Toivo Henningsson

Brief paper: Sporadic event-based control of first-order linear stochastic systems

The standard approach in computer-controlled systems is to sample and control periodically. In certain applications, such as networked control systems or energy-constrained systems, it could be advantageous to instead use event-based control schemes. Aperiodic event-based control of first-order stochastic systems has been investigated in previous work. In any real implementation, however, it is necessary to have a well-defined minimum inter-event time. In this paper, we explore two such sporadic control schemes for first-order linear stochastic systems and compare the achievable performance to both periodic and aperiodic control. The results show that sporadic control can give better performance than periodic control in terms of both reduced process state variance and reduced control action frequency.

Scheduling of event-triggered controllers on a shared network

We consider a system where a number of independent, time-triggered or event-triggered control loops are closed over a shared communication network. Each plant is described by a first-order linear stochastic system. In the event-triggered case, a sensor at each plant frequently samples the output but attempts to communicate only when the magnitude of the output is above a threshold. Once access to the network has been gained, the network is busy for T seconds (corresponding to the communication delay from sensor to actuator), after which the control action is applied to the plant. Using numerical methods, we compute the minimum-variance control performance under various common MAC-protocols, including TDMA, FDMA, and CSMA (with random, dynamic-priority, or static-priority access). The results show that event-triggered control under CSMA gives the best performance throughout.

Sporadic control of first-order linear stochastic systems

The standard approach in feedback control systems is to sample and control periodically. For some applications, such as networked control systems or severely energy-constrained systems, it could be advantageous to instead use event-based control schemes. Aperiodic control (that is, event-based control with no specified minimum inter-event time) of first-order stochastic systems has been investigated in previous work. In any real implementation, however, it is necessary to have a well-defined minimum inter-event time. In this paper, we explore two such sporadic control schemes for first-order linear stochastic systems and compare the achievable performance to both periodic and aperiodic control. The results indicate that sporadic control can give better performance than periodic control in terms of reduced process state variance and control action frequency.

A simple model for the interference between event-based control loops using a shared medium

Traditionally, control loops are closed using periodic sensing and actuation. When communication resources are scarce, much may be gained by instead transmitting only when something important has happened in the loop. However, there are no known closed form solutions to this kind of control problem. This paper presents a simple model of the interference between event-based control loops caused by sharing a common medium, based on approximating the behavior of all loops except one foreground loop. The stationary state distribution can be computed at low computational cost using mostly standard linear time-invariant system theory (applied in the spatial dimension). Control laws are optimized to minimize state variance using the limited communication resources. Comparison to Monte Carlo simulations of a full model shows the simple model to be remarkably accurate. The model is applied to investigate how the performance of N control loops sharing a common Carrier Sense Multiple Access channel approaches the ideal case of aperiodic control as the number of loops grows.

Recursive state estimation for linear systems with mixed stochastic and set-bounded disturbances

Recursive state estimation is considered for discrete time linear systems with mixed process and measurement disturbances that have stochastic and (convex) set-bounded terms. The state estimate is formed as a linear combination of initial guess and measurements, giving an estimation error of the same mixed type (and causing minimal interference between the two kinds of error). An ellipsoidal over-approximation to the set-bounded estimation error term allows to formulate a linear matrix inequality (LMI) for optimization of the filter gain, considering both parts of the estimation error in the objective. With purely stochastic disturbances, the standard Kalman filter is recovered. The state estimator is shown to work well for an event based estimation example, where measurements are very coarsely quantized.

Scalable distributed Kalman Filtering for mass-spring systems

This paper considers Kalman filtering for mass-spring systems. The aim is a scalable distributed implementation where nodes communicate in a sparse pattern and the state estimate for each node is available locally and usable for control. The focus is on translation invariant systems, to make use of the powerful results available based on Fourier transform methods. In this case it is known that Kalman filters will have a coupling that asymptotically falls off exponentially with distance. Examples are shown where the Kalman filter gains can be truncated very narrowly with small performance loss even though the coupling falls off more slowly. A step towards spatially varying systems is taken in analyzing a system with periodically placed sensors, and it is shown that the original design is insensitive to this spatial variation.