Optimal Feedback Control Laws by Legendre Pseudospectral Approximations
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Authors
Yan, Hui
Ross, I. Michael
Fahroo, Fariba
Subjects
Infinite-horizon, nonlinear, optimal, feedback control is one of the fundamental problems in control theory. In this paper we propose a solution for this problem based on
recent progress in real-time optimal control. The basic idea is to perform feedback implementations through a domain transformation technique and a Radau based pseudospectral method. Two algorithms are considered: free sampling frequency and fixed sampling frequency. For both algorithms, a theoretical analysis for the stability of the closed-loop system is provided. Numerical simulations with random initial conditions demonstrate the techniques for a flexible robot arm and a benchmark inverted pendulum problem.
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Date of Issue
2001-06-25
Date
June 25-27, 2001
Publisher
The American Institute of Aeronautics and Astronautics (AIAA)
Language
Abstract
We develop state feedback control laws for linear time-varying systems with quadratic cost criteria by an indirect Legendre pseudospectral method. This method approximates the linear two-point boundary value problem to a system of algebraic equations by way of a differentiation matrix. The algebraic system is solved to generate discrete linear transformations between the states and controls at the Legendre-Gauss-Lobatto points. Since these linear transformations involve simple matrix operations, they can be computed rapidly and efficiently. Two methods are proposed: one that circumvents solving the differential Riccati equation by a discrete solution of the boundary value problem, and another that generates a predictor feedback law without the use of transition matrices. Thus our methods obviate the need for solving the time-intensive backward integration of the matrix Riccati differential equation or inverting ill-conditioned transition matrices. A numerical example illustrates the techniques and demonstrates the accuracy and efficiency of these controllers.
Type
Conference Paper
Description
The article of record as published may be located at http://dx.doi.org/10.1109/ACC.2001.946110
Proceedings of the American Control Conference ; Arlington, VA June 25-27, 2001, pp. 2388-2393.
Proceedings of the American Control Conference ; Arlington, VA June 25-27, 2001, pp. 2388-2393.
Series/Report No
Department
Applied Mathematics
Organization
Mechanical and Aerospace Engineering (MAE)
Graduate School of Engineering and Applied Science (GSEAS)
Naval Postgraduate School (U.S.)
IEEE
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Distribution Statement
Approved for public release; distribution is unlimited.
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.