Feedback Controlled Differential Inclusions and Stabilization of Uncertain Dynamical Systems

Goodall, D.P.; Ryan, E. P.

doi:10.1137/0326082

Cited by 21 publications

(5 citation statements)

References 11 publications

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“…There have been many results reported on this subject. In early works (see for example, References [1][2][3][4][5]), the structure of the mathematical model representing the system has the form of a linear system with a perturbation nonlinear term. More recently, the attention has been focused on nonlinear systems with additive perturbation terms [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Robust stabilization of a class of uncertain system via block decomposition and VSC

Loukianov

Castillo–Toledo

Dodds

2002

Intl J Robust & Nonlinear

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SUMMARYIn this paper, a block decomposition procedure for sliding mode control of a class of nonlinear systems with matched and unmatched uncertainties, is proposed. Based on the nonlinear block control principle, a sliding manifold design problem is divided into a number of sub-problems of lower dimension which can be solved independently. As a result, the nominal parts of the sliding mode dynamics is linearized. A discontinuous feedback is then used to compensate the matched uncertainty. Finally, a step-by-step Lyapunov technique and a high gain approach is applied to obtain hierarchical fast motions on the sliding manifolds and to achieve the robustness property of the closed-loop system motion with respect to unmatched uncertainty.

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Section: Introductionmentioning

confidence: 99%

Robust stabilization of a class of uncertain system via block decomposition and VSC

Loukianov

Castillo–Toledo

Dodds

2002

Intl J Robust & Nonlinear

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“…and the saturation function sat : 1 P1 is de"ned in (4). Essentially, continuous selections from C(t, x) are saturating versions of the state-feedback controls introduced in the previous section.…”

Section: Constrained Controls and System Stabilizationmentioning

confidence: 99%

“…Discontinuous feedbacks have the potential bene"t of achieving asymptotic stability, whereas a weaker property, namely that of practical stability, may be obtained when continuous feedbacks are utilized. Hence, in this framework, the class of uncertain systems is described by a di!erential inclusion (for a di!erential inclusion approach, see, for example, Goodall and Ryan [4] and Najson and Kreindler [6]) and such a framework avoids technical di$culties associated with di!erential equations with discontinuous right-hand sides.…”

Section: Introductionmentioning

confidence: 99%

Stabilization of a class of uncertain nonlinear affine systems subject to control constraints

Goodall

Wang

2001

Intl J Robust & Nonlinear

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SUMMARYPractical and asymptotic stabilization is investigated for a class of uncertain nonlinear a$ne control systems subject to constraints on the control inputs. The uncertain systems are modelled as non-linear perturbations to a known non-linear idealized system and a problem formulation based on di!erential inclusions is adopted. A class of constrained generalized state-feedback controls (containing both continuous and discontinuous selections) is developed, which guarantees stabilization with a speci"ed region of attraction. In the presence of residual uncertainty, su$cient conditions for global stabilizability are presented, whilst local results are obtained by relaxing these conditions.

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“…A common approach is to describe the dynamics of the control system by nonlinear ordinary differential equations or differential inclusions (see [4][5][6][7][8][9]). Then Lyapunov techniques are used constructively to design a feedback control such that certain stability performance for the uncertain dynamical system is achieved.…”

Section: Introductionmentioning

confidence: 99%

Viable control for uncertain nonlinear dynamical systems described by differential inclusions

Chen¹,

Huang²,

Lo³

2006

Journal of Mathematical Analysis and Applications

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In this paper, we will study the viable control problem for a class of uncertain nonlinear dynamical systems described by a differential inclusion. The goal is to construct a feedback control such that all trajectories of the system are viable in a map. Moreover, for any initial states no viable in the map, under the feedback control, all solutions of the system are steered to the map with an exponential convergence rate and viable in the map after a finite time T . In this case, an estimate of the time T of all trajectories attaining the map is given. In the nanomedicine system, an example inspired from cerebral embolism and cerebral thrombosis problems illustrates the use of our main results.  2005 Elsevier Inc. All rights reserved.

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Feedback Controlled Differential Inclusions and Stabilization of Uncertain Dynamical Systems

Cited by 21 publications

References 11 publications

Robust stabilization of a class of uncertain system via block decomposition and VSC

Robust stabilization of a class of uncertain system via block decomposition and VSC

Stabilization of a class of uncertain nonlinear affine systems subject to control constraints

Viable control for uncertain nonlinear dynamical systems described by differential inclusions

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