A Numerical Algorithm For Linear Quadratic Optimal Control Problems With State Constraints Based On Alternating Direction Method Of Multipliers

In this thesis,a numerical algorithm for linear quadratic optimal control problems with both control and state constraints is proposed.It is known that,when the state and control are constrained,the optimality condition for optimal controls is difficult to be applied to construct a numerical algorithm.Therefore,in this thesis,by discretizing the control system and performance index of the optimal control problem,the optimal control problem is transformed directly into a quadratic convex optimization problem.The alternating direction method of multipliers is used to solve this quadratic convex optimization problem.The convergence of numerical algorithm is proved by using the theory of optimal control and optimization method.Four illustrative numerical examples are given to show the effectiveness of the algorithm.