An Iterative Method for Optimal Control of Nonlinear Quadratic Tracking Problems

In this paper, we investigate an iterative method for computing optimal controls for general affine nonlinear quadratic tracking problems. The control law is computed iteratively by solving a sequence of linear quadratic tracking problems and, in particular, it consists of solving a set of coupled differential equations derived from the Hamilton-Jacobi-Bellman equation. The convergence of the iterative scheme is shown by constructing a contraction mapping and using the fixed-point theorem. The versatility and effectiveness of the proposed method is demonstrated in numerical simulations of three structurally different nonlinear systems.