Reduction of optimal control problems of nonlinear systems to special problems of nonlinear programming

Abstract

I. The new results in the field of constructive theory [I] of optimal control are given. The quadratic problems of optimal control: (1) c ′ x t 1 + x ′ t 1 D x t 1 → min ; (2) ∫ t o t 1 [ x t ′ D x t + C u 2 t ] d t → min , c ≥ 0 ; x ˙ t = A t x t + B t u t , x t o = x o ; u t ≤ 1 , t ε [ t o , t 1 ] ; H x t 1 = g , are investigated. 2. The algorithms of optimization of bilinear systems: x ˙ t = A t x t + u t B t x t , x t o = x o , are described under conditions (I). They are based on the special network method of solving of nonlinear problems [2] 3. The algorithms of solving of optimal control problems for nonlinear systems: x ˙ t = f x t + f t u t and optimal control problems for systems with nonlinear input are given. 4. A number of nonsmooth problems for linear and nonlinear control systems are considered.