FTC synthesis for nonlinear systems: Sum of squares optimization approach

This paper studies the fault tolerant control (FTC) problem for nonlinear systems, with guaranteed cost or H_infin performance objective in the presence of actuator faults. The mode of faults under consideration is typical aberration of actuator effectiveness. To transform the FTC design problem into a semi-definite programming (SDP), the effect of the nonlinear terms is described as an index. The proposed optimization approach is to find zero optimum for this index. Combined with other performance indexes, the conceived multiobjective optimization is solved by sum of squares method (SOS) in a reliable and efficient way. Numerical examples are included to verify the applicability of this new approach for the nonlinear FTC synthesis.