An approximating state-dependent control method based on modified pattern search optimization for nonlinear optimal control problem

In this paper, an approximating state-dependent control (ASC) method with modified pattern search (MPS) optimization for nonlinear optimal control problem is proposed. First, by converting the nonlinear optimal control problem into a number of interrelated time-varying linear quadratic regulator subproblems, the ASC method can solve each subproblems iteratively until the approximate solution is obtained. Second, in each iterative control process, the MPS is used to solve the controllability optimization problem. The optimal state-dependent weighting coefficients are obtained during the MPS optimization. Moreover, the MPS uses simplex gradient to design the search direction, which makes the optimization process efficient and fast. The convergence of MPS optimization is also proved in this paper. Finally, two simulation examples are given to illustrate the effectiveness of ASC method using the MPS optimization. The result shows that the ASC method can reduce the iterations of the approximate solution, and the MPS optimization can optimize the control performance of the ASC method.