Model-based dual-stage event-triggered control of linear system with two time scales
TL;DR: The singular perturbation technique is used to analyse the stability of the event-triggered control closed-loop system with a dual-stage event-triggering condition and the relations between the parameters in the events can be selected in a range independent of the matrices in the model.
Abstract: In this paper, the model-based event-triggered control is addressed for a class of linear systems with two time scales. The singular perturbation technique is used to analyse the stability of the e...
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Cites background or methods from "Model-based dual-stage event-trigge..."
...For the equations in (16), using the same process as in [33], there exists an ε1 > 0 such that the solutions of matrices H and L are H = A12A −1 22 + (ε)Em×n and L = A−1 22 A21 + (ε)En×m when ε ∈ (0, ε1), respectively....
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...In the study of event-triggered control on singularly perturbed systems, Ren and Hao [33] investigated the robust stabilisation of modelbased event-triggered control in linear cases, while the effects of input saturation were considered in [34]....
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...ORCID Xiang Ren https://orcid.org/0000-0003-2858-6966 Fei Hao https://orcid.org/0000-0003-4942-0893...
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...From the fact that the cost of reconstructing slow dynamics is lower than that of the computing and communication in the network (see [33]), the slow subsystem model of the singularly perturbed systems is used in ETM1 and ETM2 in Figure 1....
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TL;DR: In this article , two event-triggering conditions are designed for the slow and fast subsystems of the singularly perturbed systems based on the state errors between the observer and models.
Abstract: In this paper, the stabilization of singularly perturbed systems by means of observer-based event-triggered control is studied. To obtain the ultimately bounded stability of the closed-loop system, two event-triggering conditions are designed, respectively, for the slow and the fast subsystems of the singularly perturbed systems based on the state errors between the observer and models. In each event-triggering condition, there are two different stages to be designed. In the first stage, the event-triggering conditions are given based on the observer error dynamics. While in the second stage, the absolute type event-triggering conditions are used. Under the designed event-triggering conditions, Zeno behavior can be eliminated from the closed-loop systems. Finally, numerical examples are provided to illustrate the efficiency and feasibility of the theoretical results.
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TL;DR: This note investigates a simple event-triggered scheduler based on the paradigm that a real-time scheduler could be regarded as a feedback controller that decides which task is executed at any given instant and shows how it leads to guaranteed performance thus relaxing the more traditional periodic execution requirements.
Abstract: In this note, we revisit the problem of scheduling stabilizing control tasks on embedded processors. We start from the paradigm that a real-time scheduler could be regarded as a feedback controller that decides which task is executed at any given instant. This controller has for objective guaranteeing that (control unrelated) software tasks meet their deadlines and that stabilizing control tasks asymptotically stabilize the plant. We investigate a simple event-triggered scheduler based on this feedback paradigm and show how it leads to guaranteed performance thus relaxing the more traditional periodic execution requirements.
3,695 citations
"Model-based dual-stage event-trigge..." refers background in this paper
...Event-triggered control technique can preventmany unnecessary transmissions of the signals and guarantee desired levels of control performance (Deng, Er, Yang, & Wang, 2019; Heemels, Donkers, & Teel, 2012; Tabuada, 2007; Yu & Hao, 2017)....
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10 Dec 2013
TL;DR: The PETC strategies developed in this paper apply to both static state-feedback and dynamical output-based controllers, as well as to both centralized and decentralized (periodic) event-triggering conditions.
Abstract: Event-triggered control (ETC) is a control strategy that is especially suited for applications where communication resources are scarce. By updating and communicating sensor and actuator data only when needed for stability or performance purposes, ETC is capable of reducing the amount of communications, while still retaining a satisfactory closed-loop performance. In this paper, an ETC strategy is proposed by striking a balance between conventional periodic sampled-data control and ETC, leading to so-called periodic event-triggered control (PETC). In PETC, the event-triggering condition is verified periodically and at every sampling time it is decided whether or not to compute and to transmit new measurements and new control signals. The periodic character of the triggering conditions leads to various implementation benefits, including a minimum inter-event time of (at least) the sampling interval of the event-triggering condition. The PETC strategies developed in this paper apply to both static state-feedback and dynamical output-based controllers, as well as to both centralized and decentralized (periodic) event-triggering conditions. To analyze the stability and the L2-gain properties of the resulting PETC systems, three different approaches will be presented based on 1) impulsive systems, 2) piecewise linear systems, and 3) perturbed linear systems. Moreover, the advantages and disadvantages of each of the three approaches will be discussed and the developed theory will be illustrated using a numerical example.
1,011 citations
TL;DR: An upper bound of the difference between both loops is derived, which shows that the approximation of the continuous state-feedback loop by the event-based control loop can be made arbitrarily tight by appropriately choosing the threshold parameter of the event generator.
Abstract: This paper proposes a new method for event-based state-feedback control in which a control input generator mimics a continuous feedback between two consecutive event times. The performance of the event-based control system is evaluated by comparing this loop with the continuous state-feedback loop. An upper bound of the difference between both loops is derived, which shows that the approximation of the continuous state-feedback loop by the event-based control loop can be made arbitrarily tight by appropriately choosing the threshold parameter of the event generator.
994 citations
"Model-based dual-stage event-trigge..." refers background in this paper
...In Lunze and Lehmann (2010) and Lehmann and Lunze (2011), the event-triggered control of linear systemswith disturbancewas consideredwhere the controller was designed in a model-based manner and an estimator of the disturbance was introduced into the model dynamic....
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01 Jan 1999
TL;DR: A simple event-based PID controller is presented and it is shown that it is possible to obtain large reductions in CPU utilization with only minor control performance degradation.
Abstract: A simple event-based PID controller is presented. It is shown that it is possible to obtain large reductions in CPU utilization with only minor control performance degradation. Simulations on a double-tank process are presented.
865 citations
"Model-based dual-stage event-trigge..." refers background in this paper
...Moreover, event-triggered control has been proposed where the occurrence of an event closes the feedback loop Årzén (1999); Åström and Bernhardssn (1999)....
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TL;DR: Lyapunov's theorem on stability via linearization and LaSalle's invariance principle are generalized to hybrid automata and a class of hybrids whose solutions depend continuously on the initial state is characterized.
Abstract: Hybrid automata provide a language for modeling and analyzing digital and analogue computations in real-time systems. Hybrid automata are studied here from a dynamical systems perspective. Necessary and sufficient conditions for existence and uniqueness of solutions are derived and a class of hybrid automata whose solutions depend continuously on the initial state is characterized. The results on existence, uniqueness, and continuity serve as a starting point for stability analysis. Lyapunov's theorem on stability via linearization and LaSalle's invariance principle are generalized to hybrid automata.
850 citations