Adaptive Dynamic Programming with Applications in Optimal by Derong Liu, Qinglai Wei, Ding Wang, Xiong Yang, Hongliang Li

By Derong Liu, Qinglai Wei, Ding Wang, Xiong Yang, Hongliang Li

This e-book covers the latest advancements in adaptive dynamic programming (ADP). The textual content starts with an intensive history evaluation of ADP to ensure that readers are sufficiently acquainted with the basics. within the center of the booklet, the authors handle first discrete- after which continuous-time structures. assurance of discrete-time structures begins with a extra common type of price new release to illustrate its convergence, optimality, and balance with whole and thorough theoretical research. A extra sensible kind of worth new release is studied the place price functionality approximations are assumed to have finite mistakes. Adaptive Dynamic Programming additionally info one other street of the ADP procedure: coverage new release. either simple and generalized types of policy-iteration-based ADP are studied with whole and thorough theoretical research by way of convergence, optimality, balance, and mistake bounds. between continuous-time platforms, the regulate of affine and nonaffine nonlinear structures is studied utilizing the ADP process that is then prolonged to different branches of keep an eye on conception together with decentralized regulate, strong and assured rate regulate, and video game idea. within the final a part of the booklet the real-world importance of ADP conception is gifted, concentrating on 3 program examples constructed from the authors’ work:

• renewable strength scheduling for shrewdpermanent energy grids;• coal gasification tactics; and• water–gas shift reactions.
Researchers learning clever regulate equipment and practitioners trying to observe them within the chemical-process and power-supply industries will locate a lot to curiosity them during this thorough remedy of a complicated method of control.

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2) is minimized. The optimal cost function is defined as J ∗ (x0 ) = inf J(x0 , u0 ) = J(x0 , u∗0 ), u0 which is dependent upon the initial state x0 . The control action may be determined as a function of the state. In this case, we write uk = u(xk ), ∀k. Such a relationship, or mapping u : Rn → Rm , is called feedback control, or control policy, or policy. It is also called control law. 1) starting at xk when the policy uk = μ(xk ) is applied. 1) starting at x0 is determined as ∗ J ∗ (x0 ) = inf J μ (x0 ) = J μ (x0 ), μ where μ∗ indicates the optimal policy.

1). According to Bellman, the optimal cost from time k on is equal to J ∗ (xk ) = min{U(xk , uk ) + γ J ∗ (xk+1 )} = min{U(xk , uk ) + γ J ∗ (F(xk , uk ))}. , uk∗ = arg min{U(xk , uk ) + γ J ∗ (xk+1 )}. 4) is the principle of optimality for discrete-time systems. Its importance lies in the fact that it allows one to optimize over only one control vector at a time by working backward in time. Dynamic programming is a very useful tool in solving optimization and optimal control problems. In particular, it can easily be applied to nonlinear systems with or without constraints on the control and state variables.

IEEE Trans Autom Control 51(8):1249–1260 47. Littman ML (2015) Reinforcement learning improves behaviour from evaluative feedback. Nature 521:445–451 48. Liu D (2005) Approximate dynamic programming for self-learning control. Acta Autom Sin 31(1):13–18 49. Liu D, Huang Y, Wang D, Wei Q (2013) Neural-network-observer-based optimal control for unknown nonlinear systems using adaptive dynamic programming. Int J Control 86(9):1554– 1566 50. Liu D, Javaherian H, Kovalenko O, Huang T (2008) Adaptive critic learning techniques for engine torque and air-fuel ratio control.

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