Componentwise ultimate bound and invariant set computation for switched linear systems

Haimovich, Hernan; Serón, María M.

doi:10.1016/j.automatica.2010.08.018

Cited by 41 publications

(45 citation statements)

References 19 publications

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“…Such common transformations T CL and T O are also useful for computing invariant sets and ultimate bounds in DTSS, as shown in [17,18]. Such common transformations T CL and T O are also useful for computing invariant sets and ultimate bounds in DTSS, as shown in [17,18].…”

Section: Controller Designmentioning

confidence: 99%

“…Alternatively, if the required closed-loop matrices 405 have some additional structure, such as being simultaneously triangularizable, some structure-based invariant-set computation methods can be directly applied [17,18]. Because ¹A h;CL W h 2 Hº and ¹A h;O W h 2 Hº are both stable under arbitrary switching (recall Section 3.1) and because the process disturbance w h and measurement noise Á are both bounded (i.e., w h 2 W and Á 2 N ), then attractive invariant sets Z and Q " can be computed for the error variables i and Q i .…”

Section: Fault Detection and Isolation Principle And Residual Generationmentioning

confidence: 99%

“…Recalling features 1-3 in Section 3.2, we may define the incremental variables Â i WD Â i N Â i and u c WD u c u ref and obtain, using (18)…”

Section: Assumption 1 (Fault Scenario)mentioning

confidence: 99%

“…A switching rule engages the suitable VA from the bank according to an FDI decision based on sets defined for the residual signals. An advantage of using the latter conditions is that invariant sets for the DTSS can be computed using a simple formula, as shown in [17,18].In this context, the main contribution of the present paper is to adapt and extend the VA-based FTC technique of [4] to the aforementioned controller-driven sampling setting, using a DTSS approach. An important advantage of this invariant-set approach to FDI is that fault tolerance and closed-loop stability can be guaranteed when the relevant sets have no intersection.…”

mentioning

confidence: 99%

“…Indeed, viewed from the controller, the continuous-time system can be interpreted as a DTSS under arbitrary switching, where each discrete-time equivalent of the continuous-time system sampled at some of the possible sampling periods represents a subsystem and the sampling period sequence represents the switching law. An advantage of using the latter conditions is that invariant sets for the DTSS can be computed using a simple formula, as shown in [17,18]. This common Lyapunov function may be of a more complex form than quadratic.…”

mentioning

confidence: 99%

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Integration of invariant‐set‐based FDI with varying sampling rate virtual actuator and controller

Osella

Haimovich

Serón³

2015

Adaptive Control & Signal

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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) closedloop 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 controllerdriven sampling (without VA) and objective (b) is possible under uniform sampling (without controllerdriven 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 394 E. OSELLA, H. HAIMOVICH AND M. M. SERON range. In addition, a residual signal is constructed for each VA directly from its available measurable signals. A switching rule engages the suitable VA from the bank according to an FDI decision based on sets defined for the residual signals. This set-based approach for FDI (see, e.g., [5,6]) relies on the principle that each residual signal will belong to an invariant 'correct-matching' set when the associated VA model 'matches' the actual actuator fault situation and will shift to a 'fault-transitionmatching' set when a change to a 'non-matching' fault situation occurs. An important advantage of this invariant-set approach to FDI is that fault tolerance and closed-loop stability can be guaranteed when the relevant sets have no intersection.In the present paper, we extend the approach of [4] to continuous-time linear systems operating under a controller-driven (varying) sampling setting, where both the nominal controller and the bank of VAs operate under a varying sampling rate administered by the controller. The motivation for considering this class of systems stems from the increasing popularity of networked control systems [7,8], which broadly refers to control systems that include some kind of shared communications network. In this setting, acceptable control performance and communication bandwidth preservation may be conflicting objectives: increasing control performance by sampling at a higher rate may require too much bandwidth and prevent other processes from accessing the network. Thus, research effort has been directed at control strategies able to modify the sampling rate online, according to time-dependent performance and bandwidth requirements (see [9] for further details). As opposed to the general networked control systems setting where the different component elements (sensors, actuators, and controllers) may operate asynchronously, we consider a setting with a centralized controller, with synchronous o...

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Section: Controller Designmentioning

confidence: 99%

Section: Fault Detection and Isolation Principle And Residual Generationmentioning

confidence: 99%

“…Recalling features 1-3 in Section 3.2, we may define the incremental variables Â i WD Â i N Â i and u c WD u c u ref and obtain, using (18)…”

Section: Assumption 1 (Fault Scenario)mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Integration of invariant‐set‐based FDI with varying sampling rate virtual actuator and controller

Osella

Haimovich

Serón³

2015

Adaptive Control & Signal

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Viability Criteria for a Switched System on Bounded Polyhedron

Gao

Zhao

2017

Asian Journal of Control

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The viability of a switched system on a bounded polyhedron set, which is expressed by some linear inequalities, is investigated. Based on nonsmooth analysis and the properties of the tangent cone, a necessary and sufficient condition for viability is proposed. It is shown that the viability of a system is equivalent to the consistency of some systems of linear inequalities. Specifically, a viability condition for a switched system on a bounded polyhedron is presented. According to this condition, determining the viability of a bounded polyhedron can be transformed into verifying certain conditions at vertices of each facet. The method of determining viability, which transforms verifying the condition from infinite points to finite ones, can be implemented easily in practice. An algorithm to determine the viability for the switched system is constructed by using convex analysis. In addition, the approach can be extended to the switched system in which a control input is present. Finally, an example is listed to illustrate the effectiveness of the results.

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Linear functional state bounding for linear positive singular systems with disturbances varying within a bounded set

Thuận

2021

Math Methods in App Sciences

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In this paper, the problem of linear functional state bounding for linear positive singular system with an interval time‐varying delay is investigated for the first time. First, the authors present new conditions for positivity, regularity, impulse free, and the existence of componentwise bound for the state vector of the singular systems without disturbance. Based on the obtained results, and by using state transformations, we derive the smallest componentwise ultimate bound of the state vector of the linear positive singular system with bounded disturbances. Then, we propose some sufficient criteria for linear functional state bounding problems of the positive singular system with time‐varying delays by using some new mathematical techniques. Since the conditions are given in terms of the linear programming/Hurwit matrix/spectral abscissa, we can check them easily and compute directly the smallest componentwise ultimate bound. Finally, a numerical example is given to demonstrate the correctness and the effectiveness of the proposed methodology.

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Componentwise ultimate bound and invariant set computation for switched linear systems

Cited by 41 publications

References 19 publications

Integration of invariant‐set‐based FDI with varying sampling rate virtual actuator and controller

Integration of invariant‐set‐based FDI with varying sampling rate virtual actuator and controller

Viability Criteria for a Switched System on Bounded Polyhedron

Linear functional state bounding for linear positive singular systems with disturbances varying within a bounded set

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