Multi-Constraint Performance Optimization for Control Systems with Unknown Disturbances

A multi-constraint performance optimization design method is developed for tracking control systems with unknown disturbances, which guarantees a prescribed finite-frequency
$H_{\infty}$
disturbance-rejection performance and takes into account the physical constraint of actuators. First, a generalized equivalent input disturbance (GEID) estimator is adopted for more design degree of freedom. By using the Lyapunov stability theory and generalized Kalman-Yakubovich-Popov (KYP) lemma, a sufficient condition is derived for system design, which takes into account the stability and performance of the closed-loop system and the control input constraint. In addition, by optimizing the parameters of the controller, the control performance is greatly improved. Finally, a case study of a pantograph-catenary system is used to verify the effectiveness of the developed method.