arXiv subjects

Lucas Brivadis

Publications and source records attributed to Lucas Brivadis.

29 records · Page 2Linked to original sources

arXiv2022

New perspectives on output feedback stabilization at an unobservable target

We address the problem of dynamic output feedback stabilization at an unobservable target point. The challenge lies in according the antagonistic nature of the objective and the properties of the system: the system tends to be less observable as it approaches the target. We illustrate two main ideas: well chosen perturbations of a state feedback law can yield new observability properties of the closed-loop system, and embedding systems into bilinear systems admitting observers with dissipative error systems allows to mitigate the observability issues. We apply them on a case of systems with linear dynamics and nonlinear observation map and make use of an ad hoc finite-dimensional embedding. More generally, we introduce a new strategy based on infinite-dimensional unitary embeddings. To do so, we extend the usual definition of dynamic output feedback stabilization in order to allow infinite-dimensional observers fed by the output. We show how this technique, based on representation theory, may be applied to achieve output feedback stabilization at an unobservable target.

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arXiv2021

Forwarding techniques for the global stabilization of dissipative infinite-dimensional systems coupled with an ODE

This paper deals with the stabilization of a coupled system composed by an infinite-dimensional system and an ODE. Moreover, the control, which appears in the dynamics of the ODE, is subject to a general class of nonlinearities. Such a situation may arise, for instance, when the actuator admits a dynamics. The open-loop ODE is exponentially stable and the open-loop infinite-dimensional system is dissipative, i.e., the energy is nonincreasing, but its equilibrium point is not necessarily attractive. The feedback design is based on an extension of a finite-dimensional method, namely the forwarding method. We propose some sufficient conditions that imply the well-posedness and the global asymptotic stability of the closed-loop system. As illustration, we apply these results to a transport equation coupled with an ODE.

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arXiv2021

Approximate observability and back and forth observer of a PDE model of crystallisation process

In this paper, we are interested in the estimation of Particle Size Distributions (PSDs) during a batch crystallization process in which particles of two different shapes coexist and evolve simultaneously. The PSDs are estimated thanks to a measurement of an apparent Chord Length Distribution (CLD), a measure that we model for crystals of spheroidal shape. Our main result is to prove the approximate observability of the infinite-dimensional system in any positive time. Under this observability condition, we are able to apply a Back and Forth Nudging (BFN) algorithm to reconstruct the PSD.

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arXiv2021

Avoiding observability singularities in output feedback bilinear systems

Control-affine output systems generically present observability singularities, i.e. inputs that make the system unobservable. This proves to be a difficulty in the context of output feedback stabilization, where this issue is usually discarded by uniform observability assumptions for state feedback stabilizable systems. Focusing on state feedback stabilizable bilinear control systems with linear output, we use a transversality approach to provide perturbations of the stabilizing state feedback law, in order to make our system observable in any time even in the presence of singular inputs.

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arXiv2020

New inversion methods for the single/multi-shape CLD-to-PSD problem with spheroid particles

In this paper, we express the Chord Length Distribution (CLD) measure associated to a given Particle Size Distribution (PSD) when particles are modeled as suspended spheroids in a reactor. Using this approach, we propose two methods to reconstruct the unknown PSD from its CLD. In the single-shape case where all spheroids have the same shape, a Tikhonov regularization procedure is implemented. In the multi-shape case, the measured CLD mixes the contribution of the PSD associated to each shape. Then, an evolution model for a batch crystallization process allows to introduce a Back and Forth Nudging (BFN) algorithm, based on dynamical observers. We prove the convergence of this method when crystals are split into two clusters: spheres and elongated spheroids. These methods are illustrated with numerical simulations.

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arXiv2020

Luenberger observers for infinite-dimensional systems, Back and Forth Nudging and application to a crystallization process

This paper deals with the observer design problem for time-varying linear infinite-dimensional systems. We address both the problem of online estimation of the state of the system from the output via an asymptotic observer, and the problem of offline estimation of the initial state via a Back and Forth Nudging (BFN) algorithm. In both contexts, we show under a weak detectability assumption that a Luenberger-like observer may reconstruct the so-called observable subspace of the system. However, since no exact observability hypothesis is required, only a weak convergence of the observer holds in general. Additional conditions on the system are required to show the strong convergence. We provide an application of our results to a batch crystallization process modeled by a one-dimensional transport equation with periodic boundary conditions, in which we try to estimate the Crystal Size Distribution from the Chord Length Distribution.

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arXiv2020

Forwarding design for stabilization of a coupled transport equation-ODE with a cone-bounded input nonlinearity

We propose a new design technique for the stabilization of coupled ODE-PDE systems in feedforward form. In particular, we address the stabilization problem of a one-dimensional transport equation driven by a scalar ODE which is controlled via a cone-bounded nonlinearity. The unforced transport equation is conservative but not asymptotically stable. The proposed technique is inspired by the forwarding approach early introduced in the 90's. Well-posedness and asymptotic stability of the closed-loop system are discussed.

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arXiv2020

Dynamic Output Feedback Stabilization of Non-uniformly Observable Dissipative Systems

Output feedback stabilization of control systems is a crucial issue in engineering. Most of these systems are not uniformly observable, which proves to be a difficulty to move from state feedback stabilization to dynamic output feedback stabilization. In this paper, we present a methodology to overcome this challenge in the case of dissipative systems by requiring only target detectability. These systems appear in many physical systems and we provide various examples and applications of the result.

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arXiv2020

New dynamical observer for a batch crystallization process based on solute concentration

In this paper a new observer is introduced to estimate the Crystal Size Distribution (CSD) only from the measurements of the solute concentration, temperature and a model of the growth rate. No model of the nucleation rate is needed. This approach is based on the use of a Kazantzis-Kravaris/Luenberger observer which exponentially estimates functionals of the CSD. Then, the full state is estimated by means of a Tikhonov regularization procedure. Numerical simulations are provided. Our approach relies on an infinite-dimensional observer, contrarily to the usual moment based observers.

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arXiv2020

From local to global asymptotic stabilizability for weakly contractive control systems

A nonlinear control system is said to be weakly contractive in the control if the flow that it generates is non-expanding (in the sense that the distance between two trajectories is a non-increasing function of time) for some fixed Riemannian metric independent of the control. We prove in this paper that for such systems, local asymptotic stabilizability implies global asymptotic stabilizability by means of a dynamic state feedback. We link this result and the so-called Jurdjevic and Quinn approach.

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arXiv2020

Luenberger observers for discrete-time nonlinear systems

In this paper, we consider the problem of designing an asymptotic observer for a nonlin-ear dynamical system in discrete-time following Luenberger's original idea. This approach is a two-step design procedure. In a first step, the problem is to estimate a function of the state. The state estimation is obtained by inverting this mapping. Similarly to the continuous-time context, we show that the first step is always possible provided a linear and stable discrete-time system fed by the output is introduced. Based on a weak observ-ability assumption, it is shown that picking the dimension of the stable auxiliary system sufficiently large, the estimated function of the state is invertible. This approach is illustrated on linear systems with polynomial output. The link with the Luenberger observer obtained in the continuous-time case is also investigated.

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