Journal ArticleDOI

# Event-Triggered Composite Control of a Two Time Scale System

01 Apr 2018--Vol. 65, Iss: 4, pp 471-475

TL;DR: The theory of singular perturbation is used to decouple the system into slow and fast subsystems, and stability of the system is established and the proposed control strategy guarantees convergence of system states to an adjustable region around origin excluding the Zeno behavior.

AbstractThis brief proposes an event-triggered composite control of a two time scale system. A periodic sampling requirement is relaxed and both slow and fast states of the system decide independently when transmitting their current measurements based on a time-dependent triggering rule. The distinct feature of this scheme is that it does not require synchronized measurement updates of its slow and fast dynamics. Further, the theory of singular perturbation is used to decouple the system into slow and fast subsystems, and stability of the system is established. The proposed control strategy guarantees convergence of system states to an adjustable region around origin excluding the Zeno behavior. Simulation results manifest the effectiveness of the proposed approach.

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### Cites background from "Event-Triggered Composite Control o..."

• ...Future interesting topics include exploiting event-triggered or fault-tolerant methods [28], [29] to regulate the transient performance of controlled flexible systems....

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TL;DR: This paper addresses the state estimation problem for a class of discrete-time singularly perturbed systems with distributed time-delays with dynamic event-triggered scheme and proposes a design algorithm for the desired state estimator ensuring that the error dynamics is exponentially mean-square ultimately bounded.
Abstract: This paper is concerned with the state estimation problem for a class of discrete-time singularly perturbed systems with distributed time-delays. During the data transmission through a network channel of limited bandwidth, for the sake of collision avoidance and energy saving, a dynamic event-triggered scheme is employed to schedule the data communication from the sensors to the designed estimator. First, for a given singular perturbation parameter (SPP), by constructing a novel Lyapunov–Krasovskii SPP-dependent functional, sufficient conditions are obtained to guarantee the exponentially mean-square ultimate boundedness of the error dynamics of the state estimation. Furthermore, in the case that the SPP does not exceed a predefined upper bound, a design algorithm is developed for the desired state estimator ensuring that the error dynamics is exponentially mean-square ultimately bounded. In this case, by solving certain matrix inequalities, the estimator gain is characterized without needing to know the exact SPP (as long as it stays below the given upper bound). Moreover, the ultimate bound of the error dynamics is estimated. Finally, simulation results are given to confirm the validity and advantages of the proposed design scheme of the state estimator.

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### Cites methods from "Event-Triggered Composite Control o..."

• ...In [24], an event-triggered synchronization problem has been discussed for nonlinear singularly perturbed complex networks and, in [3], a controller has been designed under the ETS by using the diagonal transformation for a standard networked SPS....

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TL;DR: A novel Lyapunov–Krasovskii functional dependent on the singular perturbation parameter (SPP) is constructed, and an output-feedback controller design scheme is developed to ensure that, for any SPP not exceeding a prescribed upper bound, the closed-loop system is asymptotically stable with a guaranteed performance index.
Abstract: In this article, the $H_{\infty }$ control problem is investigated for a class of discrete-time singularly perturbed systems (DTSPSs) with time-delays and sensor saturations. In order to save the network bandwidth with satisfactory communication reliability during the signal transmissions, a dynamic event-triggered mechanism (DETM) is put forward to regulate the data-packet transmissions from the saturated sensors to the proposed controller. By constructing a novel Lyapunov–Krasovskii functional dependent on the singular perturbation parameter (SPP), the dynamics of the DTSPSs under the DETM are rigorously analyzed, and an output-feedback controller design scheme is then developed to ensure that, for any SPP not exceeding a prescribed upper bound, the closed-loop system is asymptotically stable with a guaranteed $H_{\infty }$ performance index. By resorting to the convex programming techniques, the desired controller gain is parameterized in light of the feasible solutions to a set of matrix inequalities. Finally, the effectiveness and merits of the proposed algorithm are demonstrated by a simulation example.

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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.

2,850 citations

### "Event-Triggered Composite Control o..." refers background or methods in this paper

• ...Simulation were also performed to compare the proposed approach to ETC using uniform sampling of slow and fast states as in [3] with ETM in (15)....

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• ...In place of using full state information to determine the triggering instances (such as in [3]–[5] and [12] etc....

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• ...See [3]–[9] for some of the prevailing literature on ETC....

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Journal ArticleDOI
TL;DR: A novel control strategy for multi-agent coordination with event-based broadcasting is presented, in which each agent decides itself when to transmit its current state to its neighbors and the local control laws are based on these sampled state measurements.
Abstract: A novel control strategy for multi-agent coordination with event-based broadcasting is presented. In particular, each agent decides itself when to transmit its current state to its neighbors and the local control laws are based on these sampled state measurements. Three scenarios are analyzed: Networks of single-integrator agents with and without communication delays, and networks of double-integrator agents. The novel event-based scheduling strategy bounds each agent's measurement error by a time-dependent threshold. For each scenario it is shown that the proposed control strategy guarantees either asymptotic convergence to average consensus or convergence to a ball centered at the average consensus. Moreover, it is shown that the inter-event intervals are lower-bounded by a positive constant. Numerical simulations show the effectiveness of the novel event-based control strategy and how it compares to time-scheduled control.

894 citations

### "Event-Triggered Composite Control o..." refers methods in this paper

• ...We use triggering rule proposed in [14] and [15] which has exponential convergence property and an offset....

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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.

885 citations

### "Event-Triggered Composite Control o..." refers background in this paper

• ...In place of using full state information to determine the triggering instances (such as in [3]–[5] and [12] etc....

[...]

• ...Remark 1: If (c1 = 0) ETM has constant threshold, which has been extensively studied in [4] and [5]....

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TL;DR: The main methodologies suggested in the literature to cope with typical network-induced constraints, namely time delays, packet losses and disorder, time-varying transmission intervals, competition of multiple nodes accessing networks, and data quantization are surveyed.
Abstract: Networked control systems (NCSs) have, in recent years, brought many innovative impacts to control systems. However, great challenges are also met due to the network-induced imperfections. Such network-induced imperfections are handled as various constraints, which should appropriately be considered in the analysis and design of NCSs. In this paper, the main methodologies suggested in the literature to cope with typical network-induced constraints, namely time delays, packet losses and disorder, time-varying transmission intervals, competition of multiple nodes accessing networks, and data quantization are surveyed; the constraints suggested in the literature on the first two types of constraints are updated in different categorizing ways; and those on the latter three types of constraints are extended.

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TL;DR: This paper considers an event-driven control scheme for perturbed linear systems that triggers the control update only when the tracking or stabilization error is large, so that the average processor and/or communication load can be reduced significantly.
Abstract: Most research in control engineering considers periodic or time-triggered control systems with equidistant sample intervals. However, practical cases abound in which it is of interest to consider event-driven control in which the sampling is event-triggered. Although there are various benefits of using event-driven control like reducing resource utilization (e.g., processor and communication load), their application in practice is hampered by the lack of a system theory for event-driven control systems. To provide a first step in developing an event-driven system theory, this paper considers an event-driven control scheme for perturbed linear systems. The event-driven control scheme triggers the control update only when the (tracking or stabilization) error is large. In this manner, the average processor and/or communication load can be reduced significantly. The analysis in this paper is aimed at the control performance in terms of practical stability (ultimate boundedness). Several examples illustrate t...

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### "Event-Triggered Composite Control o..." refers background in this paper

• ...Remark 1: If (c1 = 0) ETM has constant threshold, which has been extensively studied in [4] and [5]....

[...]