Stochastic Event-Based Control and Estimation

Digital controllers are traditionally implemented using periodic sampling, computation, and actuation events. As more control systems are implemented to share limited network and CPU bandwidth with other tasks, it is becoming increasingly attractive to use some form of event-based control instead, where precious events are used only when needed. Forms of event-based control have been used in practice for a very long time, but mostly in an ad-hoc way. Though optimal solutions to most event-based control problems are unknown, it should still be viable to compare performance between suggested approaches in a reasonable manner. This thesis investigates an event-based variation on the stochastic linear-quadratic (LQ) control problem, with a fixed cost per control event. The sporadic constraint of an enforced minimum inter-event time is introduced, yielding a mixed continuous-/discrete-time formulation. The quantitative trade-off between event rate and control performance is compared between periodic and sporadic control. Example problems for first-order plants are investigated, for a single control loop and for multiple loops closed over a shared medium. Path constraints are introduced to model and analyze higher-order event-based control systems. This component-based approach to stochastic hybrid systems allows to express continuous- and discrete-time dynamics, state and switching constraints, control laws, and stochastic disturbances in the same model. Sum-of-squares techniques are then used to find bounds on control objectives using convex semidefinite programming. The thesis also considers state estimation for discrete time linear stochastic systems from measurements with convex set uncertainty. The Bayesian observer is considered given log-concave process disturbances and measurement likelihoods. Strong log-concavity is introduced, and it is shown that the observer preserves log-concavity, and propagates strong log-concavity like inverse covariance in a Kalman filter. A recursive state estimator is developed for systems with both stochastic and set-bounded process and measurement noise terms. A time-varying linear filter gain is optimized using convex semidefinite programming and ellipsoidal over-approximation, given a relative weight on the two kinds of error

Event-based H∞ consensus control of multi-agent systems with relative output feedback: The finite-horizon case

In this technical note, the H∞ consensus control problem is investigated over a finite horizon for general discrete time-varying multi-agent systems subject to energy-bounded external disturbances. A decentralized estimation-based output feedback control protocol is put forward via the relative output measurements. A novel event-based mechanism is proposed for each intelligent agent to utilize the available information in order to decide when to broadcast messages and update control input. The aim of the problem addressed is to co-design the time-varying controller and estimator parameters such that the controlled multi-agent systems achieve consensus with a disturbance attenuation level γ over a finite horizon [0,T]. A constrained recursive Riccati difference equation approach is developed to derive the sufficient conditions under which the H∞ consensus performance is guaranteed in the framework of event-based scheme. Furthermore, the desired controller and estimator parameters can be iteratively computed by resorting to the Moore-Penrose pseudo inverse. Finally, the effectiveness of the developed event-based H∞ consensus control strategy is demonstrated in the numerical simulation

Event-Based Control and Estimation with Stochastic Disturbances

This thesis deals with event-based control and estimation strategies, motivated by certain bottlenecks in the control loop. Two kinds of implementation constraints are considered: closing one or several control loops over a data network, and sensors that report measurements only as intervals (e.g. with quantization). The proposed strategies depend critically on _events_, when a data packet is sent or when a change in the measurement signal is received. The value of events is that they communicate new information about stochastic process disturbances. A data network in the control loop imposes constraints on the event timing, modelled as a minimum time between packets. A thresholdbased control strategy is suggested and shown to be optimal for firstorder systems with impulse control. Different ways to find the optimal threshold are investigated for single and multiple control loops sharing one network. The major gain compared to linear time invariant (LTI) control is with a single loop a greatly reduced communication rate, which with multiple loops can be traded for a similarly reduced regulation error. With the bottleneck that sensors report only intervals, both the theoretical and practical control problems become more complex. We focus on the estimation problem, where the optimal solution is known but untractable. Two simplifications are explored to find a realistic state estimator: reformulation to a mixed stochastic/worst case scenario and joint maximum a posteriori estimation. The latter approach is simplified and evaluated experimentally on a moving cart with quantized position measurements controlled by a low-end microcontroller. The examples considered demonstrate that event-based control considerably outperforms LTI control, when the bottleneck addressed is a genuine performance constraint on the latter