Adaptive Dynamic Programming for Control: Algorithms and - download pdf or read online

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

ISBN-10: 1447147561

ISBN-13: 9781447147565

ISBN-10: 144714757X

ISBN-13: 9781447147572

There are many tools of strong controller layout for nonlinear structures. In trying to transcend the minimal requirement of balance, Adaptive Dynamic Programming in Discrete Time methods the hard subject of optimum keep an eye on for nonlinear platforms 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 price and coverage generation. The textual content gains 3 major points of ADP within which the tools proposed for stabilization and for monitoring and video games enjoy the incorporation of optimum keep watch over tools:
• infinite-horizon keep watch over for which the trouble of fixing partial differential Hamilton–Jacobi–Bellman equations without delay is triumph over, and evidence only if the iterative price functionality updating series converges to the infimum of the entire price services acquired via admissible keep an eye on legislations sequences;
• finite-horizon keep watch over, applied in discrete-time nonlinear platforms exhibiting the reader easy methods to receive suboptimal regulate strategies inside a hard and fast variety of keep watch over steps and with effects extra simply utilized in actual platforms than these often received from infinite-horizon keep watch over;
• nonlinear video games for which a couple of combined optimum rules are derived for fixing video games either whilst the saddle aspect doesn't exist, and, while it does, keeping off the life stipulations of the saddle element.
Non-zero-sum video games are studied within the context of a unmarried community scheme within which guidelines are acquired ensuring procedure 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 specialist reader, Adaptive Dynamic Programming in Discrete Time:
• establishes the elemental idea concerned sincerely with every one bankruptcy dedicated to a truly identifiable keep an eye on paradigm;
• demonstrates convergence proofs of the ADP algorithms to deepen knowing of the derivation of balance and convergence with the iterative computational equipment used; and
• indicates how ADP tools might be placed to take advantage of either in simulation and in genuine functions.
This textual content might be of substantial curiosity to researchers drawn to optimum regulate and its functions in operations learn, utilized arithmetic computational intelligence and engineering. Graduate scholars operating up to speed and operations learn also will locate the guidelines offered the following to be a resource of robust equipment for furthering their study.

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Additional resources for Adaptive Dynamic Programming for Control: Algorithms and Stability

Example text

A closed-form explicit solution is difficult to solve, if not impossible. Therefore we need to use parametric structures, such as fuzzy models [15] or neural networks, to approximate the costate function and the corresponding control law in the iterative DHP algorithm. In this subsection, we choose radial basis function (RBF) NNs to approximate the nonlinear functions. An RBFNN consists of three-layers (input, hidden and output). Each input value is assigned to a node in the input layer and passed directly to the hidden layer without weights.

64) for jmax steps to get the approximate control law vˆi . 7. If λi+1 (x(k)) − λi (x(k)) 2 < ε0 , go to Step 9; otherwise, go to Step 8. 8. If i > imax , go to Step 9; otherwise, set i = i + 1 and go to Step 4. 9. Set the final approximate optimal control law uˆ ∗ (x) = vˆi (x). 10. 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 → ∞.

2 Infinite-Horizon Optimal State Feedback Control Based on DHP 33 i ≤ lim i→∞ x T (k + j )Qx(k + j ) + W ηi−j (x(k + j )) . , x(k) → 0 as k → ∞. Therefore there exists an upper bound Y such that i ∀i : Pi+1 (x(k)) ≤ lim i→∞ li−j (x(k + j )) ≤ Y. 2, we obtain ∀i : Vi+1 (x(k)) ≤ Pi+1 (x(k)) ≤ Y. 19) This completes the proof. 3 will be used in the proof of our main theorems. 4 (cf. 8). Then, we can conclude that {Vi } is a nondecreasing sequence satisfying Vi+1 (x(k)) ≥ Vi (x(k)), ∀i. 20) where Φ0 (·) = V0 (·) = 0.

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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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