Parameter Space Optimization for Robust Controller Synthesis With Structured Feedback Gain

Various optimal control and system designs involve searching for a feedback gain matrix with structural constraints. As an alternative solution, the parameter space methods map the constraints from the state space to another extended state-input space, in which an equivalent optimization problem is solved. However, to further extend its applications, there are still some issues need to be addressed, such as the limited type of structural constraints, the marginally stable solutions, and the low computation efficiency. In this article, we aim to make this method applicable to a class of structural constraints for some elements in the gain matrix being zero or with intrarow and intracolumn constraints. To address such structured control problem, we propose a procedure to transform the original system to an extended system with the decentralized feedback matrix. From here, the mapping rules to the parameter space are given for the decentralized feedback matrix with both intrarow and intracolumn constraints. To avoid oscillatory closed-loop dynamics, we include the closed-loop dominant pole constraints during optimization. In addition, to improve the computation efficiency during optimization, we revise the cutting plane logic, which allows adding multiple linear constraints within a single iteration. Simulation examples demonstrate the effectiveness of the proposed method.