Distributed Optimal Control of Large-Scale Higher-Order Fully Actuated Systems

This paper investigates the optimal control problem for large-scale higher-order fully actuated (HOFA) systems in discrete time. The HOFA system, derived from the strict feedback system (SFS), serves as a versatile model for various engineering applications. While the optimal control of HOFA systems has been explored in the literature, the distributed implementation of optimal controllers for large-scale HOFA systems remains an open problem. To address this challenge, we develop a distributed optimal control scheme based on a distributed gradient estimation method. Instead of working directly with a continuous-time formulation, we first obtain a discrete-time HOFA system via a step-backward discretization. The proposed approach ensures that each subsystem generates its key control signal in a fully distributed manner, relying solely on local information. Finally, numerical simulations demonstrate the effectiveness of the proposed algorithm.