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

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

ISBN-10: 1447147561

ISBN-13: 9781447147565

ISBN-10: 144714757X

ISBN-13: 9781447147572

There are many equipment of strong controller layout for nonlinear platforms. In looking to transcend the minimal requirement of balance, Adaptive Dynamic Programming in Discrete Time ways the demanding subject of optimum keep watch over for nonlinear platforms utilizing the instruments of adaptive dynamic programming (ADP). the variety of structures taken care of is broad; affine, switched, singularly perturbed and time-delay nonlinear platforms are mentioned as are the makes use of of neural networks and methods of price and coverage new release. The textual content beneficial properties 3 major elements of ADP within which the equipment proposed for stabilization and for monitoring and video games enjoy the incorporation of optimum regulate tools:
• infinite-horizon regulate for which the trouble of fixing partial differential Hamilton–Jacobi–Bellman equations without delay is triumph over, and facts only if the iterative price functionality updating series converges to the infimum of the entire worth capabilities received by way of admissible keep an eye on legislation sequences;
• finite-horizon keep watch over, applied in discrete-time nonlinear structures exhibiting the reader how one can receive suboptimal keep watch over strategies inside of a hard and fast variety of keep watch over steps and with effects extra simply utilized in actual structures than these frequently 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, whilst it does, warding off the lifestyles stipulations of the saddle aspect.
Non-zero-sum video games are studied within the context of a unmarried community scheme within which guidelines are got ensuring approach balance and minimizing the person functionality functionality yielding a Nash equilibrium.
In order to make the insurance compatible for the coed in addition to for the professional reader, Adaptive Dynamic Programming in Discrete Time:
• establishes the basic thought concerned truly with each one bankruptcy dedicated to a sincerely identifiable regulate paradigm;
• demonstrates convergence proofs of the ADP algorithms to deepen realizing of the derivation of balance and convergence with the iterative computational equipment used; and
• indicates how ADP equipment may be placed to take advantage of either in simulation and in actual purposes.
This textual content may be of substantial curiosity to researchers attracted to optimum keep watch over and its purposes in operations study, utilized arithmetic computational intelligence and engineering. Graduate scholars operating on top of things and operations study also will locate the guidelines offered right here to be a resource of strong tools for furthering their study.

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Stop. As stated in the last subsection, the iterative algorithm will be convergent with λi (x) → λ∗ (x) and the control sequence vi (x) → u∗ (x) as i → ∞. However, in practical applications, we cannot implement the iteration till i → ∞. Actually, we iterate the algorithm for a max number imax or with a pre-specified accuracy ε0 to test the convergence of the algorithm. In the above procedure, there are two levels of loops. The outer loop starts from Step 3 and ends at Step 8. There are two inner c loops in Steps 5 and 6, respectively.

Zero-sum differential game theory has been widely applied to decision making problems [23, 25, 38, 44, 52, 55], stimulated by a vast number of applications, including those in economy, management, communication networks, power networks, and in the design of complex engineering systems. In recent years, based on the work of [51], approximate dynamic programming (ADP) techniques have further been extended to the zero-sum games of linear and non-linear systems. In [4, 5], HDP and DHP structures were used to solve the discrete-time linear-quadratic zero-sum games appearing in the H∞ optimal control problem.

According to Bellman’s principle of optimality, the optimal value function J ∗ (x) should satisfy the following HJB equation: J ∗ (x(k)) = min u(·) ∞ u(i) x T (i)Qx(i) + 2 ϕ −T (U¯ −1 s)U¯ Rds 0 i=k u(k) = min x T (k)Qx(k) + 2 u(k) ϕ −T (U¯ −1 s)U¯ Rds 0 + J ∗ (x(k + 1)) . 4) The optimal control law u∗ (x) should satisfy u(k) u∗ (x(k)) = arg min x T (k)Qx(k) + 2 u(k) ϕ −T (U¯ −1 s)U¯ Rds 0 ∗ + J (x(k + 1)) . 4). However, there is currently no method for solving this value function of the constrained optimal control problem.

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

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