Abstract
We consider an optimal control problem subject to the terminal state equality constraint and continuous inequality constraints on the control and the state. By using the control parametrization method used in conjunction with a time scaling transform, the constrained optimal control problem is approximated by an optimal parameter selection problem with the terminal state equality constraint and continuous inequality constraints on the control and the state. On this basis, a simple exact penalty function method is used to transform the constrained optimal parameter selection problem into a sequence of approximate unconstrained optimal control problems. It is shown that, if the penalty parameter is sufficiently large, the locally optimal solutions of these approximate unconstrained optimal control problems converge to the solution of the original optimal control problem. Finally, numerical simulations on two examples demonstrate the effectiveness of the proposed method.
Highlights
Constrained optimal control problems often arise in a wide range of practical applications, including the swing minimization of transferring container [1], the flight maximization with a heating constraint [2], the fuel minimization of the soft landing of moon [3], and the fuel minimization of spacecraft rendezvous with collision avoidance constraint [4]
In order to further improve the accuracy of the approximate optimal control problem, the switching points are taken as decision variables
We have proven that a local minimizer of the exact penalty function optimization problem (Pη(k)) will converge to a local minimizer of the original problem (P), we need, in actual computation, to set a lower bound ε∗ = 10−9 for ε(k), so as to avoid the situation of being divided by ε(k) = 0, leading to infinity
Summary
Constrained optimal control problems often arise in a wide range of practical applications, including the swing minimization of transferring container [1], the flight maximization with a heating constraint [2], the fuel minimization of the soft landing of moon [3], and the fuel minimization of spacecraft rendezvous with collision avoidance constraint [4]. We develop a new computational approach based on the control parametrization method [13] and the exact penalty function method [14] for solving an optimal control problem subject to terminal state equality constraint and continuous inequality constraints on the state and the control. Together with the time scaling transform, the constrained optimal control problem is approximated by an optimal parameter selection problem with the terminal state equality constraint and continuous inequality constraints on the control and state.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
