Significant research efforts have been devoted to large-scale dynamical systems, with the aim of understanding their complicated behaviors and managing their responses in real-time. One pivotal technological obstacle in this process is the existence of uncertainty. Although many of these large-scale dynamical systems function well in the design stage, they may easily fail when operating in realistic environment, where environmental uncertainties modulate system dynamics and complicate real-time predication and management tasks. This dissertation aims to develop systematic methodologies to evaluate the performance of large-scale dynamical systems under uncertainty, as a step toward real-time decision support. Two uncertainty evaluation approaches are pursued: the analytical approach and the effective simulation approach. The analytical approach abstracts the dynamics of original stochastic systems, and develops tractable analysis (e.g., jump-linear analysis) for the approximated systems. Despite the potential bias introduced in the approximation process, the analytical approach provides rich insights valuable for evaluating and managing the performance of large-scale dynamical systems under uncertainty. When a system’s complexity and scale are beyond tractable analysis, the effective simulation approach becomes very useful. The effective simulation approach aims to use a few smartly selected simulations to quickly evaluate a complex system’s statistical performance. This approach was originally developed to evaluate a single uncertain variable. This dissertation extends the approach to be scalable and effective for evaluating large-scale systems under a large-number of uncertain variables. While a large portion of this dissertation focuses on the development of generic methods and theoretical analysis that are applicable to broad large-scale dynamical systems, many results are illustrated through a representative large-scale system application on strategic air traffic management application, which is concerned with designing robust management plans subject to a wide range of weather possibilities at 2-15 hours look-ahead time.

Thesis (B.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING / Includes bibliographical references. / by David Lui. / B.S.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: leaves 328-332. / by Marcel Coderch i Collell. / Ph.D.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Vita. / Includes bibliographical references. / by Pierre Dersin. / Ph.D.

This thesis deals with the design of multivariable controllers for stable linear time-invariant multi-input multi-output systems, with an unknown mathematical model, subject to constant reference/disturbance signals and actuator saturation constraints. A new controller parameter optimization approach, which can be carried out experimentally with no knowledge of the plant model nor of the order of the system, is proposed. The approach has the advantage that controllers can be optimized by perturbing only the initial conditions of the servocompensator, and that the order of the resulting controller obtained can be specified by the designer. Implementation of the proposed controller design approach is described, and an experimental application study of the proposed method applied to a multivariable system with industrial sensor/actuator components is presented to illustrate the feasibility of the design method in an industrial environment.

This thesis deals with the design of multivariable controllers for stable linear time-invariant multi-input multi-output systems, with an unknown mathematical model, subject to constant reference/disturbance signals and actuator saturation constraints. A new controller parameter optimization approach, which can be carried out experimentally with no knowledge of the plant model nor of the order of the system, is proposed. The approach has the advantage that controllers can be optimized by perturbing only the initial conditions of the servocompensator, and that the order of the resulting controller obtained can be specified by the designer. Implementation of the proposed controller design approach is described, and an experimental application study of the proposed method applied to a multivariable system with industrial sensor/actuator components is presented to illustrate the feasibility of the design method in an industrial environment.

This thesis presents decentralized model reference adaptive control techniques for systems with full-state feedback and systems with output feedback. The controllers are strictly decentralized, that is, each local controller uses feedback from only local subsystems and no information is shared between local controllers. The full-state feedback decentralized controller is effective for multi-input systems, where the dynamics matrix and control-input matrix are unknown. The decentralized controller achieves asymptotic stabilization and command following in the presence of sinusoidal disturbances with known spectrum. We present a construction technique of the reference-model dynamics such that the decentralized controller is effective for systems with arbitrarily large subsystem interconnections. The output-feedback decentralized controller is effective for single-input single-output subsystems that are minimum phase and relative degree one. The decentralized controller achieves asymptotic stabilization and disturbance rejection in the presence of an unknown disturbance, which is generated by an unknown Lyapunov-stable linear system.

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The performance modelling of large-scale systems using discrete-state approaches is fundamentally hampered by the well-known problem of state-space explosion, which causes exponential growth of the reachable state space as a function of the number of the components which constitute the model. Because they are mapped onto continuous-time Markov chains (CTMCs), models described in the stochastic process algebra PEPA are no exception. This thesis presents a deterministic continuous-state semantics of PEPA which employs ordinary differential equations (ODEs) as the underlying mathematics for the performance evaluation. This is suitable for models consisting of large numbers of replicated components, as the ODE problem size is insensitive to the actual population levels of the system under study. Furthermore, the ODE is given an interpretation as the fluid limit of a properly defined CTMC model when the initial population levels go to infinity. This framework allows the use of existing results which give error bounds to assess the quality of the differential approximation. The computation of performance indices such as throughput, utilisation, and average response time are interpreted deterministically as functions of the ODE solution and are related to corresponding reward structures in the Markovian setting. The differential interpretation of PEPA provides a framework that is conceptually analogous to established approximation methods in queueing networks based on meanvalue analysis, as both approaches aim at reducing the computational cost of the analysis by providing estimates for the expected values of the performance metrics of interest. The relationship between these two techniques is examined in more detail in a comparison between PEPA and the Layered Queueing Network (LQN) model. General patterns of translation of LQN elements into corresponding PEPA components are applied to a substantial case study of a distributed computer system. This model is analysed using stochastic simulation to gauge the soundness of the translation. Furthermore, it is subjected to a series of numerical tests to compare execution runtimes and accuracy of the PEPA differential analysis against the LQN mean-value approximation method. Finally, this thesis discusses the major elements concerning the development of a software toolkit, the PEPA Eclipse Plug-in, which offers a comprehensive modelling environment for PEPA, including modules for static analysis, explicit state-space exploration, numerical solution of the steady-state equilibrium of the Markov chain, stochastic simulation, the differential analysis approach herein presented, and a graphical framework for model editing and visualisation of performance evaluation results.