- Shorten, Robert

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- PublicationRobustness of constant-delay predictor feedback for in-domain stabilization of reactionâ€“diffusion PDEs with time- and spatially-varying input delaysThis paper discusses the in-domain feedback stabilization of reactionâ€“diffusion PDEs with Robin boundary conditions in the presence of an uncertain time- and spatially-varying delay in the distributed actuation. The proposed control design strategy consists of a constant-delay predictor feedback designed based on the known nominal value of the control input delay and is synthesized on a finite-dimensional truncated model capturing the unstable modes of the original infinite-dimensional system. By using a small-gain argument, we show that the resulting closed-loop system is exponentially stable provided that the variations of the delay around its nominal value are small enough. The proposed proof actually applies to any distributed-parameter system associated with an unbounded operator that 1) generates a -semigroup on a weighted space of square integrable functions over a compact interval; and 2) is self-adjoint with compact resolvent.
ScopusÂ© Citations 15 131 - PublicationISS of a Clamped-Free Damped String for the Configurations Associated with the Loss of the Riesz-Spectral PropertiesThis paper deals with the Input-to-State Stability (ISS) of a clamped-free damped string with respect to boundary disturbances for the configurations associated with the loss of the Riesz-spectral properties. Specifically, for most of the values of the physical parameters (namely the stiffness parameter and the damping coefficient), the ISS property of the clamped free damped string can be established based on the fact that the underlying disturbance-free operator is a Riesz-spectral operator. However, such a Riesz-spectral property does not hold true for certain configurations of the physical parameters of the damped string. This paper specifically investigates the establishment of an ISS estimate for these configurations. The proposed strategy relies on the projection of the original system trajectories in a Riesz basis obtained by adequately completing the set of eigenvectors of the disturbance-free operator.
169 - PublicationBoundary feedback stabilization of a reactionâ€“diffusion equation with Robin boundary conditions and state-delayThis paper discusses the boundary feedback stabilization of a reactionâ€“diffusion equation with Robin boundary conditions and in the presence of a time-varying state-delay. The proposed control design strategy is based on a finite-dimensional truncated model obtained via a spectral decomposition. By an adequate selection of the number of modes of the original infinite-dimensional system, we show that the design performed on the finite-dimensional truncated model achieves the exponential stabilization of the original infinite-dimensional system. In the presence of distributed disturbances, we show that the closed-loop system is exponentially input-to-state stable with fading memory.
ScopusÂ© Citations 21 193 - PublicationAn LMI condition for the robustness of constant-delay linear predictor feedback with respect to uncertain time-varying input delaysThis paper discusses the robustness of the constant-delay predictor feedback in the case of an uncertain time-varying input delay. Specifically, we study the stability of the closed-loop system when the predictor feedback is designed based on the knowledge of the nominal value of the time-varying delay. By resorting to an adequate Lyapunovâ€“Krasovskii functional, we derive an LMI-based sufficient condition ensuring the exponential stability of the closed-loop system for small enough variations of the time-varying delay around its nominal value. These results are extended to the feedback stabilization of a class of diagonal infinite-dimensional boundary control systems in the presence of a time-varying delay in the boundary control input.
ScopusÂ© Citations 33 147 - PublicationControl Law Realification for the Feedback Stabilization of a Class of Diagonal Infinite-Dimensional Systems With Delay Boundary ControlRecently, a predictor feedback control strategy has been reported for the feedback stabilization of a class of infinite-dimensional Riesz-spectral boundary control systems exhibiting a finite number of unstable modes by means of a delay boundary control. Nevertheless, for real abstract boundary control systems exhibiting eigenstructures defined over the complex field, the direct application of such a control strategy requires the embedding of the control problem into a complexified state-space which yields a complex-valued control law. This letter discusses the realification of the control law, i.e., the modification of the design procedure for obtaining a real-valued control law for the original real abstract boundary control system. The obtained results are applied to the feedback stabilization of an unstable Euler-Bernoulli beam by means of a delay boundary control.
143ScopusÂ© Citations 9 - PublicationStochastic Frequency Control of Grid-connected MicrogridsThis paper proposes a stochastic control strategy, namely the unsynchronized Addictive Increase Multiplicative Decrease (AIMD) algorithm, to manage the power flow of interconnected microgrids (MGs). The proposed control aims at achieving an optimal trade-off between the individual utility function of each MG while ensuring the stability of the grid. Both centralized and decentralized AIMD approaches are considered and compared. Extensive Monte Carlo simulations are performed on the IEEE 39-bus system, and show that the proposed control strategy is able to provide the sought trade-off.
615ScopusÂ© Citations 33 - PublicationISS Property with respect to boundary disturbances for a class of Riesz-spectral boundary control systemsThis paper deals with the establishment of Input-to-State Stability (ISS) estimates for infinite dimen-sional systems with respect to both boundary and distributed disturbances. First, a new approach isdeveloped for the establishment of ISS estimates for a class of Riesz-spectral boundary control systemssatisfying certain eigenvalue constraints. Second, a concept of weak solutions is introduced in order torelax the disturbances regularity assumptions required to ensure the existence of classical solutions.The proposed concept of weak solutions, that applies to a large class of boundary control systemswhich is not limited to the Riesz-spectral ones, provides a natural extension of the concept of bothclassical and mild solutions. Assuming that an ISS estimate holds true for classical solutions, we showthe existence, the uniqueness, and the ISS property of the weak solutions.
167 - PublicationInput-to-State Stability of a Clamped-Free Damped String in the Presence of Distributed and Boundary DisturbancesThis note establishes the exponential input-to-state stability (EISS) property for a clamped-free damped string with respect to distributed and boundary disturbances. While efficient methods for establishing ISS properties for distributed parameter systems with respect to distributed disturbances have been developed during the last decades, establishing ISS properties with respect to boundary disturbances remains challenging. One of the well-known methods for well-posedness analysis of systems with boundary inputs is the use of a lifting operator for transferring the boundary disturbance to a distributed one. However, the resulting distributed disturbance involves time derivatives of the boundary perturbation. Thus, the subsequent ISS estimate depends on its amplitude, and may not be expressed in the strict form of ISS properties. To solve this problem, we show for a clamped-free damped string equation that the projection of the original system trajectories in an adequate Riesz basis can be used to establish the desired EISS property.
281 - PublicationOn the design of cyber-physical control system for a smart pedelec (Ebike)(IEEE, 2019-12-13)
; ; ; ; We present a cyber-physical control system for deployment on a smart pedelec (Ebike). The goal of the control is to manage the interaction between a human and a motor intervention, for applications in which we wish to control physical aspects of the cycling behaviour (e.g. heart rate and breathing rate). The basis of the control is a pitchfork bifurcation system, augmented using ideas from gain-scheduling. Experiments have been conducted, showing the validity of the proposed control strategy. A use case dealing with the regulation of human ventilation characteristics in response to exogenous pollution measurements is presented.220ScopusÂ© Citations 8 - PublicationExponential input-to-state stabilization of a class of diagonal boundary control systems with delay boundary controlThis paper deals with the exponential input-to-state stabilization with respect to boundary disturbances of a class of diagonal infinite-dimensional systems via delay boundary control. The considered input delays are uncertain and time-varying. The proposed control strategy consists of a constant-delay predictor feedback controller designed on a truncated finite-dimensional model capturing the unstable modes of the original infinite-dimensional system. We show that the resulting closed-loop system is exponentially input-to-state stable with fading memory of both additive boundary input perturbations and disturbances in the computation of the predictor feedback.
ScopusÂ© Citations 11 292