In this paper we present a control method and a high accuracy solution technique in solving the linear quadratic Gaussian problems for nonstandard singularly perturbed discrete time systems. The methodology that exists in the literature for the solution of the standard singularly perturbed discrete time linear quadratic Gaussian optimal control problem cannot be extended to the corresponding nonstandard counterpart. The solution of the linear quadratic Gaussian optimal control problem is obtained by solving the pure-slow and pure-fast reduced-order continuous-time algebraic Riccati equations and by implementing the pure-slow and pure-fast reduced-order Kalman filters. In order to show the effectiveness of the proposed method, we present the numerical result for a one-link flexible robot arm.
LQG Control for Nonstandard Singularly Perturbed Discrete-Time Systems
Contributed by the Dynamic Systems, Measurement, and Control Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS publication in the ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the ASME Dynamic Systems and Control Division January 14, 2003; final revision, December 8, 2003. Review conducted by: S. Devasia.
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Kim , B., Kim , Y., and Lim, M. (March 11, 2005). "LQG Control for Nonstandard Singularly Perturbed Discrete-Time Systems ." ASME. J. Dyn. Sys., Meas., Control. December 2004; 126(4): 860–864. https://doi.org/10.1115/1.1850537
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