Observability forms for switched systems with Zeno phenomenon or high switching frequency

International audienceThis paper deals with the observability of a class of switched systems with Zeno phenomenon or high switching frequency. Particularly, three observability forms are proposed and the observability for each form with knowledge of filtered switching signal is analyzed. Meanwhile, sufficient and necessary conditions for the existence of a diffeomorphism to transform a class of switched systems into one of such forms are presented. Examples and simulations are given at the end to highlight the theoretical results

Algebraic observer for a class of switched systems with Zeno phenomenon

International audienceFor a large class of switched systems with zeno phenomenon, classical observer cannot be applied directly since the terms leading to zeno phenomenon are not derivable. However in this paper, by assuming that these terms are integrable in the less restrictive way, we can define a new output, with which algebraic observer can then be adopted to estimate the states of the studied switched systems with zeno phenomenon. For simplicity, the main idea is explained via normal forms, while it can also be extended to generic switched systems

Discussion about sliding mode algorithms, Zeno phenomena and observability

International audienceThis chapter is devoted to a discussion about the relations between first and high order slidingmode algorithms and both types of Zeno (Chattering and Genuinely) behaviors of switched dynamical systems. Firstly, the Henstock-Kurzweil integral is recalled in order to set up the problem of switched systems with Zeno phenomena, which enables to include Filippov solution and take into account some singularities. Then, observer designs based on the well-known super twisting algorithm are proposed. For this kind of problems, the importance of finite time convergence of the observation error is studied, and some simulations are given to highlight the discussion. Lastly, the two tanks example is given in order to point out the differences between both Zeno phenomena types, to show that there is life after Zeno and that a higher order sliding mode observer can be efficient before, during and after both Zeno phenomena types

Localized Dissipation in Fermionic Quantum Wires

Localized dissipation in many-body quantum systems represents an emergent focal point of non-equilibrium physics. In recent experiments, localized particle losses were realized in ultracold atomic gases, thus opening up new avenues for investigating the interplay between many-body and non-equilibrium effects. The main focus of this work is the theoretical study of collective phenomena in one-dimensional systems of interacting spinless fermions subject to a localized loss. This model constitutes a non-equilibrium counterpart of the paradigmatic Kane-Fisher potential barrier problem. In particular, strong interaction effects emerge due to the gapless nature of the system. We show that the loss and transport properties of the quantum wire in the presence of a localized loss are drastically modified by interactions as a result of the interplay between coherent and incoherent processes. In experiments with localized losses, a manifestation of the quantum Zeno effect is encountered, which can be described exhaustively in terms of local, microscopic physics. In contrast, we demonstrate that the interplay of gapless quantum fluctuations and particle interactions with the localized dissipation leads to an instance of the quantum Zeno effect of genuine many-body nature. After the localized losses are switched on, a non-equilibrium steady state emerges in the quantum wire. We derive exact results for the properties of this steady state in the non-interacting limit and formulate a theoretical description of the depletion processes by introducing the momentum-dependent loss probability of modes. Remarkably, we find that coherence properties of the initial state persist, leading to the formation of Friedel oscillations near the loss site. The presence of interactions between the fermions modifies the dynamics in the wire and leads to an energy-dependent renormalization of loss processes. We find that the loss probability is strongly renormalized for modes with an energy close to the Fermi energy, leading to the suppression of losses at the Fermi level. In the case of repulsive interactions, the suppression of losses is accompanied by the loss site becoming completely opaque, which establishes a fluctuation-induced quantum Zeno effect. For attractive interactions, instead, the localized loss becomes fully transparent to particles at the Fermi level, resulting accordingly in the suppression of losses as a fluctuation-induced transparency. The strong modifications of the loss properties are reflected in observables such as the momentum distribution in the wire, exhibiting an increased occupation at the Fermi momentum. In addition, we study the influence of self-thermalization effects on the renormalization of the effective dissipation strength. Here, we identify regimes where the generation of an effective temperature is sufficiently weak to achieve significant renormalization. Furthermore, the microscopic quantum Zeno effect affects the spectral properties of the non-Hermitian Hamiltonian associated with a localized loss for a lattice model. Here, a sharp reorganization of the spectrum is encountered at a critical dissipation strength, causing a characteristic signature in the response properties of the wire. We investigate the interplay of interactions in the wire and localized dissipation within three complementary approaches. In a microscopic real-space renormalization group analysis the physical mechanisms behind the modified depletion properties are particularly transparent. Within a dynamical Hartree-Fock approximation the resulting effects on observables such as the momentum distribution in the non-equilibrium steady states can be studied. Finally, an effective Luttinger liquid description demonstrates the universality of the findings and enables the investigation of mode-coupling effects

Hybrid modeling and control of mechatronic systems using a piecewise affine dynamics approach

This thesis investigates the topic of modeling and control of PWA systems based on two experimental cases of an electrical and hydraulic nature with varying complexity that were also built, instrumented and evaluated. A full-order model has been created for both systems, including all dominant system dynamics and non-linearities. The unknown parameters and characteristics have been identi ed via an extensive parameter identi cation. In the following, the non-linear characteristics are linearized at several points, resulting in PWA models for each respective setup. Regarding the closed loop control of the generated models and corresponding experimental setups, a linear control structure comprised of integral error, feed-forward and state-feedback control has been used. Additionally, the hydraulic setup has been controlled in an autonomous hybrid position/force control mode, resulting in a switched system with each mode's dynamics being de ned by the previously derived PWA-based model in combination with the control structure and respective mode-dependent controller gains. The autonomous switch between control modes has been de ned by a switching event capable of consistently switching between modes in a deterministic manner despite the noise-a icted measurements. Several methods were used to obtain suitable controller gains, including optimization routines and pole placement. Validation of the system's fast and accurate response was obtained through simulations and experimental evaluation. The controlled system's local stability was proven for regions in state-space associated with operational points by using pole-zero analysis. The stability of the hybrid control approach was proven by using multiple Lyapunov functions for the investigated test scenarios.publishedVersio