An improved smoothing technique-based control vector parameterization method for optimal control problems with inequality path constraints

Abstract

Summary An improved control vector parameterization (CVP) method is proposed to solve optimal control problems with inequality path constraints by introducing the l1 exact penalty function and a novel smoothing technique. Both the state and control variables are allowed to appear explicitly in the inequality path constraints simultaneously. By applying the penalty function and smoothing technique, all the inequality path constraints are firstly reformulated as non-differentiable penalty terms and incorporated into the objective function. Then, the penalty terms are smoothed by using a novel smooth function, leading to a smooth optimal control problem with no inequality path constraints. With discretizing the control space, a corresponding nonlinear programming (NLP) problem is derived, and error between the NLP problem and the original problem is discussed. Results reveal that if the smoothing parameter is sufficiently small, the solution of the NLP problem is approximately equal to the original problem, which shows the convergence of the proposed method. After clarifying some theories of the proposed approach, a concomitant numerical algorithm is put forward with furnishing the updating rules of both the penalty parameter and smoothing parameter. Simulation examples verify the advantages of the proposed method for tackling nonlinear optimal control problems with different inequality path constraints. Copyright © 2016 John Wiley & Sons, Ltd.