Infinite dimensional systems' sliding motions

Levaggi, Laura

doi:10.23919/ecc.2001.7076524

Cited by 5 publications

(11 citation statements)

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“…Theorem 5 extends similar results in [10,9], considerably enlarging the class of control systems for which the stated equivalence is valid. In [10] the operator A was assumed to generate a compact semigroup, while in [9] the requirement was the extendibility on S of the operator QA. Suppose that U is finite-dimensional, or for simplicity that the control is scalar.…”

Section: Moreover the Trajectory On S Obtained Through The Equivalentsupporting

confidence: 82%

“…For ordinary differential equations the problem is solved by introducing Filippov solutions [4]. In the Banach space setting a generalised solution concept has been proposed in [10,9] and a relationship between the equivalent control method and generalised solutions of infinite-dimensional systems with discontinuous right-hand side has been established, under some regularity assumptions. In Section 3 these results are extended to a more general setting by requiring less stringent hypotheses on the interaction between the evolution operator and the sliding surface.…”

Section: Introductionmentioning

confidence: 99%

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Discontinuous Control in Banach Spaces

Levaggi

IFIP International Federation for Information Processing

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The application of state-discontinuous feedback laws to infinite-dimensional control systems, with particular reference to sliding motions, is discussed for linear systems with distributed control. Using differential inclusions a definition of generalized solutions for the discontinuous closed loop system is introduced. Sliding modes can both be defined as viable generalized solutions or by extending the equivalent control method to infinite dimensional systems. Regularity properties of the sliding manifold under which the two methods are equivalent are investigated. Then, a comparison between classical results obtained for finite dimensional spaces and properties of infinite dimensional sliding modes is made.

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Section: Moreover the Trajectory On S Obtained Through The Equivalentsupporting

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Discontinuous Control in Banach Spaces

Levaggi

IFIP International Federation for Information Processing

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“…From the control theory point of view, sign should be a binary sensor or actuator; i.e., it takes the only values ±1. So we will define (10) sign…”

Section: The Main Result Restrictions To the Nonlinear Elementmentioning

confidence: 99%

Robust Semiglobal Stabilization of the Second Order System by Relay Feedback with an Uncertain Variable Time Delay

Shustin

Fridman

2004

IFAC Proceedings Volumes

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Abstract. We present sufficient conditions for robust relay-delayed semiglobal stabilization of second order systems, which relate the upper bound to an uncertain time delay and the parameters of the plant. We also suggest an algorithm of delayed relay control gain adaptation for semiglobal stabilization, which is based on delayed information about the sign of the controlled variable only. The proposed algorithm suppresses bounded uncertainties in the time delay; that is, being designed for the upper bound of uncertainty in the time delay, the control law ensures semiglobal stabilization independently of any variable time delay obeying the given upper bound.

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“…Similar results have been previously proved, under stronger hypotheses. In [6] the operator A was assumed to generate a compact semigroup, while in [5] the requirement was the extendability on S of the operator QA. Suppose that U is finite-dimensional, or for simplicity that the control is scalar.…”

Section: Pos(cstna2005)011mentioning

confidence: 99%

“…As sliding motions are obtained by applying feedback laws which are discontinuous on the sliding surface, the question of how to define what is the meaning of solution for the closed loop is a crucial point. A generalised solution concept has been proposed in [6,5] and a relationship between the equivalent control method and generalised solutions of infinite-dimensional systems with discontinuous right-hand side has been established, under some regularity assumptions. In Section 2 these results are extended to a more general setting by requiring less stringent hypotheses on the interaction between the evolution operator and the sliding surface.…”

Section: Introductionmentioning

confidence: 99%

Discontinuous feedback laws for infinite dimensional systems

Levaggi¹

2006

Proceedings of Control Systems: Theory, Numerics and Applications — PoS(CSTNA2005)

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The application of discontinuous feedback laws to infinite-dimensional control systems, with particular reference to sliding motions, is discussed for both linear systems with distributed control and parabolic differential equations with Neumann boundary control. In the first case it is shown how, using differential inclusions and viability theory, it is possible to interpret the constrained motion on the sliding surface as a generalised solution of the discontinuous control problem. For the second class of systems a variational approach is considered. Under some growth assumptions it is shown that Faedo-Galerkin approximations of the evolution, satisfying the sliding constraint in the limit, do converge to an ideal sliding state.

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Infinite dimensional systems' sliding motions

Cited by 5 publications

References 5 publications

Discontinuous Control in Banach Spaces

Discontinuous Control in Banach Spaces

Robust Semiglobal Stabilization of the Second Order System by Relay Feedback with an Uncertain Variable Time Delay

Discontinuous feedback laws for infinite dimensional systems

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