We study event-triggered control for stabilization of unstable linear plants over rate-limited communication channels subject to unknown, bounded delay. On one hand, the timing of event triggering carries implicit information about the state of the plant. On the other hand, the delay in the communication channel causes information loss, as it makes the state information available at the controller out of date. Combining these two effects, we show a phase transition behavior in the transmission rate required for stabilization using a given event-triggering strategy. For small values of the delay, the timing information carried by the triggering events is substantial, and the system can be stabilized with any positive rate. When the delay exceeds a critical threshold, the timing information alone is not enough to achieve stabilization, and the required rate grows. When the the delay equals the inverse of the entropy rate of the plant, the implicit information carried by the triggering events perfectly compensates the loss of information due to the communication delay, and we recover the rate requirement prescribed by the data-rate theorem. We also provide an explicit construction yielding a sufficient rate for stabilization, as well as results for vector systems. Our results do not rely on any a priori probabilistic model for the delay or the initial conditions. Index TermsData-rate theorem, event-triggered control, control under communication constraints, quantized control I. INTRODUCTIONCyber-physical systems (CPS) are engineering systems that integrate computing, communication, and control. They arise in a wide range of areas such as robotics, energy, civil infrastructure, manufacturing, and transportation [3], [4]. Due to the need for tight integration of different components, requirements and time scales, the modeling, analysis, and design of CPS present new challenges. One key aspect is the presence of finite-rate, digital communication channels in the feedback loop. Data-rate theorems quantify the effect that communication has on stabilization by stating that the communication rate available in the feedback loop should be at least as large as the intrinsic entropy rate of the system (corresponding to the sum of the logarithms of the unstable modes). In this way, the controller can compensate for the expansion of the state occurring during the communication process. Early formulations of data-rate theorems appeared in [5]-[7], followed by the key contributions in [8], [9]. More recent extensions include time-varying rate, Markovian, erasure, additive white and colored Gaussian, and multiplicative noise feedback communication channels [10]-[16], formulations for nonlinear systems [17]-[19], for optimal control [20]-[22], for systems with random parameters [23]-[26], and for switching systems [27]-[29]. Connections with information theory are highlighted in [19], [30]-[33]. Extended surveys of the literature appear in [34], [35] and in the book [36].Another key aspect of CPS to which we pay special attention he...

Robots operating in real world settings must navigate and maintain safety while interacting with many heterogeneous agents and obstacles. Multi-Agent Control Barrier Functions (CBF) have emerged as a computationally efficient tool to guarantee safety in multi-agent environments, but they assume perfect knowledge of both the robot dynamics and other agents' dynamics. While knowledge of the robot's dynamics might be reasonably well known, the heterogeneity of agents in real-world environments means there will always be considerable uncertainty in our prediction of other agents' dynamics. This work aims to learn high-confidence bounds for these dynamic uncertainties using Matrix-Variate Gaussian Process models, and incorporates them into a robust multi-agent CBF framework. We transform the resulting min-max robust CBF into a quadratic program, which can be efficiently solved in real time. We verify via simulation results that the nominal multi-agent CBF is often violated during agent interactions, whereas our robust formulation maintains safety with a much higher probability and adapts to learned uncertainties.

We present an event-triggered control strategy for stabilizing a scalar, continuous-time, time-invariant, linear system over a digital communication channel having bounded delay, and in the presence of bounded system disturbance. We propose an encoding-decoding scheme, and determine lower bounds on the packet size and on the information transmission rate which are sufficient for stabilization. We show that for small values of the delay, the timing information implicit in the triggering events is enough to stabilize the system with any positive rate. In contrast, when the delay increases beyond a critical threshold, the timing information alone is not enough to stabilize the system and the transmission rate begins to increase. Finally, large values of the delay require transmission rates higher than what prescribed by the classic data-rate theorem. The results are numerically validated using a linearized model of an inverted pendulum.Index Terms-Control under communication constraints, event-triggered control, quantized control I. INTRODUCTION Networked control systems (NCS) [1], where the feedback loop is closed over a communication channel, are a fundamental component of cyber-physical systems (CPS) [2], [3]. In this context, data-rate theorems state that the minimum communication rate to achieve stabilization is equal to the entropy rate of the system, expressed by the sum of the logarithms of the unstable modes. Early examples of datarate theorems appeared in [4], [5]. Key later contributions appeared in [6] and [7]. These works consider a "bit-pipe" communication channel, capable of noiseless transmission of a finite number of bits per unit time evolution of the system. Extensions to noisy communication channels are considered in [8]-[12]. Stabilization over time-varying bit-pipe channels, including the erasure channel as a special case, are studied in [13], [14]. Additional formulations include stabilization of systems with random open loop gains over bit-pipe channels [15], stabilization of switched linear systems [16], systems with uncertain parameters [15], [17], multiplicative noise [18], [19], optimal control [20]-[23], and stabilization using event-triggered strategies [24]-[29].This paper focuses on the case of stabilization using eventtriggered communication strategies. In this context, a key observation made in [30] is that if there is no delay in the communication process, there are no system disturbances, and the controller has knowledge of the triggering strategy, then it is possible to stabilize the system with any positive

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We introduce the problem of learning-based attacks in a simple abstraction of cyber-physical systems-the case of a discrete-time, linear, time-invariant plant that may be subject to an attack that overrides the sensor readings and the controller actions. The attacker attempts to learn the dynamics of the plant and subsequently overrides the controller's actuation signal, to destroy the plant without being detected. The attacker can feed fictitious sensor readings to the controller using its estimate of the plant dynamics and mimic the legitimate plant operation. The controller, on the other hand, is constantly on the lookout for an attack; once the controller detects an attack, it immediately shuts the plant off. In the case of scalar plants, we derive an upper bound on the attacker's deception probability for any measurable control policy when the attacker uses an arbitrary learning algorithm to estimate the system dynamics. We then derive lower bounds for the attacker's deception probability for both scalar and vector plants by assuming an authentication test that inspects the empirical variance of the system disturbance. We also show how the controller can improve the security of the system by superimposing a carefully crafted privacy-enhancing signal on top of the "nominal control policy." Finally, for nonlinear scalar dynamics that belong to the Reproducing Kernel Hilbert Space (RKHS), we investigate the performance of attacks based on nonlinear Gaussian-processes (GP) learning algorithms.

Time-triggered and event-triggered control strategies for stabilization of an unstable plant over a rate-limited communication channel subject to unknown, bounded delay are studied and compared. Event triggering carries implicit information, revealing the state of the plant. However, the delay in the communication channel causes information loss, as it makes the state information out of date. There is a critical delay value, when the loss of information due to the communication delay perfectly compensates the implicit information carried by the triggering events. This occurs when the maximum delay equals the inverse of the entropy rate of the plant. In this context, extensions of our previous results for event triggering strategies are presented for vector systems and are compared with the data-rate theorem for time-triggered control, that is extended here to a setting with unknown delay. I. INTRODUCTIONInternet of things establishes a foundation for emerging of engineering systems that integrate computing, communication, and control, these systems are know as cyber-physical systems (CPS) [1], [2]. One key aspect of CPS is the presence of finite-rate, digital communication channels in the feedback loop. To quantify their effect on the ability to stabilize the system, data-rate theorems have been developed [3], [4]. They essentially state that, in order to achieve stabilization, the communication rate available in the feedback loop should be at least as large as the entropy rate of the system, corresponding to the sum of the logarithms of the unstable modes. In this way, the controller can compensate for the expansion of the state occurring during communication More recent formulations of data-rate theorems include stochastic, time-varying, Markovian, erasure, additive white and colored Gaussian, and multiplicative noise feedback communication channels [5]-[10], formulations for nonlinear sytems [11]-[13], and for systems with uncertain and variable parameters [14]-[17]. Connections with information theory are highlighted in [13], [18]-[21]. Extended surveys of the literature appear in [22] and [23].Another important aspect of CPS is the need to use distributed resources efficiently. In this context, event-triggering control techniques [24], [25] have emerged. These are based on the idea of sending information in an opportunistic manner between the controller and the plant. In this way, communication occurs only when needed, and the primary focus is on minimizing the number of transmissions while guaranteeing the control objectives. Some recent results on event-triggered implementations in the presence of data rate

We consider the problem of stabilizing an undisturbed, scalar, linear system over a "timing" channel, namely a channel where information is communicated through the timestamps of the transmitted symbols. Each symbol transmitted from a sensor to a controller in a closed-loop system is received subject to some to random delay. The sensor can encode messages in the waiting times between successive transmissions and the controller must decode them from the inter-reception times of successive symbols. This set-up is analogous to a telephone system where a transmitter signals a phone call to a receiver through a "ring" and, after the random delay required to establish the connection; the receiver is aware of the "ring" being received. Since there is no data payload exchange between the sensor and the controller, this set-up provides an abstraction for performing event-triggering control with zero-payload rate. We show the following requirement for stabilization: for the state of the system to converge to zero in probability, the timing capacity of the channel should be at least as large as the entropy rate of the system. Conversely, in the case the symbol delays are exponentially distributed, we show a tight sufficient condition using a coding strategy that refines the estimate of the decoded message every time a new symbol is received. Our results generalize previous zero-payload event-triggering control strategies, revealing a fundamental limit in using timing information for stabilization, independent of any transmission strategy.