Rollout Event-Triggered Control: Beyond Periodic Control Performance

Abstract

Cyber-Physical Systems (CPSs) resulting from the interconnection of computational, communication, and control (cyber) devices with physical processes are wide spreading in our society. In several CPS applications it is crucial to minimize the communication burden, while still providing desirable closed-loop control properties. To this effect, a promising approach is to embrace the recently proposed event-triggered control paradigm, in which the transmission times are chosen based on well-defined events, using state information. However, few general eventtriggered control methods guarantee closed-loop improvements over traditional periodic transmission strategies. Here, we provide a new class of event-triggered controllers for linear systems which guarantee better quadratic performance than traditional periodic time-triggered control using the same average transmission rate. In particular, our main results explicitly quantify the obtained performance improvements for quadratic average cost problems. The proposed controllers are inspired by rollout ideas in the context of dynamic programming. Index Terms-Approximate dynamic programming, control over communications, event-triggered control, Markov processes, stochastic optimal control. I. INTRODUCTIONC YBER devices capable of sensing, processing, and communicating information of interest are wide spreading in our society, creating new opportunities to make our physical processes operate exceedingly better. In fact, the number of applications in which communication, computation and control elements (the cyber part) go hand in hand with motion, energy, climate, and human processes (the physical part) is steadily growing in intelligent transportation, smart buildings, energy networks, healthcare, and robotics (see, e.g., [2]-[6], respectively). To meet the challenges arising in many of these applications the traditional separation-of-concerns principle in designing control, communication, and computational algorithms must be abandoned in favor of an integrated approach. This can lead to dramatic communication and computation savings in control applications, which is crucial to prevent Manuscript

A down-sampled controller to reduce network usage with guaranteed closed-loop performance

“…Additionally, one is able to specify the slow rate according to the application and/or system characteristics. Numerical examples validate the down-sampled policy where we provide comparisons to the recent work of [20] and [21] for the deterministic case.…”

“…However, in all these works, no guarantees are given by design that the achieved trade-off between control performance and transmission rate is improved with respect to the periodic case. In [20], the authors proposed a roll-out event-triggered controller which guarantees better control performance versus transmission rate trade-off than periodic control and are able to quantify this gain. However, the method is computationally intensive and the computation of the best scheduling sequence must be computed in a receding-horizon manner.…”

Analysis, Design, and Optimization of Embedded Control Systems

“…The schedulability and response-time analysis in the presence of self-triggered controllers is still an open problem and the topic of Chapter 6. Existing approaches to the schedulability analysis in the presence of self-triggered controllers are either extremely pessimistic [AT09, SEP + 10, BMS13] or do not provide any hard guarantees [LCHZ07,VMB08,CH08,AH14]. In Chapter 6, we address this problem and propose an offline schedulability analysis technique in the presence of self-triggered control tasks that allows to leverage the potential advantages of self-triggered control compared to periodic control.…”

“…However, to provide schedulability guarantees, the authors considered the minimum inter-arrival time for all possible initial states, which is extremely pessimistic and defeats the purpose of the self-triggered control scheme. Antunes and Heemels [AH14] found the optimal sampling instants and control inputs in a given interval with respect to quadratic cost functions. However, they did not attempt to address the schedulability and response-time analysis problem.…”

Self-Triggered and Event-Triggered Set-Valued Observers

“…The strategy for an observer to self-trigger a sensor measurement based on its estimates can resort to an optimization over the update patterns such as in [5], where the disturbances and noise are assumed to be Gaussian. In [3] and [4], Kalman-like filters are proposed for state estimation, thus not providing a deterministic bound for the error.…”