This paper analyzes optimal control problems with linear time-varying dynamics defined on a smooth manifold in addition to mixed constraints and pure control constraints.The main contribution is the identification of ...This paper analyzes optimal control problems with linear time-varying dynamics defined on a smooth manifold in addition to mixed constraints and pure control constraints.The main contribution is the identification of sufficient conditions for the optimal controls to be non-singular,which enables exact(or lossless)convex relaxations of the control constraints.The problem is analyzed in a geometric framework using a recent maximum principle on manifolds,and it is shown that strong observability of the dual system on the cotangent space is the key condition.Two minimum time problems are analyzed and solved.A minimum fuel planetary descent problem is then analyzed and relaxed to a convex form.Convexity enables its efficient solution in less than one second without any initial guess.展开更多
基金The second author was partially funded by ONR Grant N00014-22-1-2131.
文摘This paper analyzes optimal control problems with linear time-varying dynamics defined on a smooth manifold in addition to mixed constraints and pure control constraints.The main contribution is the identification of sufficient conditions for the optimal controls to be non-singular,which enables exact(or lossless)convex relaxations of the control constraints.The problem is analyzed in a geometric framework using a recent maximum principle on manifolds,and it is shown that strong observability of the dual system on the cotangent space is the key condition.Two minimum time problems are analyzed and solved.A minimum fuel planetary descent problem is then analyzed and relaxed to a convex form.Convexity enables its efficient solution in less than one second without any initial guess.
