Nearly optimal sliding mode fault-tolerant control for affine nonlinear systems with state constraints

In this paper, the problem of fault-tolerant control for a class of affine nonlinear systems subject to state constraints is investigated. Firstly, the nearly optimal controller design for the constrained nominal system is considered. By introducing proper slack variables, the nonlinear optimal control problem with state constraints is transformed into an unconstrained one for an augmented nonlinear system. Then, an adaptive weight update algorithm based on neural network (NN) is given to solve the Hamilton-Jacobi-Bellman (HJB) equation, which can generate an approximated optimal control policy for the augmented system. In order to achieve the fault-tolerant control objective, an NN observer with novel adaptive laws is constructed to identify the actuator faults. An integral sliding mode fault-tolerant control scheme is employed to guarantee the stability of the constrained faulty system, which is designed using the fault estimations and the obtained nominal nearly optimal control policy. Finally, simulations are presented to illustrate the effectiveness of the proposed method.