm designed for maximum power point tracking (MPPT) in photovoltaic (PV) systems. The proposed algorithm incorporates a novel reinitialization mechanism that dynamically detects and adapts to environmental changes. Additionally, an exponentially decreasing inertia weight is utilized to balance exploration and exploitation, ensuring rapid convergence to the global maximum power point (GMPP). A deterministic initialization strategy is employed to uniformly distribute particles across the search space, thereby increasing the likelihood of identifying the GMPP. The iPSO algorithm is thoroughly evaluated using a MATLAB/Simulink simulation and validated with real-time hardware, including a boost DC-DC converter, dSPACE, and a Chroma PV simulator. Comparative analysis with conventional PSO and PSO-reinit algorithms under various irradiance patterns demonstrates that the iPSO consistently outperforms in terms of convergence speed and MPPT efficiency. The study highlights the robustness of the iPSO algorithm in bridging theoretical models with practical applications.

This grant F49620-98-1-0387 is a natural continuation of our previous grant F49620-95-1-0131 which ended on 12/31/97. Our motivation for the work reported here is the need for effective design, analysis, and optimization techniques for large, complex, stochastic Discrete Event Dynamic Systems (DEDS). DEDS are typified by communication networks, manufacturing, computer, C4I traffic and other systems governed by human-made rules and clearly important in all aspects of modem technology. In addition, we have initiated a study of hybrid systems (i.e., systems combining time-driven with even V driven dynamics) with the goat of developing a comprehensive new theory for the optimal control of such systems with direct applications to manufacturing processes. The three major research thrusts of this effort are: (1) New ways to simulate DEDS in concurrent or parallel fashion that will speed up our ability to design and analyze their performance and that are naturally matched to emerging parallel computing capabilities and software paradigms such as object-oriented programming. (2) New approaches to optimization specifically aimed at the problem of large search spaces that lack analytical structure. (3) An emerging theory for the optimal control of DEDS, as well as Hybrid Systems (HS).

This grant F49620-98-1-0387 is a natural continuation of our previous grant F49620-95-1-0131 which ended on 12/31/97. Our motivation for the work reported here is the need for effective design, analysis, and optimization techniques for large, complex, stochastic Discrete Event Dynamic Systems (DEDS). DEDS are typified by communication networks, manufacturing, computer, C4I traffic and other systems governed by human-made rules and clearly important in all aspects of modem technology. In addition, we have initiated a study of hybrid systems (i.e., systems combining time-driven with even V driven dynamics) with the goat of developing a comprehensive new theory for the optimal control of such systems with direct applications to manufacturing processes. The three major research thrusts of this effort are: (1) New ways to simulate DEDS in concurrent or parallel fashion that will speed up our ability to design and analyze their performance and that are naturally matched to emerging parallel computing capabilities and software paradigms such as object-oriented programming. (2) New approaches to optimization specifically aimed at the problem of large search spaces that lack analytical structure. (3) An emerging theory for the optimal control of DEDS, as well as Hybrid Systems (HS).

This grant F49620-98-1-0387 is a natural continuation of our previous grant F49620-95-1-0131 which ended on 12/31/97. Our motivation for the work reported here is the need for effective design, analysis, and optimization techniques for large, complex, stochastic Discrete Event Dynamic Systems (DEDS). DEDS are typified by communication networks, manufacturing, computer, C4I traffic and other systems governed by human-made rules and clearly important in all aspects of modem technology. In addition, we have initiated a study of hybrid systems (i.e., systems combining time-driven with even V driven dynamics) with the goat of developing a comprehensive new theory for the optimal control of such systems with direct applications to manufacturing processes. The three major research thrusts of this effort are: (1) New ways to simulate DEDS in concurrent or parallel fashion that will speed up our ability to design and analyze their performance and that are naturally matched to emerging parallel computing capabilities and software paradigms such as object-oriented programming. (2) New approaches to optimization specifically aimed at the problem of large search spaces that lack analytical structure. (3) An emerging theory for the optimal control of DEDS, as well as Hybrid Systems (HS).

Green cellular networking has become an important research area in recent years due to environmental and economical concerns. Switching off under-utilized BSs during off-peak traffic load conditions is a promising approach to reduce energy consumption in cellular networks. In practice, during initial cell planning, the BS locations and RAN parameters are optimized to meet the basic system design requirements like coverage, capacity, overlap, QoS etc. As these metrics are tightly coupled with each other due to co-channel interference, switching off certain BSs may affect the system requirements. Therefore, identifying a subset of large number of BSs which are to be put into sleep mode, is a challenging dynamic optimization problem. In this work, we develop a multiobjective framework for dynamic optimization framework for OFDMA based cellular systems. The objective is to identify the appropriate set of active sectors and RAN parameters that maximize coverage and area spectral efficiency while minimizing overlap and area power consumption without violating the QoS requirements for a given traffic demand density. The objective functions and constraints are obtained using appropriate analytical models which capture the traffic characteristics, propagation characteristics (pathloss, shadowing, and small scale fading) as well as load condition in neighbouring cells. A low complexity evolutionary algorithm is used for identifying the global Pareto optimal solutions at a faster convergence rate. The inter-relationships between the system objectives are studied and guidelines are provided to find an appropriate network configuration that provides the best achievable trade-offs. The results show that using the proposed framework, significant amount of energy saving can be achieved and with a low computational complexity while maintaining good trade-offs among the other objectives.

Green cellular networking has become an important research area in recent years due to environmental and economical concerns. Switching off under-utilized BSs during off-peak traffic load conditions is a promising approach to reduce energy consumption in cellular networks. In practice, during initial cell planning, the BS locations and RAN parameters are optimized to meet the basic system design requirements like coverage, capacity, overlap, QoS etc. As these metrics are tightly coupled with each other due to co-channel interference, switching off certain BSs may affect the system requirements. Therefore, identifying a subset of large number of BSs which are to be put into sleep mode, is a challenging dynamic optimization problem. In this work, we develop a multiobjective framework for dynamic optimization framework for OFDMA based cellular systems. The objective is to identify the appropriate set of active sectors and RAN parameters that maximize coverage and area spectral efficiency while minimizing overlap and area power consumption without violating the QoS requirements for a given traffic demand density. The objective functions and constraints are obtained using appropriate analytical models which capture the traffic characteristics, propagation characteristics (pathloss, shadowing, and small scale fading) as well as load condition in neighbouring cells. A low complexity evolutionary algorithm is used for identifying the global Pareto optimal solutions at a faster convergence rate. The inter-relationships between the system objectives are studied and guidelines are provided to find an appropriate network configuration that provides the best achievable trade-offs. The results show that using the proposed framework, significant amount of energy saving can be achieved and with a low computational complexity while maintaining good trade-offs among the other objectives.

This thesis investigates adaptive compiler systems that perform, during program execution, code optimizations based on the dynamic behavior of the program as opposed to current approaches that employ a fixed code generation strategy, i.e., one in which a predetermined set of code optimizations are applied at compile-time to an entire program. The main problems associated with such adaptive systems are studied in general: which optimizations to apply to what parts of the program and when. Two different optimization strategies result: an ideal scheme which is not practical to implement, and a more basic scheme that is. The design of a practical system is discussed for the FORTRAN IV language. The system was implemented and tested with programs having different behavioral characteristics.

In this report, the technical objective is the derivation of a systematic and unified theory and organization of a corresponding general computer program for the design of constrained dynamic systems by judicious selection of the most suitable methods from the following branches of mathematics and mechanics: (a) Optimization Methods, (b) Rigid Body Mechanics, (c) Numerical Integration Methods, and (d) Matrix Manipulation Methods. Accordingly, a method of formulating and automatically integrating the equations of motion and design sensitivity adjoint equations for general constrained dynamic systems is presented. Design sensitivity analysis is carried out using a state-space method that has previously been used for design optimization of linear structural systems. Application of efficient sparse matrix computational methods is shown to be suitable for both dynamic and design sensitivity analyses and for interactive strained system is treated with three degrees of freedom. Algebraic equations prescribing constraints between various bodies are then written and a Lagrangian formulation is used to write the dynamical equations of motion for each body of the system. A stiff predictor-corrector numerical integration (GEAR) algorithm is used for numerical integration of mixed systems of nonlinear differential equations of motion and algebraic equations of constraint (together with spring-damper relations and other user-supplied equations).

Recent advances in the area of gradient methods for optimal control problems are reviewed. Single-subarc problems are treated. Specifically, two classes of optimal control problems, called Problem P1 and Problem P2 are considered. Problem P1 consists of minimizing a functional 1 which depends on the n-vector state x(t), the m-vector control u(t), and the p-vector parameter pi. Problem P2 enlarges dramatically the number and variety of problems of optimal control which can be treated by gradient-restoration algorithms. Eight numerical examples are presented to illustrate the performance of the algorithms associated with Problem P1 and Problem P2. The numerical results show the feasibility as well as the convergence characteristics of these algorithms.

Recent advances in the area of gradient methods for optimal control problems are reviewed. Single-subarc problems are treated. Specifically, two classes of optimal control problems, called Problem P1 and Problem P2 for easy identification, are solved. Problem P1 consists of minimizing a functional I which depends on the n-vector state x(t), the m-vector control u(t), and the p-vector parameter 3.14. The state is given at the initial point. At the final point, the state and the parameter are required to satisfy q scalar relations. Problem P2 differs from Problem P1 in that the state, the control, and the parameter are required to satisfy k additional scalar relation along the interval of integration. Algorithms of the sequential gradient-restoration type are given for both Problem 1 and Problem 2. Problem P2 enlarges the number and variety of problems of optimal control which can be treated by gradient-restoration algorithms. Eight numerical examples are presented to illustrate the performance of the algorithms associated with Problem P1 and Problem P2. The numerical results show the feasibility as well as the convergence characteristics of these algorithms.