Satisfactory fault tolerant control with soft-constraint for discrete time-varying systems: numerical recursive approach

The problem of active fault-tolerant control (FTC) with multiple performance constraints including the closed-loop stability, the control input and system state constraints, and the optimized quadratic performance as well, is investigated for a class of discrete time-varying systems subject to sensor faults. A satisfactory FTC strategy is proposed by means of the numerical recursion to guarantee the acceptable performance constraints on the faulty closed-loop system. In the strategy, according to the constraints relaxation technique from MPC technology, a soft-constraint based online FTC design method is developed to explicitly handle the multi-objective requirements of the performance constraints. Its main contributions include that during the online FTC controller reconfiguration, the infeasibility due to the possibly inconsistent constraints is avoided by relaxing soft constraints on the one hand, such that the continuous operation of the closed-loop FTC system is ensured. On the other hand, the developed nonlinear and non-convex optimization calculation for the numerical FTC controller design is converted into a convex quadratically constrained quadratic programming (QCQP) under certain condition, to solve the NP-hard problem due to the intrinsic non-convex constraints. Moreover, the stability of the closed-loop FTC system is analyzed based on the stability theory of discrete-time nonlinear system. Finally, two simulative examples are presented to verify the effectiveness of the proposed satisfactory FTC method.