Computational method for optimal control of switched systems with input and state constraints. (November 2017)

• Record Type: Journal Article
• Authors: Wu, Xiang; Zhang, Kanjian; Cheng, Ming
• Is Part Of: Nonlinear analysis. Volume 26(2017)
• Page Start: 1
• Page End: 18
• Publication Date: 2017-11
• Subjects: Switched systems -- Optimal control -- Input and state constraints -- Improved conjugate gradient algorithm -- Filled function; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2017.04.001
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: In this paper, we consider an optimal control problem of switched systems with input and state constraints. Since the complexity of such constraint and switching laws, it is difficult to solve the problem using standard optimization techniques. In addition, although conjugate gradient algorithms are very useful for solving nonlinear optimization problem, in practical implementations, the existing Wolfe condition may never be satisfied due to the existence of numerical errors. And the mode insertion technique only leads to suboptimal solutions, due to only certain mode insertions being considered. Thus, based on an improved conjugate gradient algorithm and a discrete filled function method, an improved bi-level algorithm is proposed to solve this optimization problem. Convergence results indicate that the proposed algorithm is globally convergent. Three numerical examples are solved to illustrate the proposed algorithm converges faster and yields a better cost function value than existing bi-level algorithms. Highlights: A gradient algorithm is proposed for solving the switching time optimization problem. A filled function is developed for solving the mode sequence optimization problem. Convergence results indicate that the proposed algorithm is globally convergent. Our algorithm converges faster and yields a better value than existing methods.