Suboptimal control of singularly perturbed multiparameter discrete control system

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.