Fault Tolerant Control for Nonlinear Systems: Sum-of-Squares Optimization Approach

In this paper, the fault tolerant control problem of nonlinear systems against actuator failures is considered. By representing the open-loop nonlinear systems in a state dependent linear-like polynomial form and implementing a special class of Lyapunov functions, the above problem can be formulated in terms of state dependent linear polynomial inequalities. Semidefinite programming relaxations based on the sum of squares decomposition are then used to efficiently solve such inequalities.