Controls are often designed to meet different and conflicting goals. Consider the well-known LQR optimal control. The performance index contains a response measure and a control penalty, which are conflicting requirements. Proper linear or nonlinear combinations of the conflicting objective functions have led to single objective optimization problems. However, such a single objective optimization is dependent on the combination algorithm, and only provides a narrow window of all possible optimal solutions that a system may have.
Multi-objective optimization provides a set of optimal solutions, known as Pareto set. There have been many studies of search algorithms for Pareto sets of multi-objective optimization problems for complex dynamical systems. Recently, the simple cell mapping (SCM) method due to C.S. Hsu has been found to be a highly effective tool to compute Pareto sets. This paper applies the SCM method to several control design problems of linear and nonlinear dynamical systems. The results of the work are very exciting to report.
Comparative Study of Pontryagin Maximum Principle and Direct Method in Aircraft Optimal Control Design
