arXiv subjects

Delphine Bresch-Pietri

Publications and source records attributed to Delphine Bresch-Pietri.

5 recordsLinked to original sources

arXiv2026

Predictor-Feedback Stabilization of Linear Switched Systems with State-Dependent Switching and Input Delay

We develop a predictor-feedback control design for a class of linear systems with state-dependent switching. The main ingredient of our design is a novel construction of an exact predictor state. Such a construction is possible as for a given, state-dependent switching rule, an implementable formula for the predictor state can be derived in a way analogous to the case of nonlinear systems with input delay. We establish uniform exponential stability of the corresponding closed-loop system via a novel construction of multiple Lyapunov functionals, relying on a backstepping transformation that we introduce. We validate our design in simulation considering a switching rule motivated by communication networks.

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arXiv2025

Average Predictor-Feedback Control Design for Switched Linear Systems

We develop an input delay-compensating feedback law for linear switched systems with time-dependent switching. Because the future values of the switching signal, which are needed for constructing an exact predictor-feedback law, may be unavailable at current time, the key design challenge is how to construct a proper predictor state. We resolve this challenge constructing an average predictor-based feedback law, which may be viewed as an exact predictor-feedback law for a particular average system without switching. We establish that, under the predictor-based control law introduced, the closed-loop system is exponentially stable, provided that the plant's parameters are sufficiently close to the corresponding parameters of the average system. In particular, the allowable difference is inversely proportional to the size of delay and proportional to the dwell time of the switching signal. Since no restriction is imposed on the size of delay or dwell time themselves, such a limitation on the parameters of each mode is inherent to the problem considered (in which no a priori information on the switching signal is available), and thus, it cannot be removed. The stability proof relies on two main ingredients-a Lyapunov functional constructed via backstepping and derivation of solutions' estimates for the difference between the average and the exact predictor states. We present consistent, numerical simulation results, which illustrate the necessity of employing the average predictor-based law for achieving stabilization and desired performance of the closed-loop system.

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arXiv2019

Delay Compensated Control of the Stefan Problem and Robustness to Delay Mismatch

This paper presents a control design for the one-phase Stefan problem under actuator delay via a backstepping method. The Stefan problem represents a liquid-solid phase change phenomenon which describes the time evolution of a material's temperature profile and the interface position. The actuator delay is modeled by a first-order hyperbolic partial differential equation (PDE), resulting in a cascaded transport-diffusion PDE system defined on a time-varying spatial domain described by an ordinary differential equation (ODE). Two nonlinear backstepping transformations are utilized for the control design. The setpoint restriction is given to guarantee a physical constraint on the proposed controller for the melting process. This constraint ensures the exponential convergence of the moving interface to a setpoint and the exponential stability of the temperature equilibrium profile and the delayed controller in the ${\cal H}_1$ norm. Furthermore, robustness analysis with respect to the delay mismatch between the plant and the controller is studied, which provides analogous results to the exact compensation by restricting the control gain.

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arXiv2015

Finite-dimensional predictor-based feedback stabilization of a 1D linear reaction-diffusion equation with boundary input delay

We consider a one-dimensional controlled reaction-diffusion equation, where the control acts on the boundary and is subject to a constant delay. Such a model is a paradigm for more general parabolic systems coupled with a transport equation. We prove that this is possible to stabilize (in H 1 norm) this process by means of an explicit predictor-based feedback control that is designed from a finite-dimensional subsystem. The implementation is very simple and efficient and is based on standard tools of pole-shifting. Our feedback acts on the system as a finite-dimensional predictor. We compare our approach with the backstepping method.

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arXiv2013

Backstepping Transformation of Input Delay Nonlinear Systems

We present here the details of a backstepping transformation aiming at reformulating the dynamics of a nonlinear systems subject to unknown long input delay in a form which is suitable for Lyapunov stability analysis. The control law underlying this transformation is predictor-based, as often considered for long delays. The proposed transformation follows recent results of the literature, based on the representation of the constant actuator delay as a transport Partial Differential Equation (PDE).

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