arXiv subjects

Samir Aberkane

Publications and source records attributed to Samir Aberkane.

5 recordsLinked to original sources

arXiv2023

An Addendum to the Problem of Zero-Sum LQ Stochastic Mean-Field Dynamic Games\\ (Extended version)

In this paper, we first address a linear quadratic mean-field game problem with a leader-follower structure. By adopting a Riccati-type approach, we show how one can obtain a state-feedback representation of the pairs of strategies which achieve an open-loop Stackelberg equilibrium in terms of the global solutions of a system of coupled matrix differential Riccati-type equations. In the second part of this paper, we obtain necessary and sufficient conditions for the solvability of the involved coupled generalized Riccati equations.

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arXiv2020

Simultaneous Detectability of Process and Sensor Faults: Application to Water Distribution Networks

Detecting leaks in Water Distribution Networks (WDN) using sensors has become crucial towards an efficient management of water resources. The leak detection methods that use this data rely on the correctness of the acquired data. However, this assumption is often violated in practice. Consequently, leak detection under sensor faults is a problem of practical importance. This relates to the more general problem of simultaneous detectability in sensor and process faults for a class of systems modelled as a network, by exploiting the redundancies available through the topological relationship between the sensors. This paper hence aims at i) modeling WDN as graphs containing both systems and sensors faults ii) providing theoretical joint detectability results for such graphs and iii) applying these results to the scenario of leak identification under sensor faults conditions on real data issued from a rural WDN.

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arXiv2020

On the existence of the stabilizing solution of generalized Riccati equations arising in zero sum stochastic difference games: The time-varying case

In this paper, a large class of time-varying Riccati equations arising in stochastic dynamic games is considered. The problem of the existence and uniqueness of some globally defined solution, namely the bounded and stabilizing solution, is investigated. As an application of the obtained existence results, we address in a second step the problem of infinite-horizon zero-sum two players linear quadratic (LQ) dynamic game for a stochastic discrete-time dynamical system subject to both random switching of its coefficients and multiplicative noise. We show that in the solution of such an optimal control problem, a crucial role is played by the unique bounded and stabilizing solution of the considered class of generalized Riccati equations.

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arXiv2014

On control of discrete-time state-dependent jump linear systems with probabilistic constraints: A receding horizon approach

In this article, we consider a receding horizon control of discrete-time state-dependent jump linear systems, particular kind of stochastic switching systems, subject to possibly unbounded random disturbances and probabilistic state constraints. Due to a nature of the dynamical system and the constraints, we consider a one-step receding horizon. Using inverse cumulative distribution function, we convert the probabilistic state constraints to deterministic constraints, and obtain a tractable deterministic receding horizon control problem. We consider the receding control law to have a linear state-feedback and an admissible offset term. We ensure mean square boundedness of the state variable via solving linear matrix inequalities off-line, and solve the receding horizon control problem on-line with control offset terms. We illustrate the overall approach applied on a macroeconomic system.

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arXiv2014

Stochastic stability and stabilization of a class of state-dependent jump linear systems

This paper deals a continuous-time state-dependent jump linear system, a particular kind of stochastic switching system. In particular, we consider a situation when the transition rate of the random jump process depends on the state variable, and addressed the problem of stochastic stability and stabilization analysis for the proposed system. Numerically solvable sufficient conditions for the stochastic stability and stabilization of the proposed system is established in terms of linear matrix inequalities. The obtained results are illustrated in numerical examples.

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