Differential Dynamic Programming Approach for Parameter Dependent System Control

Abstract

Abstract This paper gives a differential dynamic programming (DDP) method for parameter-dependent system control. Parameter dependent system appears in the chemical and biological process engineering field, due to variable feed conditions, plant deterioration, etc. Model predictive control (MPC) has been applied to it in various forms, but its high online computation requirement makes practical application unrealistic. In contrast, DDP approach offers a simple state feedback control policy by approximating the value function based on the assumption of quadratic system dynamics and objectives. To handle parameter-dependent system without online re-calculation of the value function and control policy, parameter-dependent DDP (PDDP) method is proposed. PDDP method utilizes hyper-state, state and parameter augmented vector, and least square (LS) parameter estimator. Hyper-state enables PDDP method to retain the benefits of DDP method while incorporating parameter sensitivity information within its dynamics. The method was applied to a simple discrete-time linear system and outperformed its DDP counterpart.