Delayed state feedback and chaos control for time-periodic systems via a symbolic approach

Ma, Haitao; Deshmukh, Venkatesh; Butcher, Eric A.; Averina, Victoria

doi:10.1016/j.cnsns.2003.12.007

Cited by 28 publications

(14 citation statements)

References 21 publications

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“…(5) and (7) with system matrix (Â(t) −B(t)K(t)) by numerical integration over one period, other numerical techniques such as Chebyshev collocation [14] and semidiscretization [2] may be directly applied to the closed-loop DDE to more efficiently generate an approximation to the infinite-dimensional monodromy operator. This was employed in [15] using semidiscretization as well as in [3] via Chebyshev polynomial expansion. An infinite dimensional dynamic map can be defined for the closed-loop system as [14] …”

Section: (T) B(t)]mentioning

confidence: 99%

“…An alternative strategy is to use an infinite (or large) number of control gains to control all (or many) of the poles via the use of feedback control with either distributed delay and/or periodic control gains with an arbitrary number of Fourier coefficients [2]. The use of time-periodic control gains results in the closed-loop system having the form of time-periodic delay differential equations (DDEs), for which stability analysis requires the use of the infinite-dimensional Floquet theory [3].…”

Section: Introductionmentioning

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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Section: (T) B(t)]mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal feedback control strategies for periodic delayed systems

Nazari

Butcher

Bobrenkov³

2014

Int. J. Dynam. Control

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“…Some important methods can be cited as Ott-Grebogi-Yorke method [8], Pecora-Carroll method [9], backstepping method [10][11][12], sliding control method [13][14][15], active control method [16][17][18], adaptive control method [19][20], sampled-data control method [21], delayed feedback method [22], etc.…”

Section: Introductionmentioning

confidence: 99%

Active Controller Design for the Hybrid Synchronization of Hyperchaotic Xu and Hyperchaotic Li Systems

Vaidyanathan¹

2013

IJITMC

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“…For the synchronization of chaotic systems, there are many methods available in the chaos literature like OGY method [8], PC method [9], backstepping method [10][11][12], sliding control method [13][14][15], active control method [16][17][18], adaptive control method [19][20], sampled-data feedback control method [21], time-delay feedback method [22], etc.…”

Section: Introductionmentioning

confidence: 99%