Multi-objective Optimal Design of Feedback Controls for Dynamical Systems Time Delay

There have been many studies of control of dynamical systems with time delay. Stability of the delayed control system has been a primary concern. It is usually difficult to explicitly design feedback controls of dynamical systems with time delay to meet time domain specifications such as rise time, overshoot and tracking error. Furthermore, these time domain specifications tend to be conflicting to each other to make the optimal feedback control design even more challenging. This paper presents a hybrid algorithm for multi-objective optimal feedback control of dynamical systems with time delay. In particular, we consider the time domain specifications of the feedback control for second order linear systems as well as nonlinear systems. We first review the multiobjective optimization problem (MOP) and its formulation for feedback control design. We then introduce the global MOP solution method, i.e. the cell mapping method, and the hybrid search algorithm for optimal solutions. Preliminary results show that the hybrid algorithm of the cell mapping method for MOP design is very promising.