Adaptive actor-critic neural optimal control for constrained nonstrict feedback nonlinear systems via command filter

The actor-critic neural optimal control is investigated for the state-constrained nonlinear systems in the nonstrict feedback form with unmodeled dynamics in this paper. The filtering errors in the traditional dynamic surface control (DSC) are countervailed by the introduced compensation signals. Two design phases together determine the input: the feedforward input design and the near optimal input design. In the feedforward input design, a mapping rule is established to keep all the states in the finite range, and a first-order adjunctive signal is designed to treat the unmodeled dynamics. In the near optimal input design, the cost function relying on the reconstructed error system is minimized by the near optimal input via adaptive dynamic programming (ADP). In the whole design processing, the unknown nonlinear uncertain parts are fitted by the radial basis function neural networks (RBFNNs). The stability analysis illustrates all the signals are bounded in the controlled system. Two simulation examples are employed to verify the theoretical findings.