Spectral method for constrained linear–quadratic optimal control

• Published in: Mathematics and Computers in Simulation Vol. 58; no. 2; pp. 159 - 169
• Main Author: Jaddu, Hussein
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 2002; Elsevier BV; Elsevier
• Subjects: Calculus of variations and optimal control; Chebyshev polynomials; Constrained linear–quadratic problem; Exact sciences and technology; Mathematical analysis; Mathematics; Sciences and techniques of general use; Spectral method; Constrained linear–quadratic problem; Spectral method; Chebyshev polynomials; Approximate method; Chebyshev polynomial; Minimization; State control; Quadratic programming; Terminal; Implementation; System; Constrained optimization; State variable; Control constraint; State equation; Linear system; Optimal control; Inequality constraint; Equality constraint; State constraint
• ISSN: 0378-4754; 1872-7166
• DOI: 10.1016/S0378-4754(01)00359-7

A computational method based on Chebyshev spectral method is presented to solve the linear–quadratic optimal control problem subject to terminal state equality constraints and state-control inequality constraints. The method approximates each of the system state variables and each of the control variables by a finite Chebyshev series of unknown parameters. The method converts the optimal control problem into a quadratic programming problem which can be solved more easily than the original problem. This paper gives explicit results that simplify the implementation of the method. To show the numerical behavior of the proposed method, the simulation results of an example are presented.