Optimal Feedback Control Laws by Legendre Pseudospectral Approximations
Ross, I. Michael
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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.
The article of record as published may be located at http://dx.doi.org/10.1109/ACC.2001.946110Approved for public display, distribution unlimitedProceedings of the American Control Conference ; Arlington, VA June 25-27, 2001, pp. 2388-2393.
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