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Published in:
2013 | OriginalPaper | Chapter
5. Optimal Tracking Control of Nonlinear Systems with Time Delays
Authors : Huaguang Zhang, Derong Liu, Yanhong Luo, Ding Wang
Published in: Adaptive Dynamic Programming for Control
Publisher: Springer London
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Abstract
In this chapter, the optimal tracking control problems of nonlinear systems with time delays are studied using HDP algorithm. First, the HJB equation for discrete time-delay systems is derived based on state error and control error. Then, a novel iterative HDP algorithm containing the iterations of state, control law, and cost functional is developed. We also give the convergence proof for the present iterative HDP algorithm. Finally, two neural networks, i.e., the critic neural network and the action neural network, are used to approximate the value function and the corresponding control law, respectively. It is the first time that the optimal tracking control problem of nonlinear systems with time delays is solved using the HDP algorithm. Two examples are used to demonstrate the effectiveness of the present control scheme.