Reliable control to actuator signal attenuation-type faults

Controller designs are presented that are robust to partial actuator signal losses in linear systems. Design ranges are specified for the attenuation factor on each actuator signal. Both closed-loop stability and a prespecified H_∞ norm bound are guaranteed for any combination of actuator attenuation-type failures in the design ranges. The reliable controller designs derived are related to associated soft-constrained (nonlinear) min-max-max game problems. Two choices of regulated-output variable are made. When the control signal is weighted by the attenuation factor in the cost functional, no nontrivial Nash equilibrium solution exists among pure strategies, but a reliable controller design is found corresponding to the upper value of the game. When the control signal is not weighted by the attenuation factor in the cost functional, a Nash (saddle-point) equilibrium solution exists with game value zero, resulting in a second reliable controller design