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Technical Brief

Control of a Linear Time-Varying System With a Forward Riccati Formulation in Wavelet Domain

[+] Author and Article Information
Biswajit Basu

School of Engineering,
Trinity College Dublin,
Dublin 2, Ireland
e-mail: basub@tcd.ie

Andrea Staino

School of Engineering,
Trinity College Dublin,
Dublin 2, Ireland
e-mail: stainoa@tcd.ie

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.

J. Dyn. Sys., Meas., Control 138(10), 104502 (Jun 27, 2016) (6 pages) Paper No: DS-15-1082; doi: 10.1115/1.4033839 History: Received March 03, 2015; Revised May 26, 2016

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.

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Figures

Grahic Jump Location
Fig. 1

Control of the system for example 1 with forward DRE controller by Chen and Kao [13]: (a) time history of the controlled system states, (b) time history of the controlled inputs, (c) time history of the controlled system states (R2(t)=0.1 I2×2), and (d) time history of the controlled inputs (R2(t)=0.1 I2×2)

Grahic Jump Location
Fig. 2

Controlled system response for example 1 (forward DRE wavelet controller proposed in the present paper): (a) time history of the controlled system states (frequency-dependent gains) and (b) time history of the controlled inputs (frequency-dependent gains)

Grahic Jump Location
Fig. 3

Controlled response of SDOF system using TV backward DRE controller

Grahic Jump Location
Fig. 4

Controlled response of SDOF system: (a) time histories of the controlled response for example 2 and (b) Fourier amplitude of the SDOF system controlled response

Grahic Jump Location
Fig. 5

Control gains for example 2: (a) time history of the control gains (low-frequency band) for example 2 and (b) time history of the control gains (high-frequency band) for example 2

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