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.

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Event-Triggered Real-Time Scheduling of Stabilizing Control Tasks

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.

Coverage control for mobile sensing networks

Event-driven strategies for multi-agent systems are motivated by the future use of embedded microprocessors with limited resources that will gather information and actuate the individual agent controller updates. The controller updates considered here are event-driven, depending on the ratio of a certain measurement error with respect to the norm of a function of the state, and are applied to a first order agreement problem. A centralized formulation is considered first and then its distributed counterpart, in which agents require knowledge only of their neighbors' states for the controller implementation. The results are then extended to a self-triggered setup, where each agent computes its next update time at the previous one, without having to keep track of the state error that triggers the actuation between two consecutive update instants. The results are illustrated through simulation examples.

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Distributed Event-Triggered Control for Multi-Agent Systems

Recent developments in computer and communication technologies have led to a new type of large-scale resource-constrained wireless embedded control systems. It is desirable in these systems to limit the sensor and control computation and/or communication to instances when the system needs attention. However, classical sampled-data control is based on performing sensing and actuation periodically rather than when the system needs attention. This paper provides an introduction to event- and self-triggered control systems where sensing and actuation is performed when needed. Event-triggered control is reactive and generates sensor sampling and control actuation when, for instance, the plant state deviates more than a certain threshold from a desired value. Self-triggered control, on the other hand, is proactive and computes the next sampling or actuation instance ahead of time. The basics of these control strategies are introduced together with a discussion on the differences between state feedback and output feedback for event-triggered control. It is also shown how event- and self-triggered control can be implemented using existing wireless communication technology. Some applications to wireless control in process industry are discussed as well.

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An introduction to event-triggered and self-triggered control

This paper examines event-triggered data transmission in distributed networked control systems with packet loss and transmission delays. We propose a distributed event-triggering scheme, where a subsystem broadcasts its state information to its neighbors only when the subsystem's local state error exceeds a specified threshold. In this scheme, a subsystem is able to make broadcast decisions using its locally sampled data. It can also locally predict the maximal allowable number of successive data dropouts (MANSD) and the state-based deadlines for transmission delays. Moreover, the designer's selection of the local event for a subsystem only requires information on that individual subsystem. Our analysis applies to both linear and nonlinear subsystems. Designing local events for a nonlinear subsystem requires us to find a controller that ensures that subsystem to be input-to-state stable. For linear subsystems, the design problem becomes a linear matrix inequality feasibility problem. With the assumption that the number of each subsystem's successive data dropouts is less than its MANSD, we show that if the transmission delays are zero, the resulting system is finite-gain Lp stable. If the delays are bounded by given deadlines, the system is asymptotically stable. We also show that those state-based deadlines for transmission delays are always greater than a positive constant.

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Event-Triggering in Distributed Networked Control Systems

This paper examines a class of real-time control systems in which each control task triggers its next release based on the value of the last sampled state. Prior work used simulations to demonstrate that self-triggered control systems can be remarkably robust to task delay. This paper derives bounds on a task's sampling period and deadline to quantify how robust the control system's performance will be to variations in these parameters. In particular we establish inequality constraints on a control task's period and deadline whose satisfaction ensures that the closed-loop system's induced L 2 gain lies below a specified performance threshold. The results apply to linear time-invariant systems driven by external disturbances whose magnitude is bounded by a linear function of the system state's norm. The plant is regulated by a full-information H infin controller. These results can serve as the basis for the design of soft real-time systems that guarantee closed-loop control system performance at levels traditionally seen in hard real-time systems.

Self-Triggered Feedback Control Systems With Finite-Gain ${\cal L}_{2}$ Stability

This paper studies the event design in event-triggered feedback systems with asymptotic stability. A new event-triggering scheme is presented that may postpone the occurrence of events over previously proposed methods. Our approach pertains to nonlinear state-feedback systems. The resulting event-triggered feedback systems are guaranteed to be asymptotically stable, provided that the continuous systems are stabilizable. We also show that the task periods and deadlines generated by our scheme are bounded strictly away from zero if the continuous systems are input-to-state stable with respect to measurement errors. Simulation results indicate that our event-triggered scheme has a much larger average period compared with the prior work. Moreover, our scheme also appears to be robust to task delays.

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Event design in event-triggered feedback control systems

Technical communique: On event design in event-triggered feedback systems

This note extends the prior work in L2 stability of self-triggered feedback systems, where the next task release time and finishing time are predicted based on the sampled states. A self-triggering scheme is proposed, which relaxes the assumption in the prior work that the magnitude of the process noise is bounded by a linear function of the norm of the system state. We show that the sample periods generated by this scheme are always greater than a positive constant. We also provide state-based deadlines for delays and propose a way that may enlarge those deadlines without breaking L2 stability.

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Xiaofeng Wang

Papers

Event-Triggering in Distributed Networked Control Systems

Self-Triggered Feedback Control Systems With Finite-Gain ${\cal L}_{2}$ Stability

Event design in event-triggered feedback control systems

Technical communique: On event design in event-triggered feedback systems

Self-Triggering Under State-Independent Disturbances