Adaptive Critics for Decentralized Stabilization of Constrained-Input Nonlinear Interconnected Systems

Abstract

This article considers the decentralized stabilization problem of continuous-time nonlinear systems subject to unmatched interconnections and asymmetric input constraints. Initially, with the nonquadratic value functions being introduced to constrained auxiliary subsystems, the decentralized stabilization problem is converted into an array of nonlinear optimal control problems. It is proved that all solutions of these nonlinear optimal control problems together assure asymptotic stability of the entire system. Then, in the framework of adaptive critics, the critic-only architecture is built to solve the Hamilton–Jacobi–Bellman equations associated with these solutions. The critic-only architecture is implemented via critic neural networks (NNs) with their weight vectors being tuned through an improved gradient descent method. A remarkable feature of the present gradient descent approach is that it simultaneously utilizes previously stored and instantaneous state data, which makes the persistence of excitation conditions relaxed. After that, with Lyapunov’s techniques being employed, asymptotic stability of the closed-loop auxiliary subsystems and uniform ultimate boundedness of the critic NNs’ weight estimation errors are demonstrated. Finally, simulations of an unmatched interconnected nonlinear plant are provided to validate the present decentralized control method.