Nonlinear optimal reliable control of constrained polynomial systems

This paper studies the optimal fault tolerant control (FTC) problem for polynomial systems with guaranteed cost in the presence of actuator faults. The consider fault mode is a multi-model framework of the typical aberration in actuator effectiveness. To transform the FTC design problem into a semi-definite programming (SDP), a novel technique is presented by optimizing an index of the effect of the nonlinear terms in the formulated HJI inequalities. Combined with other performance indexes, the multiobjective optimization problem can be numerically computed by using sum of squares method (SOS) in a reliable and efficient way. A numerical example is given to show the effectiveness of the proposed approach.