In this paper we study an event based control algorithm for trajectory tracking in nonlinear systems. The desired trajectory is modelled as the solution of a reference system with an exogenous input and it is assumed that the desired trajectory and the exogenous input to the reference system are uniformly bounded. Given a continuous-time control law that guarantees global uniform asymptotic tracking of the desired trajectory, our algorithm provides an event based controller that not only guarantees uniform ultimate boundedness of the tracking error, but also ensures non-accumulation of inter-execution times. In the case that the derivative of the exogenous input to the reference system is also uniformly bounded, an arbitrarily small ultimate bound can be designed. If the exogenous input to the reference system is piecewise continuous and not differentiable everywhere then the achievable ultimate bound is constrained and the result is local, though with a known region of attraction. The main ideas in the paper are illustrated through simulations of trajectory tracking by a nonlinear system.

In this paper we propose a systematic methodology for designing implicitly verified event-triggered dynamic output feedback controllers for LTI systems that are observable and controllable. Event-triggering conditions that depend only on local information are proposed for sampled-data implementation of the observer and the controller in three different architectures. It is demonstrated that the triggering conditions provide a global lower bound on the inter-sample times and guarantee asymptotic stability of the closed loop system. The proposed design methodology is illustrated through simulation results.

This paper studies the multi-agent average consensus problem under the requirement of differential privacy of the agents' initial states against an adversary that has access to all the messages. We first establish that a differentially private consensus algorithm cannot guarantee convergence of the agents' states to the exact average in distribution, which in turn implies the same impossibility for other stronger notions of convergence. This result motivates our design of a novel differentially private Laplacian consensus algorithm in which agents linearly perturb their state-transition and message-generating functions with exponentially decaying Laplace noise. We prove that our algorithm converges almost surely to an unbiased estimate of the average of agents' initial states, compute the exponential mean-square rate of convergence, and formally characterize its differential privacy properties. We show that the optimal choice of our design parameters (with respect to the variance of the convergence point around the exact average) corresponds to a one-shot perturbation of initial states and compare our design with various counterparts from the literature. Simulations illustrate our results.

We study a class of distributed convex constrained optimization problems where a group of agents aim to minimize the sum of individual objective functions while each desires that any information about its objective function is kept private. We prove the impossibility of achieving differential privacy using strategies based on perturbing the inter-agent messages with noise when the underlying noise-free dynamics are asymptotically stable. This justifies our algorithmic solution based on the perturbation of individual functions with Laplace noise. To this end, we establish a general framework for differentially private handling of functional data. We further design postprocessing steps that ensure the perturbed functions regain the smoothness and convexity properties of the original functions while preserving the differentially private guarantees of the functional perturbation step. This methodology allows us to use any distributed coordination algorithm to solve the optimization problem on the noisy functions. Finally, we explicitly bound the magnitude of the expected distance between the perturbed and true optimizers which leads to an upper bound on the privacyaccuracy trade-off curve. Simulations illustrate our results.

Abstract-This paper addresses the problem of exponential practical stabilization of linear time-invariant systems with disturbances using event-triggered control and bounded communication bit rate. We consider both the case of instantaneous communication with finite precision data at each transmission and the case of non-instantaneous communication with bounded communication rate. Given a prescribed rate of convergence, the proposed event-triggered control implementations opportunistically determine the transmission instants and the finite precision data to be transmitted on each transmission. We show that our design exponentially practically stabilizes the origin while guaranteeing a uniform positive lower bound on the intertransmission and inter-reception times, ensuring that the number of bits transmitted on each transmission is upper bounded uniformly in time, and allowing for the possibility of transmitting fewer bits at any given time if more bits than prescribed were transmitted earlier. We also characterize the necessary and sufficient average data rate for exponential practical stabilization. Several simulations illustrate the results.

Abstract-This paper considers nonlinear systems with full state feedback, a central controller and distributed sensors not co-located with the central controller. We present a methodology for designing decentralized asynchronous event-triggers, which utilize only locally available information, for determining the time instants of transmission from the sensors to the central controller. The proposed design guarantees a positive lower bound for the inter-transmission times of each sensor, while ensuring asymptotic stability of the origin of the system with an arbitrary, but priorly fixed, compact region of attraction. In the special case of Linear Time Invariant (LTI) systems, global asymptotic stability is guaranteed and scale invariance of intertransmission times is preserved. A modified design method is also proposed for nonlinear systems, with the addition of eventtriggered communication from the controller to the sensors, that promises to significantly increase the average sensor intertransmission times compared to the case where the controller does not transmit data to the sensors. The proposed designs are illustrated through simulations of a linear and a nonlinear example.

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...

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