Adaptive control scheme for uncertain time-delay systems

Bresch‐Pietri, Delphine; Chauvin, Jonathan; Petit, Nicolas

doi:10.1016/j.automatica.2012.05.056

Cited by 179 publications

(82 citation statements)

References 22 publications

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“…From its definition, z(t) > 0 for t ∈ [0, t 1 ) and, from the analytical expression of y and as both 8 The existence of such a continuous function is obtained by considering the equality corresponding to (50) for which continuous (and even more) solutions exist assuming the initial condition ψ smooth enough [2]. Such a solution is then also a solution of the inequality (50).…”

Section: B Preliminary Results: Extension Of the Halanay Inequality mentioning

confidence: 99%

“…Initial step: the same arguments as above apply for m = 2. Lemma 6,7,9,and 8 As the dynamics matrix that we consider in (6) is of companion type, Cayley-Hamilton theorem gives…”

Section: A Preliminary Resultsmentioning

confidence: 99%

“…Prediction is already widely used for systems with constant input time-delays (see for instance [8], [14], [19], [25], [26] or [31] and the references therein) but is still not of general use for time-varying delays (see [28] or, more recently, [22]). In such cases, to compensate the varying input delay, the prediction has to be calculated over a time window of which length matches the value of the future delay.…”

Section: Proposed Methodology and Comparison With State-of-theart Tecmentioning

confidence: 99%

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Prediction-Based Stabilization of Linear Systems Subject to Input-Dependent Input Delay of Integral-Type

Bresch‐Pietri

Chauvin

Petit

2014

IEEE Trans. Automat. Contr.

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Abstract-In this paper, it is proved that a predictor-based feedback controller can effectively yield asymptotic convergence for a class of linear systems subject to input-dependent input delay. This class is characterized by the delay being implicitly related to past values of the input via an integral model. This situation is representative of systems where transport phenomena take place, as is frequent in the process industry. The sufficient conditions obtained for asymptotic stabilization bring a local result and require the magnitude of the feedback gain to be consistent with the initial conditions scale. Arguments of proof for this novel result include general Halanay inequalities for delay differential equations and build on recent advances of backstepping techniques for uncertain or varying delay systems.

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Section: B Preliminary Results: Extension Of the Halanay Inequality mentioning

confidence: 99%

“…Initial step: the same arguments as above apply for m = 2. Lemma 6,7,9,and 8 As the dynamics matrix that we consider in (6) is of companion type, Cayley-Hamilton theorem gives…”

Section: A Preliminary Resultsmentioning

confidence: 99%

Section: Proposed Methodology and Comparison With State-of-theart Tecmentioning

confidence: 99%

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Prediction-Based Stabilization of Linear Systems Subject to Input-Dependent Input Delay of Integral-Type

Bresch‐Pietri

Chauvin

Petit

2014

IEEE Trans. Automat. Contr.

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“…In [22], parameter, state and delay estimation is proposed for chaotic and hyperchaotic delayed systems. In [5], the authors present an observation technique for linear systems that may be seen as a specific case of the more general framework treated here. A method based on a particular sample/hold technique is given in [7] but no interconnection is made between delay estimation and state observation.…”

Section: Introductionmentioning

confidence: 99%

Interconnected delay and state observer for nonlinear systems with time-varying input delay

Léchappé

Moulay

Plestan

et al. 2016

2016 American Control Conference (ACC)

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Abstract-This work presents a general framework to estimate both state and delay thanks to two interconnected observers. This scheme can be applied to a large class of nonlinear systems with time-varying input delay. In order to illustrate this approach, a new delay observer based on an optimization technique is proposed. Theoretical results are illustrated and compared with existing works in simulation.

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“…For linear systems subject to input-delay, prediction-based control strategies, more commonly known as Smith Predictor (see [1], [13], [16]) are state-of-the-art for systems with constant input time-delays (see for instance [2], [3], [5], [9], [14], or [15] and the references therein). Grounding on the use of a prediction of the system state on a time horizon equal to the delay, this technique aims at compensating it, which notably improves transient performances.…”

Section: Introductionmentioning

confidence: 99%

Adaptive compensation of diffusion-advection actuator dynamics using boundary measurements

Bresch‐Pietri

Krstić

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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Abstract-For (potentially unstable) Ordinary Differential Equation (ODE) systems with actuator delay, delay compensation can be obtained with a prediction-based control law. In this paper, we consider another class of PDE-ODE cascade, in which the Partial Differential Equation (PDE) accounts for diffusive effects. We investigate compensation of both convection and diffusion and extend a previously proposed control design to handle both uncertainty in the ODE parameters and boundary measurements. Robustness to small perturbations in the diffusion and convection coefficients is also proved.

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Adaptive control scheme for uncertain time-delay systems

Cited by 179 publications

References 22 publications

Prediction-Based Stabilization of Linear Systems Subject to Input-Dependent Input Delay of Integral-Type

Prediction-Based Stabilization of Linear Systems Subject to Input-Dependent Input Delay of Integral-Type

Interconnected delay and state observer for nonlinear systems with time-varying input delay

Adaptive compensation of diffusion-advection actuator dynamics using boundary measurements

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