Parametric Control to Second-Order Quasi-Linear Systems Based on Dynamic Compensator and Multi-Objective Optimization

This paper presents the parametric design approach to the second-order quasi-linear (SQ) systems by using dynamic compensator and multi-objective optimization. Based on the solutions to a type of the second-order generalized Sylvester equations (SGSEs), the generally parametric form of the dynamic compensator is established, the completely parameterized expressions of left and right eigenvector matrices are obtained, and it also provides two groups of arbitrary parameter matrices. With the parametrized method, the closed-loop system is converted into a linear constant one. Simultaneously, it also investigates a novel technique to multi-objective design and 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, robustness criteria and low gain criteria can be expressed by a synthetic objective function which includes each performance index weighted. By using the degrees of freedom (DOFs) in arbitrary parameters, a dynamic compensator can be established by solving a multi-objective optimization problem. Finally, the spacecraft rendezvous problem is proposed to verify the feasibility and effectiveness of the parametrized approach.