A wavelet domain forward differential Ricatti formulation is proposed in this paper for control of linear time-varying (LTV) systems. The control feedback gains derived are time-frequency dependent, and they can be appropriately tuned for each wavelet scale or frequency band. The gains in the proposed forward formulation are functions of the present and past states and hence lead to a nonlinear controller. This nonlinear controller does not require information or approximation about future system matrices. The proposed controller is suitable for systems with time-varying (TV) system matrices and also for controlling transient dynamics. The performance of the proposed controller is compared with two other control strategies, namely, a TV linear quadratic regulator (LQR) based on a backward formulation of the differential Ricatti equation (DRE) and a multiscale wavelet-LQR controller based on asymptotic assumptions. Two numerical examples demonstrate promising results on the performance of the controller.
Control of a Linear Time-Varying System With a Forward Riccati Formulation in Wavelet Domain
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received March 3, 2015; final manuscript received May 26, 2016; published online June 27, 2016. Assoc. Editor: Zongxuan Sun.
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Basu, B., and Staino, A. (June 27, 2016). "Control of a Linear Time-Varying System With a Forward Riccati Formulation in Wavelet Domain." ASME. J. Dyn. Sys., Meas., Control. October 2016; 138(10): 104502. https://doi.org/10.1115/1.4033839
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