Cooperative-Critic Learning-Based Secure Tracking Control for Unknown Nonlinear Systems With Multisensor Faults

This article develops a cooperative-critic learning-based secure tracking control (CLSTC) method for unknown nonlinear systems in the presence of multisensor faults. By introducing a low-pass filter, the sensor faults are transformed into "pseudo" actuator faults, and an augmented system that integrates the system state and the filter output is constructed. To reduce design costs, a joint neural network Luenberger observer (NNLO) structure is established by using neural network and input/output data of the system to identify unknown system dynamics and sensor faults online. To achieve the optimal secure tracking control, an augmented tracking system is formed by integrating the dynamics of tracking error, reference trajectory, and filter output. Then, a novel cost function is designed for the augmented tracking system, which employs the fault estimation and the discount factor. The Hamilton-Jacobi-Bellman equation is solved to obtain the CLSTC strategy through an adaptive critic structure with cooperative tuning laws. Besides, the Lyapunov stability theorem is utilized to prove that all signals of the closed-loop system converge to a small neighborhood of the equilibrium point. Simulation results demonstrate that the proposed control method has good fault tolerance performance and is suitable for solving secure control problems of nonlinear systems with various sensor faults.