Networked Control Systems (NCSs) are spatially distributed systems for which the communication between sensors, actuators, and controllers is supported by a shared communication network. In this paper we review several recent results on estimation, analysis, and controller synthesis for NCSs. The results surveyed address channel limitations in terms of packet-rates, sampling, network delay and packet dropouts. The results are presented in a tutorial fashion, comparing alternative methodologies. I.

The interrelationship between control and communication theory is becoming of fundamental importance in many distributed control systems. Particular examples are systems comprised of multiple agents. When it comes to coordinately control a group of autonomous mobile agents in order to achieve a common task, communication constraints impose limits on the achievable control performance. In this paper we consider a widely studied problem in the robotics and control communities, called consensus or state agreement problem. The aim of the paper is to characterize the relationship between the amount of information exchanged by the agents and the rate of convergence to the agreement. Time-invariant communication networks that exhibit particular symmetries are shown to yield slow convergence if the amount of information exchanged does not scale with the number of agents. On the other hand, we show that, randomly time-varying communication networks allow very fast convergence rates. The last part of the paper is devoted to the study of time-invariant communication networks with logarithmic quantized data exchange among the agents. It is shown that, by adding quantized data links to the network, the control performance significantly improves with little growth of the required communication effort.

The interrelationship between control and communication theory is becoming of fundamental importance in many distributed control systems, such as the coordination of a team of autonomous agents. In such a problem, communication constraints impose limits on the achievable control performance. We consider as instance of coordination the consensus problem. The aim of the paper is to characterize the relationship between the amount of information exchanged by the agents and the rate of convergence to the consensus. We show that time-invariant communication networks with circulant symmetries yield slow convergence if the amount of information exchanged by the agents does not scale well with their number. On the other hand, we show that randomly time-varying communication networks allow very fast convergence rates. We also show that, by adding logarithmic quantized data links to time-invariant networks with symmetries, control performance significantly improves with little growth of the required communication effort.

Abstract — The analysis and design of practical control systems requires that stochastic models be employed. Analysis and design tools have been developed, for example, for Markovian jump linear continuous and discrete-time systems, piecewisedeterministic processes (PDP’s), and general stochastic hybrid systems (GSHS’s). These model classes have been used in many applications, including fault tolerant control and networked control systems. This paper presents initial results on the analysis of a sampled-data PDP representation of a nonlinear sampled-data system with a jump linear controller. In particular, it is shown that the state of the sampled-data PDP satisfies the strong Markov property. In addition, a relation between the invariant measures of a sampled-data system driven by a stochastic process and its associated discrete-time representation are presented. As an application, when the plant is linear with no external input, a sufficient testable condition for the convergence in distribution to the invariant delta Dirac measure is given. I.

Abstract — Safety-critical control systems use fault tolerant interconnections of components to minimize the effect of randomly triggered faults. The system availability process indicates whether or not the interconnection is operating correctly at each time instant. It is a 2-state process that results from the transformation of the stochastic processes characterizing the availability processes of the interconnected components. To analyze closed-loop systems controlled by these fault tolerant interconnected components, it is important to determine the characteristics of the system availability process. When the availability processes of the interconnected components are independent homogeneous Markov chains, the statistical nature of the system availability process is characterized. In particular, it is shown that the system availability process is not necessarily Markov, but has a well-defined one-step transition probability matrix that approaches a constant stochastic matrix at steady-state. Since it is simpler to analyze switched closed-loop systems when the switching process is Markov, conditions for the system availability process to be a Markov chain for all initial distributions are determined. A sufficient stability condition is given when the system availability process is a non-homogeneous Markov chain for a class of initial distributions. I.

Keywords — Sampled-data systems, stochastic jump-linear hybrid systems, stability. Abstract — In this paper an equivalence between the stochastic stability of a sampled-data system and its associated discrete-time representation is established. The sampled-data system consists of a deterministic, linear, time-invariant, continuous-time plant and a stochastic, linear, time-invariant, discrete-time, jump linear controller. The jump linear controller models computer systems and communication networks that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the

This paper considers the robustness of stochastic stability of Markovian jump linear systems in continuous- and discrete-time with respect to their transition rates and probabilities respectively. The continuous-time (discrete-time) system is described via a continuous-valued state vector and a discrete-valued mode which varies according to a Markov process (chain). By using stochastic Lyapunov function approach and Kronecker product transformation techniques, sufficient conditions are obtained for the robust stochastic stability of the underlying systems, which are in terms of upper bounds on the perturbed transition rates and probabilities. Analytical expressions are derived for scalar systems, which are straightforward to use. Numerical examples are presented to show the potential of the proposed techniques. 1