Suboptimal control of singularly perturbed multiparameter discrete control system

Abstract

Study of a generalized problem is very important in the sense it provides complete picture of the problem. Accordingly a generalized singularly perturbed multiparemter discrete control system is considered. An open-loop optimal control problem based on Pontriagin's Minimum Principle (PMP) is formulated. The resulting optimal control solution needs special numerical techniques as the system is highly stiff due to multitime scale nature of the system with n small parameters. Hence it is proposed to go for a suboptimal controller that mitigates this problem. Singular Perturbation Method (SPM) that reduces the order and removes the stiffness of the system is an ideal choice for this problem. Here a generalized SPM is presented for this multiparameter problem. The SPM consists of an outer, n initial boundary layer correction (BLC) solutions and n terminal BLC solutions for this problem. An example is provided. The numerical results substantiate the proposed suboptimal controller.