LFE-Based Composite Fault-Tolerant Control for Nonlinear Systems: An Offline Policy-Iteration Zero-Sum Game Approach

This article addresses the composite fault-tolerant control problem for nonlinear systems subject to both multiplicative actuator faults and bias actuator faults, using an offline policy-iteration zero-sum game approach. First, the multiplicative and bias faults are consolidated into a lumped fault, based on which, a novel lumped fault estimator (LFE) is devised. This LFE is designed to estimate the lumped fault while ensuring that the estimation error remains bounded, and the fault estimate is utilized as the first component of the control input. Compared to existing game-theoretic fault-tolerant schemes that assume worst case fault scenarios, the proposed approach significantly reduces conservatism. This is achieved by incorporating the negative fault estimates into the control input and framing the remaining control input and the lumped fault estimation error as the two players in a game. By introducing a tailored value function, the task of resolving the Hamilton–Jacobi–Isaacs (HJI) equation is recast as a relaxed optimization problem subject to nonlinear inequality constraints. Then, leveraging the policy-iteration technique in conjunction with the sum of squares (SOSs) constraint inequality, the relaxed optimization problem is broken down into a series of tractable semi-infinite programming tasks, which facilitates the offline solution of the aforementioned second component of the control input. The above two components make up the composite fault-tolerant control law. Lastly, simulation results on a single-joint manipulator validate the effectiveness and superiority of the developed composite fault-tolerant scheme.