It is demonstrated that neural networks can be used effectively for the identification and control of nonlinear dynamical systems. The emphasis is on models for both identification and control. Static and dynamic backpropagation methods for the adjustment of parameters are discussed. In the models that are introduced, multilayer and recurrent networks are interconnected in novel configurations, and hence there is a real need to study them in a unified fashion. Simulation results reveal that the identification and adaptive control schemes suggested are practically feasible. Basic concepts and definitions are introduced throughout, and theoretical questions that have to be addressed are also described. >

Identification and control of dynamical systems using neural networks

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Convex Analysisの二,三の進展について

Meyn & Tweedie is back! The bible on Markov chains in general state spaces has been brought up to date to reflect developments in the field since 1996 - many of them sparked by publication of the first edition. The pursuit of more efficient simulation algorithms for complex Markovian models, or algorithms for computation of optimal policies for controlled Markov models, has opened new directions for research on Markov chains. As a result, new applications have emerged across a wide range of topics including optimisation, statistics, and economics. New commentary and an epilogue by Sean Meyn summarise recent developments and references have been fully updated. This second edition reflects the same discipline and style that marked out the original and helped it to become a classic: proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background.

Markov Chains and Stochastic Stability

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

1. Introduction. Control System Design Steps. Adaptive Control. A Brief History. 2. Models for Dynamic Systems. Introduction. State-Space Models. Input/Output Models. Plant Parametric Models. Problems. 3. Stability. Introduction. Preliminaries. Input/Output Stability. Lyapunov Stability. Positive Real Functions and Stability. Stability of LTI Feedback System. Problems. 4. On-Line Parameter Estimation. Introduction. Simple Examples. Adaptive Laws with Normalization. Adaptive Laws with Projection. Bilinear Parametric Model. Hybrid Adaptive Laws. Summary of Adaptive Laws. Parameter Convergence Proofs. Problems. 5. Parameter Identifiers and Adaptive Observers. Introduction. Parameter Identifiers. Adaptive Observers. Adaptive Observer with Auxiliary Input. Adaptive Observers for Nonminimal Plant Models. Parameter Convergence Proofs. Problems. 6. Model Reference Adaptive Control. Introduction. Simple Direct MRAC Schemes. MRC for SISO Plants. Direct MRAC with Unnormalized Adaptive Laws. Direct MRAC with Normalized Adaptive Laws. Indirect MRAC. Relaxation of Assumptions in MRAC. Stability Proofs in MRAC Schemes. Problems. 7. Adaptive Pole Placement Control. Introduction. Simple APPC Schemes. PPC: Known Plant Parameters. Indirect APPC Schemes. Hybrid APPC Schemes. Stabilizability Issues and Modified APPC. Stability Proofs. Problems. 8. Robust Adaptive Laws. Introduction. Plant Uncertainties and Robust Control. Instability Phenomena in Adaptive Systems. Modifications for Robustness: Simple Examples. Robust Adaptive Laws. Summary of Robust Adaptive Laws. Problems. 9. Robust Adaptive Control Schemes. Introduction. Robust Identifiers and Adaptive Observers. Robust MRAC. Performance Improvement of MRAC. Robust APPC Schemes. Adaptive Control of LTV Plants. Adaptive Control for Multivariable Plants. Stability Proofs of Robust MRAC Schemes. Stability Proofs of Robust APPC Schemes. Problems. Appendices. Swapping Lemmas. Optimization Techniques. Bibliography. Index. License Agreement and Limited Warranty.

Robust adaptive control

We consider stochastic dynamic games in large population conditions where multiclass agents are weakly coupled via their individual dynamics and costs. We approach this large population game problem by the so-called Nash Certainty Equivalence (NCE) Principle which leads to a decentralized control synthesis. The McKean-Vlasov NCE method presented in this paper has a close connection with the statistical physics of large particle systems: both identify a consistency relationship between the individual agent (or particle) at the microscopic level and the mass of individuals (or particles) at the macroscopic level. The overall game is decomposed into (i) an optimal control problem whose Hamilton-Jacobi-Bellman (HJB) equation determines the optimal control for each individual and which involves a measure corresponding to the mass effect, and (ii) a family of McKean-Vlasov (M-V) equations which also depend upon this measure. We designate the NCE Principle as the property that the resulting scheme is consistent (or soluble), i.e. the prescribed control laws produce sample paths which produce the mass effect measure. By construction, the overall closed-loop behaviour is such that each agent’s behaviour is optimal with respect to all other agents in the game theoretic Nash sense.

https://www.intlpress.com/site/pub/files/_fulltext/journals/cis/2006/0006/0003/CIS-2006-0006-0003-a005.pdf

Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle

Large Population Stochastic Dynamic Games: Closed-Loop McKean-Vlasov Systems and the Nash Certainty Equivalence Principle

We consider linear quadratic Gaussian (LQG) games in large population systems where the agents evolve according to nonuniform dynamics and are coupled via their individual costs. A state aggregation technique is developed to obtain a set of decentralized control laws for the individuals which possesses an epsiv-Nash equilibrium property. A stability property of the mass behavior is established, and the effect of inaccurate population statistics on an isolated agent is also analyzed by variational techniques.

Large-Population Cost-Coupled LQG Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized $\varepsilon$ -Nash Equilibria

This paper establishes global convergence for a class of adaptive control algorithms applied to discrete time multi-input multi-output deterministic linear systems. It is shown that the algorithms will ensure that the system inputs and outputs remain bounded for all time and that the output tracking error converges to zero.

Discrete-time multivariable adaptive control

Stochastic Processes Linear Stochastic Systems Estimation Theory Stochastic Realization Theory System Identification: Foundations and Basic Concepts Least Squares Parameter Estimation Maximum Likelihood Estimation of Gaussian Armax and State-Space System Minimum Prediction Error Identification Methods Non-Stationary System Identification Feedback, Causality, and Closed Loop System Identification Linear-Quadratic Stochastic Control Stochastic Adaptive Control Appendix 1: Probability Theory Appendix 2: System Theory Appendix 3: Harmonic Analysis.

Peter E. Caines

Papers

Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle

Large Population Stochastic Dynamic Games: Closed-Loop McKean-Vlasov Systems and the Nash Certainty Equivalence Principle

Large-Population Cost-Coupled LQG Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized $\varepsilon$ -Nash Equilibria

Discrete-time multivariable adaptive control

Linear stochastic systems