The main goal of this paper is to formulate and prove,under simplified hypothesis,a maximumprinciple in a mathematical framework governed by geometric tools.More precisely,using some techniques of calculus of variatio...The main goal of this paper is to formulate and prove,under simplified hypothesis,a maximumprinciple in a mathematical framework governed by geometric tools.More precisely,using some techniques of calculus of variations,the notion of adjointness and a geometrical context,we establish necessary optimality conditions for two optimal control problems governed by:(i)multiple integral cost functional and(ii)curvilinear integral(mechanical work)cost functional,both subject to fundamental tensor(state variable)evolution as constraint.The control variable is a connection in the considered optimisation problems.Finally,as an application of the geometric maximum principle introduced in this paper,we derive exterior Euler-Lagrange and Hamilton-Pfaff PDEs.展开更多
文摘The main goal of this paper is to formulate and prove,under simplified hypothesis,a maximumprinciple in a mathematical framework governed by geometric tools.More precisely,using some techniques of calculus of variations,the notion of adjointness and a geometrical context,we establish necessary optimality conditions for two optimal control problems governed by:(i)multiple integral cost functional and(ii)curvilinear integral(mechanical work)cost functional,both subject to fundamental tensor(state variable)evolution as constraint.The control variable is a connection in the considered optimisation problems.Finally,as an application of the geometric maximum principle introduced in this paper,we derive exterior Euler-Lagrange and Hamilton-Pfaff PDEs.
