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The problem of the recursive formulation of the MOESP class of subspace identification algorithms is considered and two novel instrumental variable approaches are introduced. The first one leads to an RLSlike implementation, the second to a gradient type iteration. The relative merits of both approaches are analysed and discussed, while simulation results are used to compare their performance with one of the existing techniques.

Hydrogen from water electrolysis associated with renewable energies is one of the most attractive solutions for the green energy storage. To improve the efficiency and the safety of such stations, some technological studies are still under investigation both on methods and materials. As methods, control, monitoring and diagnosis algorithms are relevant tools. These methods are efficient when they use an accurate mathematical model representing the real behaviour of hydrogen production system. This work focuses on the dynamical modelling and the monitoring of Proton Exchange Membrane (PEM) electrolyser. Our contribution consists in three parts: to develop an analytical dynamical PEM electrolyser model dedicated to the control and the monitoring; to identify the model parameters and to propose adequate monitoring tools. The proposed model is deduced from physical laws and electrochemical equations and consists in a steady-state electric model coupled with a dynamical thermal model. The estimation of the model parameters is achieved using identification and data fitting techniques based on experimental measurements. Taking into account the information given by the proposed analytical model and the experimentation data (temperature T, voltage U and current I) given by a PEM electrolyser composed of seven cells, the model parameters are identified. After estimating the dynamical model, model based diagnosis approach is used in order to monitoring the PEM electrolyser and to ensure its safety. We illustrate how our algorithm can detect and isolate faults on actuators, on sensors or on electrolyser system. INTRODUCTIONIn recent decades, the global warming increases the average temperature of the air and oceans near the earth surface. This problem caused by CO 2 gas and several polluting wastes continuing to affect the lives in the world. In order to overcome this problem, the use of renewable energy and its optimization become a humanity challenge [3]. An attractive solution is to integrate efficient energy storages. The hydrogen is one of most promising vectors to store green energy. In the last years, numerous stations including renewable energy and electrolyser have been developed in order to optimise the electric energy production by increasing the storage capacity. The key idea is to convert the hydrogen into electricity using Fuel Cell (FC) when the renewable energy is off (no wind, no sun). In order to have this fuel, during the high potential periods, the extra renewable energy is converted using a Proton Exchange Membrane (PEM) electrolyser into H 2 . The global efficiency and safety of such installations (renewable energy source, fuel cell and electrolyser) lead to important research works in modelling, control [1] and monitoring. More precisely, it is necessary to propose an efficient supervision system. It permits to the user to decide if the hydrogen production station is faulty and if risk for itself and its environment could occur. For example, when sensor or actuator fault is detected, control l...

This article is concerned with the identification of switched linear multiple-inputs-multiple-outputs state-space systems in a recursive way. First, a structured subspace identification scheme for linear systems is presented which turns out to have many attractive features. More precisely, it does not require any singular value decomposition but is derived using orthogonal projection techniques; it allows a computationally appealing implementation and it is closely related to input-output models identification. Second, it is shown that this method can be implemented on-line to track both the range space of the extended observability matrix and its dimension and thereby, the system matrices. Third, by making use of an on-line switching times detection strategy, this method is applied to blindly identify switched systems and to label the obtained submodels. Simulation results on noisy data illustrate the abilities and the benefits of the proposed approach.

We consider the problem of identifying switched linear state space models from a finite set of input-output data. This is a challenging problem, which requires inferring both the discrete state and the parameter matrices associated with each discrete state. An important contribution of our work is that we do not make the restrictive assumption of minimum dwell time between the switches, as it is customary in methods that deal with such models. We first propose a technique for eliminating the unknown continuous state from the model equations under an appropriate assumption of observability. On a time horizon, this gives us a new switched input-output relation that involves structured intermediary matrices, which depend on the state space representation matrices. To estimate the intermediary matrices, we present a randomly initialized algorithm that alternates between data classification and parameter update via recursive least squares. Given these matrices, the parameters associated to the different discrete states can be computed after a correct estimation of the discrete state.

We consider the problem of identifying a switched nonlinear system from a finite collection of input-output data. The constituent subsystems of such a switched system are all nonlinear systems. We model each individual subsystem as a sparse expansion over a dictionary of elementary nonlinear smooth functions shaped by the whole available dataset. Estimating the switched model from data is a doubly challenging problem. First one needs, without any knowledge of the parameters, to decide which subsystem is active at which time instant. Second, the representation of each nonlinear subsystem over the considered basis shall be performed in a high dimensional space. We tackle both tasks simultaneously by sparse optimization. More specifically, we view the switched nonlinear system identification problem as the problem of minimizing the 0 norm of an error vector. We subsequently relax it into an 1 convex minimization problem for which powerful numerical tools exist.

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