A novel multidimensional penalty‐free approach for constrained optimal control of switched control systems

Abstract

SummaryIn this article, a novel multidimensional penalty‐free method is proposed for the optimal control problem of switched control systems with path constraints. First, by introducing a Boolean vector, the switched control system and path constraints are transformed into affine forms. Typically, the complementary constrained method and piecewise constant function are used to relax and approximate the Boolean vector. Moreover, numerical methods are used to solve the approximated constrained optimal control problem (COCP), which relies on a discrete grid of the control function by using a piecewise linear function. Furthermore, the approximated COCP of affine control systems is equivalently transformed into a constrained dynamic parameter optimization problem by a refined time‐scaling transformation. Finally, the global convergence of the proposed multidimensional penalty‐free algorithm is proved and the feasibility of the algorithm is verified by numerical examples.