Pareto robust reliability-based controller design for probabilistic uncertain systems using fuzzy rules

Abstract

In this paper, An optimal fuzzy system (OFS), instead of crisp threshold values, have been used for optimal reliability-based multi-objective Pareto design of robust state feedback controllers for a two-mass-spring system having parameters with probabilistic uncertainties. The objective functions that have been considered are, namely, the probabilities of failure of settling time (P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Ts</sub> ), of control effort (P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u</sub> ) and of stability of closed-loop system (P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> ) in the reliability-based design optimization (RBDO) approach. A new multi-objective uniform-diversity genetic algorithm (MUGA) is used for Pareto optimum design of state feedback controllers for two-mass-spring problem. It is shown that multi-objective reliability-based Pareto optimization of the robust state feedback controllers using MUGA with OFS includes those that may be obtained by various crisp threshold values of probability of failures and, thus, remove the difficulty of selecting suitable crisp values. Besides, the multi-objective Pareto optimization of such robust feedback controllers using MUGA unveils some very important and informative trade-offs among those objective functions.