Robust control of interval plants using genetic algorithms

Design of a robust controller which stabilizes an interval plant from the signal energy point of view via genetic algorithms (GAs) is proposed in this paper. When a controller is placed in series with the interval plant and closed under unity feedback, it is understood that the closed-loop system can also be characterized as an interval family via overbounding. Because stable systems always possess finite impulse response energy, we can obtain the continuous signal energy for each of the four closed-loop vertex systems associated with the four Kharitonov polynomials. With symbolic manipulation of the coefficients of the transfer function of the vertex systems, the parameter identification problem of a robust controller can be transformed into a multi-objective optimization problem. A proposed GA incorporating a fitness assignment mechanism is then used to search for a set of optimal parameters for the controller which stabilizes the interval plant by minimizing the aggregated continuous signal energy of the four vertex systems. The constraints on higher-order plants and controller order commonly encountered by conventional design methods are therefore removed. Several examples are illustrated to demonstrate the effectiveness of the proposed approach.