Optimal control of unknown continuous-time nonaffine nonlinear systems

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Abstract

In this chapter, we consider optimal control problems of continuous-time nonaffine nonlinear systems with completely unknown dynamics via adaptive dynamic programming (ADP) methods. First, we develop an ADP-based identifier-actor-critic architecture to obtain the approximate optimal control for continuous-time unknown nonaffine nonlinear systems. The identifier is constructed by a dynamic neural network, which transforms nonaffine nonlinear systems into a kind of affine nonlinear systems. After that, the actor-critic dual networks are employed to derive the optimal control for the newly formulated affine nonlinear systems. Second, we present an ADP-based observer-critic architecture to obtain the approximate optimal output regulation for unknown nonaffine nonlinear systems. The present observer is composed of a three-layer feedforward neural network, which aims to obtain the knowledge of system states. Meanwhile, a single critic neural network is employed for estimating the performance of the systems as well as for constructing the optimal control signal.

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Liu, D., Wei, Q., Wang, D., Yang, X., & Li, H. (2017). Optimal control of unknown continuous-time nonaffine nonlinear systems. In Advances in Industrial Control (pp. 309–344). Springer International Publishing. https://doi.org/10.1007/978-3-319-50815-3_8

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