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 good controller layout for nonlinear structures. In trying to transcend the minimal requirement of balance, Adaptive Dynamic Programming in Discrete Time ways the difficult subject of optimum regulate for nonlinear structures utilizing the instruments of adaptive dynamic programming (ADP). the diversity of structures handled is broad; affine, switched, singularly perturbed and time-delay nonlinear structures are mentioned as are the makes use of of neural networks and strategies of price and coverage generation. The textual content good points 3 major elements of ADP within which the equipment 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 facts only if the iterative worth functionality updating series converges to the infimum of all of the price features bought through 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 an eye on options inside a set variety of keep an eye on steps and with effects extra simply utilized in genuine platforms than these frequently received from infinite-horizon regulate;

• nonlinear video games for which a couple of combined optimum regulations are derived for fixing video games either whilst the saddle aspect doesn't exist, and, while it does, fending off the lifestyles stipulations of the saddle element.

Non-zero-sum video games are studied within the context of a unmarried community scheme during which regulations are got ensuring process balance and minimizing the person functionality functionality yielding a Nash equilibrium.

In order to make the assurance compatible for the coed in addition to for the professional reader, Adaptive Dynamic Programming in Discrete Time:

• establishes the elemental conception concerned basically with every one bankruptcy dedicated to a in actual fact identifiable keep watch over paradigm;

• demonstrates convergence proofs of the ADP algorithms to deepen figuring out of the derivation of balance and convergence with the iterative computational tools used; and

• indicates how ADP equipment should be positioned to exploit either in simulation and in genuine functions.

This textual content may be of substantial curiosity to researchers drawn to optimum keep watch over and its functions in operations study, utilized arithmetic computational intelligence and engineering. Graduate scholars operating up to speed and operations learn also will locate the information awarded the following to be a resource of strong equipment for furthering their study.

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

**Example text**

Combining with the (l) definition J ∗ (x(k)) = infl {P∞ (x(k))}, we can obtain lim Vi (x(k)) ≥ J ∗ (x(k)). , J ∗ is the limit of the value function sequence {Vi }. The proof is completed. 9). The left hand side is simply V∞ (x). But for the right hand side, it is not obvious to see since the minimum will reach at different u(k) for different i. However, the following result can be proved. 6 For any state vector x(k), the “optimal” value function J ∗ (x) satisfies the HJB equation J ∗ (x(k)) = inf x T (k)Qx(k) + W (u(k)) + J ∗ (x(k + 1)) .

Dreyfus SE, Law AM (1977) The art and theory of dynamic programming. Academic Press, New York 31. Engwerda J (2008) Uniqueness conditions for the affine open-loop linear quadratic differential game. Automatica 44(2):504–511 32. Enns R, Si J (2002) Apache helicopter stabilization using neural dynamic programming. J Guid Control Dyn 25(1):19–25 33. Enns R, Si J (2003) Helicopter trimming and tracking control using direct neural dynamic programming. IEEE Trans Neural Netw 14(4):929–939 34. Ferrari S, Stengel RF (2004) Online adaptive critic flight control.

5, we can conclude that Vi (x(k)) ≤ Vi+1 (x(k)), ∀i and limi→∞ Vi (x(k)) = J ∗ (x(k)). 6, we have J ∗ (x(k)) = infu(k) {x T (k)Qx(k) + W (u(k)) + J ∗ (x(k + 1))}. , Vi → J ∗ as i → ∞. 8), we can conclude that the corresponding control law sequence {vi } converges to the optimal control law u∗ as i → ∞. It should be mentioned that the value function Vi (x) we constructed is a new function that is different from ordinary cost function. 4, we have showed that for any x(k) ∈ Ω, the function sequence {Vi (x(k))} is a nondecreasing sequence, which will increase its value with an upper bound.

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

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