Two Classes Of Numerical Algorithms For Time Optimal Control Problems Of Linear Systems

For the time optimal control problem of the control system being a linear ordinary differential equation,two new numerical algorithms for solving the time optimal control problem are proposed.The equivalence between time optimal control problem and norm optimal control problem is the main tool to construct those algorithm.The main difference between the two classes of algorithms is that the algorithms of norm optimal control.In the first class of algorithm,the norm optimal control subproblem is solved by the derivative free optimization algorithm and the augmented Lagrange multiplier method.In the second class of algorithm,the norm optimal control subproblem is converted into an unconstrained dual optimization problem by the dual theory,and then using the proximal point algorithm and derivative free optimization algorithm solves the dual problem.Under appropriate conditions,the convergence of the two classes of algorithms is proved.Numerical experiments show the effectiveness of the two algorithms.