Numerical algorithm for optimal control of switched systems and its application in cancer chemotherapy

Abstract

This paper considers an optimal control problem of switched dynamical systems with control input and system state constraints. Unlike in traditional switched dynamical systems, the switching times cannot be specified directly and they are governed by a state-dependent switching condition. Thus, the existing methods cannot be directly used to solve this problem. To overcome this difficulty, the switching conditions are transformed into a continuous-time inequality constraint by introducing an integer constraint. Further, the original optimal control problem is approximated by using a sequence of constrained non-convex nonlinear parameter optimization problems by using a relaxation method, a control vector parameterization technique, and a time-scaling transformation. Following that, a penalty function-based intelligent optimization algorithm is proposed for obtaining a global optimal solution based on a more effective penalty function method and a more effective intelligent optimization algorithm. The convergence results show that the proposed method is globally convergent. Numerical simulation results show that the proposed method is lower time-consuming, has faster convergence speed, can obtain a better objective function value than the existing typical algorithms, and can achieve a stable and robust performance when considering the small perturbations in constraint conditions or the small perturbations of the model parameters.