Graded Optimization Strategy for Time-Optimal Control Problems

The essential of time-optimal control problems is to determine the critical time when restrictions of states are just satisfied.There is some inconvenience in using the penalty function strategy for those problems.A new strategy,named as graded optimization,was developed in combination with penalty function strategy.The first optimization is to construct optimal control problem with free final states under a given final time.The second optimization,whose objective function is constructed using penalty function,is to adjust the final time according to the results of the first optimization.By repeating the first and second optimization,the restrictions of states will finally be just satisfied.The proposed strategy(divides) a complex problem into a series of simple problems that can be solved by classic optimization(methods.) Case studies show that the graded optimization is feasible,and it provides enough accuracy for(states) requirements and more accurate results.