Optimal Selection of the Coefficient Matrix in State-Dependent Control Methods

This paper presents a state-dependent method for solving nonlinear, control-affine, finite-time optimal control problems. The problem is set in a state-dependent form and solved as a sequence of time-varying linear-quadratic regulators, for which an approach based on state transition matrices has been developed. The novelty of the method consists of the possibility of managing a number of different state-dependent coefficient factorizations of the uncontrolled dynamics, for use with various state-dependent control methods. At each iteration, a nonlinear programming problem is solved to select the state-dependent combination that maximizes the controllability, so minimizing the control effort and, likely, the objective function. Test problems are presented to show the effectiveness of the method