## Section: New Results

### Control design and networked control

#### Control design for hydro-electric power-plants

Participants : C. Canudas de Wit [Contact person] , S. Gerwig, F. Garin, B. Sari [Alstom] .

We have a collaboration with Alstom on collaborative and resilient control of hydro-electric power-plants, with the CIFRE PhD thesis of Simon Gerwig. The first goal of this research is to improve performance of a hydro-electric power-plant outside its design operation conditions, by cancellation of oscillations that occur in such an operation range. Indeed, current operation of power-plants often requires to operate on a variety of conditions, often different from the ones initially considered when designing the plant. At off-design operation pressure, the hydraulic turbine exhibits a vortex rope below the runner. This vortex generates pressure fluctuations after the turbine and can excite the hydraulic pipes. Indeed the water is compressible and the pipe walls elastic, so the system can oscillate. The goal is to damp these pressure oscillations as they create vibrations in the system and can lead to damages. Our first contribution has been to model the effect of the vortex rope on the hydraulic system as an external perturbation source acting on pipes. The pipes themselves are described with equations taking into account water compressibility and pipe-wall elasticity. The resulting model is nonlinear with hyperbolic functions in the equations (analogous to high-frequency transmission lines), from which we obtain a suitably linearized model.

#### Collaborative source seeking

Participants : C. Canudas de Wit [Contact person] , R. Fabbiano, F. Garin.

The problem of source localization consists in finding, with one or several agents possibly cooperating with each other, the point or the spatial region from which a quantity of interest is being emitted. Source-seeking agents can be fixed sensors, that collect and exchange some information about the signal field and try to identify the position of the source (or the smallest region in which it is included), or moving devices equipped with one or more sensors, that physically reach the source in an individual or cooperative way. This is particularly difficult when the agents have limited or no position information and GPS navigation is not available, as in underwater navigation or in cave exploration: for instance, source localization is relevant to many applications of vapor emitting sources such as explosive detection, drug detection, sensing leakage or hazardous chemicals, pollution sensing and environmental studies. Other fields of interest are sound source localization, heat source localization and vent sources in underwater field. Techniques present in literature either are based on a specific knowledge of the solution of the diffusion process, or make use of an extremum-seeking approach, exciting the system with a periodic signal so as to explore the field and collect enough information to reconstruct the gradient of the quantity of interest. Our approach lies in the computation of derivatives (potentially of any order) from Poisson integrals that, for isotropic diffusive source in steady-state, whose solution satisfies the Laplace equation, allows for a gradient search with a small computation load (derivatives are computed by integrals) and without requiring any knowledge of the closed-form solution, avoiding in the same time extremum-seeking oscillations; this has the additional advantage of an intrinsic high-frequency filtering, that makes the method robust to measurement noise. We also propose a distributed version of this algorithm, where agents communicate in order to reconstruct gradient information from local pointwise measurements, and a control law combines the two objectives of formation control (to have a circular formation, so that measurements are taken around circle) and gradient ascent (so as to move towards the source); differently from previous literature, the moving agents do not need to know their absolute position, but only relative bearing angle of their neighbours. This work is the topic of the Ph.D. thesis of Ruggero Fabbiano [12] .

#### Synchronization of heterogenous networks

Participants : E. Lovisari [Contact person] , C.-Y. Kao [National Sun Yat-Sen University, Taiwan] .

Syncronization of agents in large-scale networks is studied in [19] . Each agent is modeled as a Single Input Single Output operator composed of the series of a common Linear Time-Invariant system and a possibly nonlinear perturbation. Interconnection is represented via a graph whose edges model communication channels between agents, in turn modeled as a nominal component and a possibly nonlinear perturbation. Two agents are synchronized if their outputs are the same, possibly time-varying signal. The main result provides synchronization certificates based on the Robust Control Technique of Integral Quadratic Constraints. Exploitation of graph structures allows then to reduce the computational burden of the certificate in a way that scales with the dimension of the network. This provides framework which unifies and extendes several results already presented in the literature.

#### Observer-based FDI scheme for switched systems with sensor faults

Participants : H. Fourati [Contact person] , D. E. C. Belkhiat [U. Setif] , D. Jabri [U. Setif] .

The Fault Detection and Isolation (FDI) problem for a class of Switched Linear Systems (SLS) subject to sensor faults and unknown bounded Disturbances is proposed in [24] . The main work is based on the design of a generalized switched observer scheme. The FDI problems have been solved by using a robust control techniques. A suitable trade-off between the robustness to disturbances and the sensitivity to sensor faults was obtained. The main results are reformulated by using Linear Matrix Inequality (LMI) formulation. An example is included to illustrate the efficiency of the proposed approach.