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Maria M Seron - One of the best experts on this subject based on the ideXlab platform.
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integration of Invariant Set based fdi with varying sampling rate virtual actuator and controller
International Journal of Adaptive Control and Signal Processing, 2016Co-Authors: Esteban N Osella, Hernan Haimovich, Maria M SeronAbstract:We present a new output feedback fault-tolerant control strategy for continuous-time linear systems with bounded disturbances. The strategy combines a digital nominal controller under controller-driven varying sampling with virtual actuator VA-based controller reconfiguration to compensate for abrupt actuator faults and Invariant-Set-based fault detection and isolation. Two independent objectives are considered: a closed-loop stability with Setpoint tracking and b controller reconfiguration under faults. Our main contribution is to extend an existing fault detection and isolation and VA-based controller reconfiguration strategy to systems under controller-driven sampling in such a way that if objective a is possible under controller-driven sampling without VA and objective b is possible under uniform sampling without controller-driven sampling, then closed-loop stability and Setpoint tracking will be preserved under both healthy and faulty operations for any possible sampling rate evolution that may be selected by the controller. Copyright © 2015i¾?John Wiley & Sons, Ltd.
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Invariant Set based fault diagnosis in lure systems
International Journal of Robust and Nonlinear Control, 2014Co-Authors: Maria M Seron, Juan Antonio Cordoba Doña, Jan H RichterAbstract:SUMMARY In this paper, we present an Invariant-Set-based method for actuator and sensor fault detection and isolation in Lure systems. The Lure plant is controlled by an observer-based feedback tracking controller, designed for the nominal (fault-free) system. Suitable residual signals are constructed from measurable system outputs and estimates associated with the nominal observer. Faults are diagnosed by online contrasting the residual signal trajectories against Sets of values that the residuals are shown to attain under healthy or faulty operation. These values are obtained via Set-invariance analysis of the system closed-loop trajectories. Copyright © 2013 John Wiley & Sons, Ltd.
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brief paper componentwise ultimate bound and Invariant Set computation for switched linear systems
Automatica, 2010Co-Authors: Hernan Haimovich, Maria M SeronAbstract:We present a novel ultimate bound and Invariant Set computation method for continuous-time switched linear systems with disturbances and arbitrary switching. The proposed method relies on the existence of a transformation that takes all matrices of the switched linear system into a convenient form satisfying certain properties. The method provides ultimate bounds and Invariant Sets in the form of polyhedral and/or mixed ellipsoidal/polyhedral Sets, is completely systematic once the aforementioned transformation is obtained, and provides a new sufficient condition for practical stability. We show that the transformation required by our method can easily be found in the well-known case where the subsystem matrices generate a solvable Lie algebra, and we provide an algorithm to seek such transformation in the general case. An example comparing the bounds obtained by the proposed method with those obtained from a common quadratic Lyapunov function computed via linear matrix inequalities shows a clear advantage of the proposed method in some cases.
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Invariant Set approach to actuator fault tolerant control
IFAC Proceedings Volumes, 2009Co-Authors: Maria M Seron, Jose A De Dona, John J MartinezAbstract:We present a new actuator fault-tolerant control strategy based on the separation of Sets that characterise healthy system operation from Sets that characterise faulty operation. The new scheme is an extension of a similar strategy recently proposed by the authors. In the present paper we propose a new criterion for fault detection and isolation that leads to less conservative conditions for fault tolerant closed-loop stability. These new conditions employ discrete-time models for the plant, reference system and observers and allow for quicker fault detection and consequent reconfiguration of the controller.
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actuator fault tolerant control based on Invariant Set separation
IFAC Proceedings Volumes, 2008Co-Authors: Carlos Ocampomartinez, Juan Antonio Cordoba Doña, Maria M SeronAbstract:Abstract In this paper an actuator fault-tolerant control (FTC) strategy based on Invariant Set computation is presented. The proposed scheme is based on a bank of observers which match different fault situations that can occur in the plant. Each of these observers produces an estimation error with a distinctive behavior when the observer matches the current fault situation in the plant. With the information of the estimation errors from each of the considered observers, a fault diagnosis and isolation (FDI) module is able to reconfigure the control loop by selecting the appropriate stabilising controller from a bank of precomputed control laws, each of them related to one of the considered fault models. The decision criteria of the FDI is based on the computation of Invariant Sets of the estimation errors for each fault scenario and for each control configuration. Conditions for the design of the FDI module and for fault-tolerant closed-loop stability are given, and the effectiveness of the approach is illustrated with an example.
Bin Liang - One of the best experts on this subject based on the ideXlab platform.
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Invariant Set based robust fault detection and optimal fault estimation for discrete time lpv systems with bounded uncertainties
International Journal of Systems Science, 2019Co-Authors: Feng Xu, Xueqian Wang, Jun Yang, Bin LiangAbstract:ABSTRACTThis paper proposes an Invariant Set-based robust fault detection (FD) and optimal fault estimation (FE) method for discrete-time linear parameter varying (LPV) systems with bounded uncerta...
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Invariant Set-Based Analysis of Minimal Detectable Fault for Discrete-Time LPV Systems With Bounded Uncertainties
IEEE Access, 2019Co-Authors: Sorin Olaru, Monica Roman, Feng Xu, Bin LiangAbstract:This paper proposes an Invariant-Set based minimal detectable fault (MDF) computation method based on the Set-separation condition between the healthy and faulty residual Sets for discrete-time linear parameter varying (LPV) systems with bounded uncertainties. First, a novel Invariant-Set computation method for discrete-time LPV systems is developed exclusively based on a sequence of convex-Set operations. Notably, this method does not need to satisfy the existence condition of a common quadratic Lyapunov function for all the vertices of the parametric uncertainty compared with the traditional Invariant-Set computation methods. Based on asymptotic stability assumptions, a family of robust positively Invariant (RPI) outer-approximations of minimal robust positively Invariant (mRPI) Set are obtained by using a shrinking procedure. Based on the mRPI Set, the healthy and faulty residual Sets can be obtained. Then, by considering the dual case of the Set-separation constraint regarding the healthy and faulty residual Sets, we transform the guaranteed MDF problem based on the Set-separation constraint into a simple linear programming (LP) problem to compute the magnitude of MDF. Since the proposed MDF computation method is robust regardless of the value of scheduling variables in a given convex Set, fault detection (FD) can be guaranteed whenever the magnitude of fault is larger than that of the MDF. At the end of the paper, a practical vehicle model is used to illustrate the effectiveness of the proposed method.
Sorin Olaru - One of the best experts on this subject based on the ideXlab platform.
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Interpolating Control with Periodic Invariant Sets
2020 European Control Conference (ECC), 2020Co-Authors: Sheila Scialanga, Sorin Olaru, Konstantinos AmpountolasAbstract:This paper presents a novel low-complexity interpolating control scheme involving periodic invariance or vertex reachability of target Sets for the constrained control of LTI systems. Periodic invariance relaxes the strict one-step positively Invariant Set notion, by allowing the state trajectory to leave the Set temporarily but return into the Set in a finite number of steps. To reduce the complexity of the representation of the required controllable Invariant Set, a periodic Invariant Set is employed. This Set should be defined within the controllable stabilising region, which is considered unknown during the design process. Since periodic Invariant Sets are not traditional Invariant Sets, a reachability problem can be solved off-line for each vertex of the outer Set to provide an admissible control sequence that steers the system state back into the original target Set after a finite number of steps. This work develops a periodic interpolating control (pIC) scheme between such periodic Invariant Sets and a maximal admissible inner Set by means of an inexpensive linear programming problem, solved on-line at the beginning of each periodic control sequence. Theorems on recursive feasibility and asymptotic stability of the pIC are given. A numerical example demonstrates that pIC provides similar performance compared to more expensive optimization-based schemes previously proposed in the literature, though it employs a naive representation of the controllable Invariant Set.
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Invariant Set-Based Analysis of Minimal Detectable Fault for Discrete-Time LPV Systems With Bounded Uncertainties
IEEE Access, 2019Co-Authors: Sorin Olaru, Monica Roman, Feng Xu, Bin LiangAbstract:This paper proposes an Invariant-Set based minimal detectable fault (MDF) computation method based on the Set-separation condition between the healthy and faulty residual Sets for discrete-time linear parameter varying (LPV) systems with bounded uncertainties. First, a novel Invariant-Set computation method for discrete-time LPV systems is developed exclusively based on a sequence of convex-Set operations. Notably, this method does not need to satisfy the existence condition of a common quadratic Lyapunov function for all the vertices of the parametric uncertainty compared with the traditional Invariant-Set computation methods. Based on asymptotic stability assumptions, a family of robust positively Invariant (RPI) outer-approximations of minimal robust positively Invariant (mRPI) Set are obtained by using a shrinking procedure. Based on the mRPI Set, the healthy and faulty residual Sets can be obtained. Then, by considering the dual case of the Set-separation constraint regarding the healthy and faulty residual Sets, we transform the guaranteed MDF problem based on the Set-separation constraint into a simple linear programming (LP) problem to compute the magnitude of MDF. Since the proposed MDF computation method is robust regardless of the value of scheduling variables in a given convex Set, fault detection (FD) can be guaranteed whenever the magnitude of fault is larger than that of the MDF. At the end of the paper, a practical vehicle model is used to illustrate the effectiveness of the proposed method.
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Invariant Set design for constrained discrete time linear systems with bounded matched disturbance
9th IFAC Symposium on Robust Control Design, 2018Co-Authors: Nathan Michel, Sorin Olaru, Giorgio Valmorbida, Sylvain Bertrand, Didier DumurAbstract:Invariant Set theory has been recognized as an important tool for control design of constrained systems subject to disturbances. Indeed, for a given control law, entering an Invariant Set guarantees recursive state and input constraint satisfaction in closed-loop. This paper focuses on discrete-time linear systems subject to bounded matched additive disturbance. The problem of the joint synthesis of control laws and associated Invariant Sets that are optimized with regards to the state constraints is investigated. An interpolation method is used to enlarge the controllable region.
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a bilevel optimization approach for d Invariant Set design
IFAC-PapersOnLine, 2016Co-Authors: Mohammedtahar Laraba, Sorin Olaru, Morten Hovd, Silviu-iulian NiculescuAbstract:Abstract This paper is dedicated to the Set invariance characterization of dynamical systems affected by time-delays. Starting from a discrete-time dynamical system described by a delay-difference equation, the construction of a positive Invariant Set is sought. An optimization-based procedure is defined to include the properties related to the polyhedral structure, boundedness and positive invariance. This last property is related to the Minkowski sum and its translation into linear constraints or optimization-based subproblems is discussed together with the computational details. It will be shown that bilevel optimization problems can be used for D-invariance design problems. The difficulties related to the nonlinearity of the optimization and the complementarity constraints will be discussed as well as the objective functions which can translate additional features of the D-Invariant Sets.
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on the construction of Invariant Sets for piecewise affine systems using the transition graph
International Conference on Control and Automation, 2009Co-Authors: Hichem Benlaoukli, Sorin Olaru, Morten Hovd, P BoucherAbstract:The present paper introduces an algorithmic construction of the maximal Invariant Set for a PWA (piecewise affine) system. The classical analysis of this type of dynamical systems is based on the construction of a Lyapunov function which lead subsequently to the Invariant Set description by means of the Lyapunov function level Sets. As an alternative, expansive/contractive schemes exploit the global one-step forward/backward evolution of the system dynamics in order to obtain the Invariant Set as a fixed point of the Set iterates. Both approaches address the problem of finding an Invariant Set from a global point of view, and therefore result in very demanding computations. The conditions under which the resulting Invariant Sets are finitely determined are not clear. The approach proposed in this paper is different in the sense that each polyhedral region is treated separately considering only the infinite-time endogenous (by the same region of the state space) transitions, providing (at least from a local point of view) clear conditions on the finite determinedness. In order to address with the global behavior, a transition graph between local piecewise descriptions is used.
Feng Xu - One of the best experts on this subject based on the ideXlab platform.
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Invariant Set based robust fault detection and optimal fault estimation for discrete time lpv systems with bounded uncertainties
International Journal of Systems Science, 2019Co-Authors: Feng Xu, Xueqian Wang, Jun Yang, Bin LiangAbstract:ABSTRACTThis paper proposes an Invariant Set-based robust fault detection (FD) and optimal fault estimation (FE) method for discrete-time linear parameter varying (LPV) systems with bounded uncerta...
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Invariant Set-Based Analysis of Minimal Detectable Fault for Discrete-Time LPV Systems With Bounded Uncertainties
IEEE Access, 2019Co-Authors: Sorin Olaru, Monica Roman, Feng Xu, Bin LiangAbstract:This paper proposes an Invariant-Set based minimal detectable fault (MDF) computation method based on the Set-separation condition between the healthy and faulty residual Sets for discrete-time linear parameter varying (LPV) systems with bounded uncertainties. First, a novel Invariant-Set computation method for discrete-time LPV systems is developed exclusively based on a sequence of convex-Set operations. Notably, this method does not need to satisfy the existence condition of a common quadratic Lyapunov function for all the vertices of the parametric uncertainty compared with the traditional Invariant-Set computation methods. Based on asymptotic stability assumptions, a family of robust positively Invariant (RPI) outer-approximations of minimal robust positively Invariant (mRPI) Set are obtained by using a shrinking procedure. Based on the mRPI Set, the healthy and faulty residual Sets can be obtained. Then, by considering the dual case of the Set-separation constraint regarding the healthy and faulty residual Sets, we transform the guaranteed MDF problem based on the Set-separation constraint into a simple linear programming (LP) problem to compute the magnitude of MDF. Since the proposed MDF computation method is robust regardless of the value of scheduling variables in a given convex Set, fault detection (FD) can be guaranteed whenever the magnitude of fault is larger than that of the MDF. At the end of the paper, a practical vehicle model is used to illustrate the effectiveness of the proposed method.
Poom Kumam - One of the best experts on this subject based on the ideXlab platform.
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coupled fixed point theorems for f Invariant Set
Applied Mathematics & Information Sciences, 2013Co-Authors: Wutiphol Sintunavarat, Stojan Radenovic, Zorana Golubovic, Poom KumamAbstract:In this paper, we extend and complement some recent results of coupled fixed point theorems of Luong and Thuan in (N. V. Luong, N. X. Thuan, Coupled fixed point theorems for mixed monotone mappings and an application to integral equations, Computers and Mathematics with Applications 62 (2011) 4238-4248.) by weaken the concept of the mixed monotone property. The example of a nonlinear contraction mapping which is not applied by the results of Luong and Thuan, but can be applied to our results is given. The presented results extend and complement results of Luong and Thuan and some known existence results from the literature.
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coupled fixed point theorems for weak contraction mappings under Invariant Set
Abstract and Applied Analysis, 2012Co-Authors: Wutiphol Sintunavarat, Poom KumamAbstract:We extend the recent results of the coupled fixed point theorems of Cho et al. (2012) by weakening the concept of the mixed monotone property. We also give some examples of a nonlinear contraction mapping, which is not applied to the existence of the coupled fixed point by the results of Cho et al. but can be applied to our results. The main results extend and unify the results of Cho et al. and many results of the coupled fixed point theorems.
