This method is based on a special method of successive approximations, which allows, under standard assumptions, to find optimal control within any finite time interval and to get the procedure of its construction. Nonlinear Optimization for Optimal Control Pieter Abbeel UC Berkeley EECS Many slides and figures adapted from Stephen Boyd [optional] Boyd and Vandenberghe, Convex Optimization, Chapters 9 – 11 [optional] Betts, Practical Methods for Optimal Control Using Nonlinear Programming TexPoint fonts used in EMF. Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. One of the main difficulties with classic optimal control theory is that, to determine optimal control for a nonlinear system, the Hamilton–Jacobi–Bellman (HJB) partial differential equations (PDEs) have to be solved Bryson & Ho, 1975. : AAAAAAAAAAAA. Read the TexPoint manual before you delete this box. Approximation theorems are available in the literature. 2.10 Nonlinear Least Squares 56 3 Optimal Control Preliminaries 61 3.1 The Transcription Method 61 3.2 Dynamic Systems 61 3.3 Shooting Method 62 3.4 Multiple Shooting Method 63 3.5 Initial Value Problems 65 3.6 Boundary Value Example 72 vn . We present a method for synthesis of optimal control with feedback of nonlinear systems with separated linear part via quadratic criteria. Optimal control of nonlinear systems is one of the most active subjects in control theory.