Recursive Approximation Method for Solving Constrained Nonlinear Optimal Control Problems Using Legendre Polynomials
Hussein Jaddu1, Amjad Majdalawi2
1Hussein Jaddu, Associate Professor, Faculty of Engineering, Al Quds University, Jerusalem, Palestine.
2Amjad Majdalawi, Graduated, Faculty of Engineering, Al Quds University, Jerusalem, Palestine.
Manuscript received on April 20, 2015. | Revised Manuscript received on April 28, 2015. | Manuscript published on March 05, 2015. | PP: 41-47 | Volume-5, Issue-2, May 2015. | Retrieval Number: B2599055215 /2015©BEIESP
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Abstract: A computational method is presented to solve a nonlinear quadratic optimal control problems subject to terminal state constraints, path inequality constraints on both the state and the control variables. The method is based on using a recursive approximation technique to replace the original constrained nonlinear dynamic system by a sequence of constrained linear time-varying systems. Then each of constrained linear time-varying quadratic optimal control problems is approximated by a quadratic programming problem by parameterizing each of the state variable by a finite length Legendre polynomials with unknown parameters. To show the effectiveness of the proposed method, simulation results of two constrained nonlinear optimal control problems are presented.
Keywords: Nonlinear constrained quadratic optimal control problem; Iterative Technique; Legendre polynomials; State parameterization.