Reliable nonlinear control system design using duplicated control elements

Reliable L₂ gain bounding (i.e., H_∞) controllers for nonlinear systems are designed by using redundant control elements. One sensor and one actuator are duplicated, and the resulting closed-loop system is reliable with respect to both the single contingency case and the primary contingency case. The design procedures for reliable controllers are developed by using the Hamilton-Jacobi inequalities from nonlinear H_∞ control theory. Linear reliable controller design methods are also obtained by restricting the proposed nonlinear methods to the linear case, and the linear methods are found to be less conservative than existing methods for linear reliable controller design. Examples are given to illustrate the design procedures for both linear and nonlinear reliable controllers and the advantages of the proposed linear method over existing ones.