This presentation addresses some of the open problems in multiobjective control. The aim of this research was to compare two emerging techniques in multiobjective control: evolutionary algorithms (EAs) and convex optimisation over linear matrix inequalities (LMIs).
In the multiobjective control problem, a trade-off is sought between competing objectives. In such a problem, no single optimal solution exists, rather a set of equally valid solutions, known as the Pareto optimal set. It has been shown that the multiobjective control problem can be tackled with LMI techniques, due to its ability to include convex constraints such as H-2 performance, H-infinity performance, and pole-placement. The multiobjective control problem is formulated as a semidefinite programming (SDP) problem, which is a single objective convex optimisation problem, solved using interior-point methods.
As a novel alternative, multiobjective optimisation using EAs can offer a truly multiobjective treatment of control systems specifications. This approach is described herein and compared with numerical results from the counterpart LMI techniques.
This investigation addresses some of the drawbacks of LMI techniques, such as the inability to reduce the order of the controller and the LMI technique's inherent conservatism when tackling multiobjective problems. The truly multiobjective optimisation using an EA is proposed to overcome these problems. Reduction of the order of the controller is achieved for problems such as the H-infinity controller design with time-domain specifications. The mixed H2/H-infinity control problem is treated as a multiobjective H-2/H-infinity control problem, and an improvement of the Pareto optimal set is achieved.
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