Parametric control to linear time-varying systems based on dynamic compensator and multi-objective optimization

This paper investigates the parametric approach for linear time-variant systems by using dynamic compensator and multi-objective optimization. Based on the solution to a class of generalized Sylvester matrix equations, the generally completely parametrized expression of the dynamic compensator is established, meanwhile, the completely parametric forms of left and right closed-loop eigenvectors and two groups of arbitrary parameters are obtained. With the proposed parametric approach, the closed-loop system can be transformed into a linear time-invariant one with expected eigenstructure. Simultaneously, it also considers a novel technique to multi-objective optimization design for linear time-varying systems. Multiple performance objectives, including the overall sensitivity function, H₂ norm and H_∞ norm, are formulated by two groups of arbitrary parameters. Based on these performance objectives, the robustness criteria is expressed by a comprehensive objective function which includes each performance objective weighted. By utilizing the degrees of freedom in parameters to optimize the comprehensive objective function, an optimized dynamic compensator can be obtained to satisfy the robustness criteria. Finally, an example of spacecraft rendezvous problem is presented to illustrate the effectiveness of the proposed approach.