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.

/pdf/event-triggered-real-time-scheduling-of-stabilizing-control-t1gebqsndp.pdf

Event-Triggered Real-Time Scheduling of Stabilizing Control Tasks

We introduce some analysis tools for switched and hybrid systems. We first present work on stability analysis. We introduce multiple Lyapunov functions as a tool for analyzing Lyapunov stability and use iterated function systems theory as a tool for Lagrange stability. We also discuss the case where the switched systems are indexed by an arbitrary compact set. Finally, we extend Bendixson's theorem to the case of Lipschitz continuous vector fields, allowing limit cycle analysis of a class of "continuous switched" systems.

Multiple Lyapunov functions and other analysis tools for switched and hybrid systems

Motivated by navigation and tracking applications within sensor networks, we consider the problem of performing Kalman filtering with intermittent observations. When data travel along unreliable communication channels in a large, wireless, multihop sensor network, the effect of communication delays and loss of information in the control loop cannot be neglected. We address this problem starting from the discrete Kalman filtering formulation, and modeling the arrival of the observation as a random process. We study the statistical convergence properties of the estimation error covariance, showing the existence of a critical value for the arrival rate of the observations, beyond which a transition to an unbounded state error covariance occurs. We also give upper and lower bounds on this expected state error covariance.

/pdf/kalman-filtering-with-intermittent-observations-4grpsuwr1c.pdf

Kalman filtering with intermittent observations

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.

/pdf/distributed-event-triggered-control-for-multi-agent-systems-4p46fy7wt3.pdf

Distributed Event-Triggered Control for Multi-Agent Systems

Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

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.

/pdf/event-triggering-in-distributed-networked-control-systems-3q6ke0ouvy.pdf

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 describes a method for constructing a Petri net feedback controller for a discrete event system modeled by a Petri net. The controller enforces a set of linear constraints on the plant and consists of places and arcs. It is computed using the concept of Petri net place invariants. The size of the controller is proportional to the number of constraints which must be satisfied. The method is very attractive computationally, and it makes possible the systematic design of Petri net controllers for complex industrial systems. >

/pdf/feedback-control-of-petri-nets-based-on-place-invariants-1ymbkp1mb8.pdf

Feedback control of Petri nets based on place invariants

In this paper, we combine inertial sensing and sensor network technology to create a pedestrian dead reckoning system. The core of the system is a lightweight sensor-and-wireless-embedded device called NavMote that is carried by a pedestrian. The NavMote gathers information about pedestrian motion from an integrated magnetic compass and accelerometers. When the NavMote comes within range of a sensor network (composed of NetMotes), it downloads the compressed data to the network. The network relays the data via a RelayMote to an information center where the data are processed into an estimate of the pedestrian trajectory based on a dead reckoning algorithm. System details including the NavMote hardware/software, sensor network middleware services, and the dead reckoning algorithm are provided. In particular, simple but effective step detection and step length estimation methods are implemented in order to reduce computation, memory, and communication requirements on the Motes. Static and dynamic calibrations of the compass data are crucial to compensate the heading errors. The dead reckoning performance is further enhanced by wireless telemetry and map matching. Extensive testing results show that satisfactory tracking performance with relatively long operational time is achieved. The paper also serves as a brief survey on pedestrian navigation systems, sensors, and techniques.

/pdf/design-of-a-wireless-assisted-pedestrian-dead-reckoning-16ri2z06mz.pdf

Design of a wireless assisted pedestrian dead reckoning system - the NavMote experience

In this paper, the supervisory control of hybrid systems is introduced and discussed at length. Such control systems typically arise in the computer control of continuous processes, for example, in manufacturing and chemical processes, in transportation systems, and in communication networks. A functional architecture of hybrid control systems consisting of a continuous plant, a discrete-event controller, and an interface is used to introduce and describe analysis and synthesis concepts and approaches. Our approach highlights the interaction between the continuous and discrete dynamics, which is the cornerstone of any hybrid system study. Discrete abstractions are used to approximate the continuous plant. Properties of the discrete abstractions to be appropriate representations of the continuous plant are presented, and important concepts such as determinism and controllability are discussed. Supervisory control design methodologies are presented to satisfy control specifications described by formal languages. Several examples are used throughout the paper to illustrate our approach.

/pdf/supervisory-control-of-hybrid-systems-zx2n9faknm.pdf

Michael D. Lemmon

Papers

Event-Triggering in Distributed Networked Control Systems

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

Feedback control of Petri nets based on place invariants

Design of a wireless assisted pedestrian dead reckoning system - the NavMote experience

Supervisory control of hybrid systems