Optimal Control of Time Delay Systems via Hybrid of Block-Pulse Functions and Orthonormal Taylor Series

Abstract

A new method to find the optimal control of time delay systems with quadratic performance index is discussed. The method is based on hybrid functions. The properties of the hybrid functions which consists of block-pulse functions and orthonormal Taylor series are presented. The operational matrices of integration, delay, dual and product are used to reduce the solution of optimal control time delay system to the solution of algebraic equations. Numerical examples are included to illustrate the effectiveness and validity of the technique.

A decentralized observer-based optimal control for interconnected systems using the block pulse functions

“…First, we give a brief overview to specify our strict framework, that is to say, the BPFs parameterization technique. Then, the challenging tasks investigated in this section will concern the extension of the direct approach (BPFs) to decentralized optimal control with observers of interconnected systems (Bichiou et al, 2018; Dadkhah and Farahi, 2015; Ghali et al, 2017a, b; Hosseinpour and Nazemi, 2016; Marzban, 2016; Tang et al, 2017; Warrad et al, 2018; Xie and Huang, 2016; Ziari et al, 2019).…”

Hybrid Functions Direct Approach and State Feedback Optimal Solutions for a Class of Nonlinear Polynomial Time Delay Systems

“…Among them, we recall the application of Pontryagins maximum principle to the optimization of control systems with time delays which was firstly proposed by [14]. It had been shown that it results in a system of coupled two-point boundaryvalue (TPBV) problem involving both delay and advance terms whose exact solution, except in very special cases, is very difficult to determine (see [15]). Perhaps one of the most effective techniques is dynamic programming approaches (see [2]) for overcoming the complexity of the nonlinear time delay systems in optimal control problems.…”

“…In recent years, a growing interest has been appeared toward the application of hybrid functions, which is a combination of block pulse and an orthogonal polynomials basis [26]. In the nonlinear time delay optimal control problems context, an approach using hybrid functions which consist of block pulse functions and orthonormal Taylor series (see [15,29]) had been proposed, where authors propose to solve the necessary and sufficient condition equations for stationary emanating from the Hamiltonian based on state and control coefficients over the basis. Similarly, [28] propose a direct approach based on a hybrid of block pulse functions and Lagrange interpolating polynomials in order to convert the original optimal problem containing multiple delay into a mathematical programming one, where the resulting optimization problem is solved numerically by the Lagrange multipliers method.…”