A multiobjective robust controller synthesis approach aided by multicriteria decision analysis

Abstract

This paper proposes a methodology for robust dynamic output-feedback control synthesis of uncertain linear systems represented by polytopic models. This control problem results in a semi-infinite optimization problem. The proposed synthesis procedure improves a previous two-step procedure, composed of synthesis and analysis, by employing both a multiobjective evolutionary algorithm (MOEA) and a multiple criteria decision making (MCDM) strategy in the synthesis step. The analysis stage is performed via a Branch and Bound (B&B) algorithm, enabling the validation of the former step. In the proposed multiobjective approach, the project aim is to meet the specifications of (i) reference signal tracking response, (ii) disturbance rejection and (iii) measurement noise attenuation. The project specifications are quantified in terms of H∞ and H2 norms of closed-loop transfer functions. Essentially, this technique combines the flexibility of a dedicated MOEA together with the minimax semi-infinite programming problem. Since a MOEA evolves a set of candidate solutions in parallel, the suggested strategy provides a diverse set of controller designs, which is very useful for an a posteriori decision-making process. A proposed multicriteria decision-aid strategy is employed, in addition, as a controller design tool, aiming to incorporate the decision-maker preferences throughout the process, which (i) enables a guided evolutionary search to a trade-off region (of solutions) of practical interest and (ii) assists the definition of an adequate final controller, characterized by a reasonable practical trade-off concerning the criteria. The application of the suggested framework is illustrated on three case studies in order to demonstrate the effectiveness of the method presented.