Control of Dynamic Systems with Time-Periodic Coefficients via the                 Lyapunov-Floquet Transformation and Backstepping Technique

Deshmukh, Venkatesh; Sinha, Subhash C.

doi:10.1177/1077546304042064

Cited by 25 publications

(16 citation statements)

References 19 publications

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“…Note that due to use of the least squares inverse (non-empty left-null space of the input matrix B), asymptotic stability of the closed-loop tracking error dynamics is not guaranteed and one must search for aB matrix that provides acceptable response [17]. It should be mentioned here that the controlled response using LFT and time-invariant LQR changes according to the selection ofB and the weight matrices Q and R. Here, we chooseB = B, R = I 3×3 , Q = I 6×6 .…”

Section: Control Via Lft and Time-invariant Lqrmentioning

confidence: 99%

Fuel efficient periodic gain control strategies for spacecraft relative motion in elliptic chief orbits

Nazari

Butcher

2014

Int. J. Dynam. Control

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Periodic gain continuous control strategies are applied to the nonlinear time periodic equations of spacecraft relative motion when the chief orbit is elliptic. Specifically, control strategies based on time-varying linear quadratic regulator (LQR), Lyapunov-Floquet transformation (LFT) with time-invariant LQR, LFT with backstepping, and feedback linearization are implemented and shown to be much more fuel efficient than constant gain feedback control. Both natural and constrained leader-follower two-spacecraft formations are studied. Furthermore, a dead-band control is added for the constrained formation to reduce the amount of the fuel used. The closed-loop response and control effort required are investigated and compared for the same settling time envelopes for all control strategies.

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Section: Control Via Lft and Time-invariant Lqrmentioning

confidence: 99%

Fuel efficient periodic gain control strategies for spacecraft relative motion in elliptic chief orbits

Nazari

Butcher

2014

Int. J. Dynam. Control

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“…As is discussed in [33], due to use of the least squares inverse, asymptotic stability of the closed-loop dynamics is not guaranteed and one must search for aB matrix that provides an acceptable response. Alternatively, the use of a backstepping strategy as detailed in [33] guarantees asymptotic stability for underactuated systems, although that is not employed here.…”

Section: Q −1 (T)b(t)u(t) = −Bkw(t)mentioning

confidence: 99%

“…Alternatively, the use of a backstepping strategy as detailed in [33] guarantees asymptotic stability for underactuated systems, although that is not employed here. In practice,Q −1 (t) can be evaluated in two different ways: (1) inverting theQ(t) given in Eq.…”

Section: Q −1 (T)b(t)u(t) = −Bkw(t)mentioning

confidence: 99%

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Optimal feedback control strategies for periodic delayed systems

Nazari

Butcher

Bobrenkov³

2014

Int. J. Dynam. Control

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In this study, three strategies based on infinitedimensional Floquet theory, Chebyshev spectral collocation, and the Lyapunov-Floquet transformation (LFT) are proposed for optimal feedback control of linear time periodic delay differential equations using periodic control gains. First, a periodic-gain discrete-delayed feedback control is implemented where optimization of the control gains is included to obtain the minimum spectral radius of the closedloop response. Second, a large set of ODEs is obtained using the Chebyshev spectral continuous time approximation, after which optimal (time-varying LQR) control is used to obtain a periodic-gain distributed-delayed feedback control. The third strategy involves the use of both CSCTA and the reduced LFT, along with either pole-placement or time-invariant LQR used on a linear time invariant auxiliary system, to obtain a periodic-gain non-delayed feedback control that asymptotically stabilizes the original system. The delayed Mathieu equation is used as an illustrative example for all three control strategies.

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“…Robust and adaptive analysis and synthesis techniques can be used to design suitable controllers, which fulfill the desired disturbance attenuation and other performance characteristics of the closed-loop system. Despite of the fact that LTP (Linear Time Periodic) system theory has been under research for years (Deskmuhk & Sinha, 2004;Montagnier et al, 2004) the analysis on LTPs with experimental data has been seriously considered only recently (Allen, 2007). The importance of new innovative ideas and products is of utmost importance in modern industrial society.…”

Section: Introductionmentioning

confidence: 99%