A Generalized Approach for Analysis and Control of Discrete-Time Piecewise Affine and Hybrid Systems

Cuzzola, Francesco Alessandro; Morari, Manfred

doi:10.1007/3-540-45351-2_18

Cited by 51 publications

(40 citation statements)

References 11 publications

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“…Clearly, it is possible to apply the control approach proposed in [5] directly to the extended system (Equation (23)). This can be conservative because is not an unknown disturbance but a known term.…”

Section: Stochastic Pwa Model For Wecsmentioning

confidence: 99%

“…The piecewise linear system framework can be used to analyze smooth nonlinear systems with arbitrary accuracy. Many other classes of nonlinear systems can also be approximated by piecewise linear systems [5].…”

Section: Introductionmentioning

confidence: 99%

“…In the case of discrete time, the authors of [10] presented an approach for stabilization of piecewise linear systems based on a global quadratic Lyapunov function. In [5,11], the authors gave a number of results on stability analysis, controller design, analysis, and controller design for the piecewise linear systems based on a piecewise Lyapunov function. In [5], for control synthesis, the affine term was treated as a disturbance.…”

Section: Introductionmentioning

confidence: 99%

“…In [5,11], the authors gave a number of results on stability analysis, controller design, analysis, and controller design for the piecewise linear systems based on a piecewise Lyapunov function. In [5], for control synthesis, the affine term was treated as a disturbance. In a recent paper [12], a new method was presented to synthesize the controller for the piecewise discrete time linear systems.…”

Section: Introductionmentioning

confidence: 99%

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H∞ Fault Tolerant Control of WECS Based on the PWA Model

et al. 2014

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Abstract:The main contribution of this paper is the development of fault tolerant control for a wind energy conversion system (WECS) based on the stochastic piecewise affine (PWA) model. In this paper the normal and fault stochastic PWA models for WECS including multiple working points at different wind speeds are established. A reliable piecewise linear quadratic regulator state feedback is designed for the fault tolerant actuator and sensor. A sufficient condition for the existence of the passive fault tolerant controller is derived based on some linear matrix inequalities (LMIs). It is shown that the fault tolerant controller of WECS can control the wind turbine exposed to multiple simultaneous sensor faults or actuator faults; that is, the reliability of wind turbines can be improved.

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Section: Stochastic Pwa Model For Wecsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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H∞ Fault Tolerant Control of WECS Based on the PWA Model

et al. 2014

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“…The set S can be computed using reachability analysis for MLD systems, see Cuzzola and Morari (2001).…”

Section: Piecewise Affine Systemsmentioning

confidence: 99%

Reconfigurability of Piecewise Affine Systems Against Actuator Faults

Tabatabaeipour

Gholami

Bak

et al. 2011

IFAC Proceedings Volumes

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In this paper, we consider the problem of reconfigurability of peicewise affine (PWA) systems. Actuator faults are considered. A system subject to a fault is considered as reconfigurable if it can be stabilized by a state feedback controller and the optimal cost of the performance of the systems is admissible. Sufficient conditions for reconfigurability are derived in terms of feasibility of a set of Linear Matrix Inequalities (LMIs). The method is implemented on a large scale livestock hybrid ventilation model which was obtained during previous research.

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On the complexity and dynamical properties of mixed logical dynamical systems via an automaton‐based realization of discrete‐time hybrid automaton

Hejri

Giua

Mokhtari

2018

Intl J Robust & Nonlinear

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Summary Modeling of hybrid systems using mixed logical dynamical (MLD) systems is an art. The MLD framework often introduces numerous constraints and auxiliary binary and continuous variables, which, in turn, increase the computational complexity of the optimization problems. This paper presents an automaton‐based realization for discrete‐time hybrid automaton (DHA) with both controlled and uncontrolled switching phenomena by which it is attempted to develop efficient translation techniques to MLD systems and reduce the total number of decision variables in the MLD model. Based on this DHA model, a modified version of MLD systems, which is called extended MLD (EMLD) is formally defined and represented. EMLD is derived based on the concept of forward evolution in which the one‐step delay between the change of discrete states and continuous dynamics of the existing evolution in the conventional MLD systems is eliminated. The result is that the size of EMLD model in terms of the number of variables, which determines the complexity of the synthesis problems on MLD systems, is reduced. The dynamical properties such as the nonblocking, determinism, and well‐posedness of the proposed DHA and its equivalent MLD models are investigated, and the necessary and sufficient conditions are derived. The effectiveness of the proposed ideas is shown by the numerical examples.

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A Generalized Approach for Analysis and Control of Discrete-Time Piecewise Affine and Hybrid Systems

Cited by 51 publications

References 11 publications

H∞ Fault Tolerant Control of WECS Based on the PWA Model

H∞ Fault Tolerant Control of WECS Based on the PWA Model

Reconfigurability of Piecewise Affine Systems Against Actuator Faults

On the complexity and dynamical properties of mixed logical dynamical systems via an automaton‐based realization of discrete‐time hybrid automaton

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