Distributed Fuzzy Adaptive Backstepping Optimal Control for Nonlinear Multi-missile Guidance Systems with Input Saturation

Abstract

This paper investigates the distributed optimal tracking control problem for nonlinear multiagent systems with a fixed directed graph. The dynamics of followers are in strict-feedback form with unknown nonlinearities and input saturation. Fuzzy logic systems and auxiliary system are introduced to identify the unknown nonlinearities and compensate the effect of input saturation, respectively. Then, by using the command-filtered backstepping technique, the distributed optimal tracking control problem is transformed into a distributed optimal regulation problem of tracking error dynamics in affine form. Subsequently, the distributed optimal feedback controller is derived via adaptive dynamic programming technique, in which a critic network is constructed to approximate the associated cost function online with a designed weight update law. Therefore, the whole controller, consisting of distributed adaptive feedforward tracking controller and distributed optimal feedback controller, not only guarantees that all signals in the closed-loop system are uniformly ultimately bounded, but also guarantees that the cooperative cost function is minimized. The effectiveness of the proposed method is demonstrated by simulation on the cooperative guidance problem of multimissile systems.