Multiplicative Optimal Control Problem

In this paper, we consider a multiplicative optimal control problem subject to a system of linear differential equation.It has been shown that product of two concave functions defined positively over a feasible set is quasiconcave. It allows us to consider the original problem from a view point of quasiconvex maximization theory and algorithm. Global optimality conditions use level set of the objective function and convex programming as subproblem. The objective function is product of two concave functions. We consider minimization of the objective functional. The problem is nonconvex optimal control and application of Pontriyagin’s principle does not always guarantee finding a global optimal control. Based on global optimality conditions, we develop an algorithm for solving the minimization problem globally.