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

This paper investigates the parametric design approach to second-order linear time-varying systems by using dynamic compensator and multi-objective optimization. On the basis of the solution to a type of second-order generalized Sylvester matrix equations, the generally completely parameterized expression of the dynamic compensator is established, meanwhile, the completely parametric forms of left and right eigenvectors are obtained, it also provides two groups of arbitrary parameters. With the parametric method, the closed-loop system can be converted into a linear constant one with desired eigenstructure. Simultaneously, it also considers a novel technique to multi-objective optimization. Multiple performance indexes such as regional pole assignment, low sensitivity, disturbance attenuation, robustness degree and low gains are formulated by arbitrary parameters. Based on the above indexes, a synthetic objective function which includes each performance index weighted is formulated to express the comprehensive performances of control system. By using the degrees of freedom in arbitrary parameters, a dynamic compensator can be established by solving a multi-objective optimization problem. Finally, an example of spacecraft rendezvous problem is presented to verify that the parametric approach is effective.