Adaptive Dynamic Programming for Control: Algorithms and by Huaguang Zhang, Derong Liu, Yanhong Luo, Ding Wang

By Huaguang Zhang, Derong Liu, Yanhong Luo, Ding Wang

There are many tools of solid controller layout for nonlinear platforms. In trying to transcend the minimal requirement of balance, Adaptive Dynamic Programming in Discrete Time techniques the difficult subject of optimum keep watch over for nonlinear structures utilizing the instruments of adaptive dynamic programming (ADP). the variety of structures taken care of is vast; affine, switched, singularly perturbed and time-delay nonlinear structures are mentioned as are the makes use of of neural networks and methods of worth and coverage new release. The textual content beneficial properties 3 major facets of ADP during which the tools proposed for stabilization and for monitoring and video games enjoy the incorporation of optimum regulate equipment:
• infinite-horizon keep an eye on for which the trouble of fixing partial differential Hamilton–Jacobi–Bellman equations at once is conquer, and evidence only if the iterative price functionality updating series converges to the infimum of all of the price features bought through admissible regulate legislations sequences;
• finite-horizon keep watch over, applied in discrete-time nonlinear structures displaying the reader the way to receive suboptimal keep watch over suggestions inside a hard and fast variety of keep an eye on steps and with effects extra simply utilized in genuine structures than these often won from infinite-horizon keep watch over;
• nonlinear video games for which a couple of combined optimum guidelines are derived for fixing video games either while the saddle aspect doesn't exist, and, while it does, fending off the life stipulations of the saddle element.
Non-zero-sum video games are studied within the context of a unmarried community scheme during which rules are got making certain procedure balance and minimizing the person functionality functionality yielding a Nash equilibrium.
In order to make the insurance appropriate for the coed in addition to for the specialist reader, Adaptive Dynamic Programming in Discrete Time:
• establishes the elemental thought concerned truly with every one bankruptcy dedicated to a truly identifiable regulate paradigm;
• demonstrates convergence proofs of the ADP algorithms to deepen realizing of the derivation of balance and convergence with the iterative computational tools used; and
• indicates how ADP tools may be placed to exploit either in simulation and in genuine purposes.
This textual content might be of substantial curiosity to researchers attracted to optimum keep watch over and its functions in operations learn, utilized arithmetic computational intelligence and engineering. Graduate scholars operating on top of things and operations examine also will locate the tips awarded right here to be a resource of robust tools for furthering their study.

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Extra info for Adaptive Dynamic Programming for Control: Algorithms and Stability

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Zhang HG, Wang ZS, Liu D (2007) Robust exponential stability of recurrent neural networks with multiple time-varying delays. IEEE Trans Circuits Syst II, Express Briefs 54(8):730– 734 116. Zhang HS, Xie L, Duan G (2007) H∞ control of discrete-time systems with multiple input delays. IEEE Trans Autom Control 52(2):271–283 117. Zhang HG, Yang DD, Chai TY (2007) Guaranteed cost networked control for T-S fuzzy systems with time delays. IEEE Trans Syst Man Cybern, Part C, Appl Rev 37(2):160–172 118.

We will study the optimal control problems with an ε-error bound using ADP algorithms. First, the HJB equation for finite-horizon optimal control of discrete-time systems is derived. In order to solve this HJB equation, a new iterative ADP algorithm is developed with convergence and optimality proofs. Second, the difficulties of obtaining the optimal solution using the iterative ADP algorithm is presented and then the ε-optimal control algorithm is derived based on the iterative ADP algorithms.

IEEE Trans Syst Man Cybern, Part B, Cybern 38(4):1002–1007 78. Rovithakis GA (2001) Stable adaptive neuro-control design via Lyapunov function derivative estimation. Automatica 37(8):1213–1221 79. Saeks RE, Cox CJ, Mathia K, Maren AJ (1997) Asymptotic dynamic programming: preliminary concepts and results. In: Proceedings of the 1997 IEEE international conference on neural networks, Houston, TX, pp 2273–2278 80. Saridis GN, Lee CS (1979) An approximation theory of optimal control for trainable manipulators.

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