Simple cell mapping method for multi-objective optimal feedback control design

This paper introduces the simple cell mapping (SCM) method for the multi-objective optimal time domain design of feedback controls for linear systems with or without time delay. The SCM method is originally developed for the global analysis of nonlinear dynamical systems, and is extended to the multi-objective optimal design problem of feedback controls in this paper. We consider two feedback control design problems to demonstrate the method: a linear quadratic regulator based approach with the weighting matrices as design parameters, and a direct optimization with feedback control gains as design parameters. The Pareto set and Pareto front consisting of the peak time, overshoot and integrated absolute tracking error are obtained for two linear control systems, one of which has a control time delay. It is interesting to note that for the second order linear system, we have found a structure of the Pareto front, which has been very difficult to obtain using stochastic search algorithms. This study suggests that the SCM method is an effective method that can provide global and fine-structured solutions of MOPs for complex dynamical systems