Numerical solution to optimal control of switched systems with state-dependent switchings

Given the fixed order of subsystems, the numerical solution to the optimal control of switched systems with state-dependent switchings and control constraints is explored. For the optimal control problem, when solving numerical solution by control vector parameterization based algorithm, a singular Jacobian problem is encountered in the process of solving ordinary differential equations (ODEs) with multi-point boundary value. In order to avoid the problem, an improved numerical algorithm is proposed in the paper, and the numerical solution can be obtained through the algorithm. Moreover, to find a global optimal solution, the filled function method is first adopted in such optimization problem. Numerical examples testify to the effectiveness of the proposed approach.