A Self-Healing Predictive Control Method for Discrete-Time Nonlinear Systems

In this work, a self-healing predictive control method for discrete-time nonlinear systems is presented to ensure the system can be safely operated under abnormal states. First, a robust MPC controller for the normal case is constructed, which can drive the system to the equilibrium point when the closed-loop states are in the predetermined safe set. In this controller, the tubes are built based on the incremental Lyapunov function to tighten nominal constraints. To deal with the infeasible controller when abnormal states occur, a self-healing predictive control method is further proposed to realize self-healing by driving the system towards the safe set. This is achieved by an auxiliary soft-constrained recovery mechanism that can solve the constraint violation caused by the abnormal states. By extending the discrete-time robust control barrier function theory, it is proven that the auxiliary problem provides a predictive control barrier bounded function to make the system asymptotically stable towards the safe set. The theoretical properties of robust recursive feasibility and bounded stability are further analyzed. The efficiency of the proposed controller is verified by a numerical simulation of a continuous stirred-tank reactor process.