Samir Aberkane

Fault Tolerant Control Design For Polytopic LPV Systems

Fault Tolerant Control Design For Polytopic LPV Systems This paper deals with a Fault Tolerant Control (FTC) strategy for polytopic Linear Parameter Varying (LPV) systems. The main contribution consists in the design of a Static Output Feedback (SOF) dedicated to such systems in the presence of multiple actuator faults/failures. The controllers are synthesized through Linear Matrix Inequalities (LMIs) in both fault-free and faulty cases in order to preserve the system closed-loop stability. Hence, this paper provides a new sufficient (but not necessary) condition for the solvability of the stabilizing output feedback control problem. An example illustrates the effectiveness and performances of the proposed FTC method.

Stochastic stabilization of a class of nonhomogeneous Markovian jump linear systems

This paper deals with the problem of stochastic stability analysis and control synthesis of a class of Markovian jump linear systems (MJLS) with time-varying transition probabilities (TPs) in the discrete-time domain. The time-varying character is considered to be in a polytopic sense. The approach followed in this note is based on the use of a parameter dependent stochastic Lyapunov function. We give a stability condition in terms of a linear matrix inequality (LMI) feasibility problem. The obtained results are illustrated in a numerical example.

H ∞ Stochastic Stabilization of Active Fault Tolerant Control Systems: Convex Approach

This paper deals with the problem of H<inf>∞</inf>and robust H<inf>∞</inf>control, via dynamic output feedback, of continuous time Active Fault Tolerant Control Systems with Markovian Parameters (AFTCSMP) subject to structured parameter uncertainties. The above problematic are addressed under a convex programming approach. Indeed, the fundamental tool in the analysis is an LMI (Linear Matrix Inequalities) characterization of dynamical compensators that stochastically (robustly) stabilize the closed loop system and ensure H<inf>∞</inf>and robust H<inf>∞</inf>constraints.

Output feedback robust control of uncertain active fault tolerant control systems via convex analysis

This paper deals with the problem of and robust control, via dynamic output feedback, of continuous time active fault tolerant control systems with Markovian parameters (AFTCSMP) subject to both structured and unstructured parameter uncertainties. The above problematic is addressed under a convex programming approach. Indeed, the fundamental tool in the analysis is a linear matrix inequalities (LMI) characterization of dynamical compensators that stochastically (robustly) stabilize the closed loop system and ensure and robust performances. Numerical examples are presented to illustrate the theoretical results.

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, a particular kind of stochastic switching systems, subject to possibly unbounded random disturbances and probabilistic state constraints. Due to the 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 horizon 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.

OUTPUT FEEDBACK STOCHASTIC STABILIZATION OF ACTIVE FAULT TOLERANT CONTROL SYSTEMS: LMI FORMULATION

Abstract In this paper, we address the dynamic output feedback control problem of continuous time active fault tolerant control system with Markovian parameters (AFTCSMP). We will first derive a necessary and sufficient condition for the exponential stability in the mean square of the AFTCSMP under a dynamic output feedback control, in terms of coupled matrix inequalities, and then we will give an LMI (Linear Matrix Inequalities) characterization of dynamical compensators that stabilize the closed-loop system in the mean square sense.

Output-feedback H ∞ control of a class of networked fault tolerant control systems

This paper deals with static output feedback Hinfin control of a class of discrete-time networked control systems (NCSs) subject to random failures and random delays. The different random processes are modeled as Markovian chains, and the resulting closed-loop system belongs to the class of discrete-time Markovian jump linear systems (MJLS). For synthesis purposes, we adopt a new framework, based on the synthesis of ellipsoidal sets of controllers. Results are formulated as matrix inequalities. A numerical algorithm based on nonconvex optimization is provided and its running is illustrated on a classical example from literature.

H 2 optimal filtering for continuous-time periodic linear stochastic systems with state-dependent noise

Abstract This note addresses the problem of optimal H 2 filtering for a class of continuous-time time-varying stochastic systems. The time-variation character is considered to be periodic. The state space representation of the optimal filter is designed based on the unique periodic solution of a suitable Lyapunov differential equation and the periodic and stabilizing solution of a suitable generalized periodic Riccati differential equation. Some numerical experiments are also added to show the effectiveness of the proposed method.

Fault isolation filter and sensors scheduling co-design for networked control systems

This paper addresses the problem of multiple fault detection and isolation under communication constraints. More specifically, we consider the issue of sensor scheduling and fault isolation co-design under limited bandwidth capacity. The proposed isolation filter can be viewed as special structure of the traditional Kalman filter. The sensor scheduling sequence and the proposed filter are built in order to ensure the fault isolability property and noise effect minimization.

Fault detection and isolation in networked control systems with access constraints and packet dropouts

This paper deals with the problem of fault detection and isolation (FDI) of a networked control system (NCS). In this configuration a linear time invariant(LTI) system communicates with controller/FDI over a shared medium. The medium supports a limited number of simultaneous connections between sensors and FDI system. Furthermore, it is assumed that there is the random and unknown packet dropouts in the controller-to-actuator link. Objective is to find a strategy for residual signals generating which network effects are taken into account. In addition, by means of these residuals fault detection and isolation of system is possible. A set of structured residual based on parity relation approach is proposed. It guarantees robustness to system disturbances and packet dropout while each residual is designed to be sensitive to some sensor faults. The efficiency of the proposed approach will be illustrated with a simulation example.