Distributed Optimal Tracking Control for Strict-Feedback Nonlinear Large-Scale Systems

What is it about?

In this paper, a novel distributed H∞ optimal tracking control scheme is designed for a class of physically interconnected large-scale nonlinear systems in the presence of strict-feedback form, external disturbance and saturating actuators. First, by designing feedforward control, the distributed H∞ optimal tracking control problem of a physically interconnected large-scale system is transformed into equivalent control of a decoupled multiagent system. Subsequently, a feedback control algorithm is designed to learn the optimal control input and the worst-case disturbance policy. The algorithm guarantees that the function approximation error and the distributed tracking error are uniformly ultimately bounded while the cost function converges to the bounded L₂-gain optimal value. Finally, the effectiveness of the proposed scheme is demonstrated by simulation results of distributed control for the mobile multirobot system.

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Why is it important?

This paper exploits advantages of physical interconnection to reduce the burden of communications and interconnection through communications to optimize the consensus performance. These aspects are considered carefully when designing distributed control of interconnected large-scale systems in strict-feedback form with external disturbances and input constraints. The novelty of this paper lies in the fact that: 1) compared with the works related to control methods of the physically interconnected large-scale systems [4]–[6], our method deals with not only physical interconnection effects but also distributed consensus in the presence of external disturbances and input constraints; 2) unlike the works in [4]–[6] and [22]–[24] when designing feedforward control to cancel interconnection effects, we relax the system identification to reduce the computational burden; and 3) while distributed control methods for multiagent systems [14]–[16], [25]–[29] or physically interconnected large-scale systems [7]–[13] were not considered optimization, our method achieves it. To our best knowledge, this paper may be the first work that proposes distributed optimal control of physically interconnected large-scale systems in strict-feedback form with external disturbance and input constraints. To this end, first, we design feedforward control for the interconnection effect rejection to transform the distributed H∞ optimal tracking control problem of interconnected large-scale systems to control of decoupled multiagent systems. Then, by utilizing an ADP technique [39], we propose a feedback control algorithm. The algorithm can approximate the worst-case disturbance policy and constrained-input optimal control policy, synchronously. Finally, by Lyapunov analysis, we prove that all signals of the closed-loop system are UUB and the consensus performance function converges to the bounded L2-gain optimal value.