On Lie-algebraic-solvability-based feedback stabilization of systems with controller-driven sampling

Nonlinear Analysis: Hybrid Systems

2013

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“…Consider the setV defined in (33) and let p ∈ R n be nonzero and satisfy p ′ v = 0 for all v ∈V. Suppose that there existsū ∈ R n−1 so that the real numbers…”

Section: Theorem 2 Consider the Vsr-dtss (3)-(5) With Ct Matricesã Cmentioning

confidence: 99%

“…These sufficient conditions are not limited by the number of subsystems of the switched system. The current paper contains substantial extensions of the preliminary results presented in [33,34].…”

mentioning

confidence: 93%

On controller-driven varying-sampling-rate stabilization via Lie-algebraic solvability

Nonlinear Analysis: Hybrid Systems

2013

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“…The DTSS arises from sampling a single continuous-time system at different rates [9,[27][28][29]. The system has input redundancy, in order to achieve successful trajectory tracking in the presence of total actuator loss, as explained in Section 2.1 [30].…”

Section: Controller Designmentioning

confidence: 99%

“…Consider the matrices X h i as defined in (27). Suppose that the continuous-time system matrices A and B are such that .A; BF i / are stabilizable for i D 0; 1;…”

Section: Lemmamentioning

confidence: 99%

“…In some cases, K h and L h can be found so that not only CQLFs exist but also additional properties hold for the closed-loop matrices (20) and (21) [17,18]. In addition, several works address the computation of K h (and L h ) so that this simultaneous triangularization is achieved for A h;CL (and A h;O ) for general switched linear systems [25,26] and specifically for cases as the current one, where A h and B h arise from sampling a single continuous-time system at different rates [9,[27][28][29]. While for general DTSS, this design criterion may be restrictive, a reduction on such restrictiveness can be observed in this specific context, considering the following facts:…”

Section: Controller Designmentioning

confidence: 99%

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

Adaptive Control & Signal

Serón³

2015

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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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Fault-tolerant control under controller-driven sampling using a virtual actuator strategy

2013 Australian Control Conference

Serón³

2013

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