Direct method to solve linear-quadratic optimal control problems

Abstract

In this work, we have proposed a new approach for solving the linear-quadratic optimal control problem, where the quality criterion is a quadratic function, which can be convex or non-convex. In this approach, we transform the continuous optimal control problem into a quadratic optimization problem using the Cauchy discretization technique, then we solve it with the active-set method. In order to study the efficiency and the accuracy of the proposed approach, we developed an implementation with MATLAB, and we performed numerical experiments on several convex and non-convex linearquadratic optimal control problems. The obtained simulation results show that our method is more accurate and more efficient than the method using the classical Euler discretization technique. Furthermore, it was shown that our method fastly converges to the optimal control of the continuous problem found analytically using the Pontryagin's maximum principle.

Operational Matrix of New Shifted Wavelet Functions for Solving Optimal Control Problem

“…Numerous studies have focused on the approximate solutions of optimal control problems, which can be found in many fields [5][6][7][8][9]. Different algorithms were used for solving optimal control problems, including the indirect modified pseudospectral method [10], A direct Chebyshev cardinal functions method [11], Cauchy discretization technique [12], the synthesized optimal control technique [13], Legendre functions method [14], Evolutionary Algorithm-Control Input Range Estimation [15]. See [16][17][18][19][20] for some other articles exploring various optimal control problems.…”

Operational Matrix of New Shifted Wavelet Functions for Solving Optimal Control Problem

“…Optimal control in natural methods is seen as a standard optimization problem by searching for the control function u(t) that optimizes the performance index. Different algorithms were used for solving optimal control problems, including the indirect modified pseudospectral method [6], a direct Chebyshev cardinal functions method [7], Cauchy discretization technique [8], the synthesized optimal control technique [9], Legendre functions method [10], Evolutionary Algorithm-Control Input Range Estimation [11], a hybrid of block-pulse function, and orthonormal Taylor polynomials [12]. (See [13][14][15][16][17] for some other articles exploring various optimal control problems.)…”

Optimal control design for linear time-varying systems by interpolated variational iteration method

“…The method reduced the problem to a quadratic programming problem, which could be solved by a system of linear equations. For other direct methods and their comparisons, see Aliane et al (2021) and the references therein.…”