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This work focuses on optimal pollution controls. The main effort is devoted to obtaining approximation methods for optimal pollution control. To take into consideration of random environment and other random factors, the control system is formulated as a controlled switching diffusion. Markov chain approximation techniques are used to design the computational schemes. Convergence of the algorithms are obtained. To demonstrate, numerical experimental results are presented. A particular feature is that computation using real data sets is provided. [ABSTRACT FROM AUTHOR]

Connected and automated vehicles mandate integrated design of communications and control to achieve coordination of highway vehicles. Random features of wireless communications introduce new types of uncertainties into networked systems and impact control performance significantly. Due to typical packet loss, erasure channels create random link interruption and switching in network topologies. This paper models such switching network topologies by Markov chains and derives their probability transition matrices from stochastic characterizations of the channels. Impact of communication erasure channels on vehicle platoon formation and robustness under a weighted and constrained consensus framework is analyzed. By comparing convergence properties of networked control algorithms under different communication channel features, we characterize some intrinsic relationships between packet delivery ratio and convergence rate. Simulation case studies are performed to verify the theoretical findings. [ABSTRACT FROM PUBLISHER]

This paper investigates controllability for linear time-invariant systems under irregular and random sampling, and develops adaptive control algorithms with respect to sampling intervals. Using block erasure channels as the main motivating communication platform, it first establishes a sufficient condition on sampling density that ensures controllability of sampled systems, which is necessary for feedback design and adaptation. Then, it continues with causal adaptive feedback algorithms to accommodate time-varying sampling intervals. Implementation of such algorithms encounters technical challenges because future sampling intervals are uncertain or random. Under deterministic slowly-varying and stochastic infrequent Markovian jumping sampling intervals, overall system stability is established. Simulation results are used to illustrate the algorithms and their effectiveness. [ABSTRACT FROM AUTHOR]

This work is devoted to analyzing adaptive filtering algorithms with the use of sign-regressor for randomly time-varying parameters (a discrete-time Markov chain). In accordance with different adaption and transition rates, we analyze the corresponding asymptotic properties of the algorithms. When the adaptation rate is in line with the transition rate, we obtain a limit of a Markov switched differential equation. When the Markov chain is slowly changing the parameter process is almost a constant, and we derive a limit differential equation. When the Markov chain is fast varying, the limit system is again a differential equation that is an average with respect to the stationary distribution of the Markov chain. In addition to the limit dynamic systems, we obtain asymptotic properties of centered and scaled tracking errors. We obtain mean square errors to illustrate the dependence on the stepsize as well as on the transition rate. The limit distributions in terms of scaled errors are studied by examining certain centered and scaled error sequences. [ABSTRACT FROM AUTHOR]

Abstract: This work is concerned with tracking and system identification for time-varying parameters. The parameters are Markov chains and the observations are binary valued with noise corruption. To overcome the difficulties due to the limited measurement information, Wonham-type filters are developed first. Then, based on the filters, two popular estimators, namely, mean squares estimator (MSQ) and maximum posterior (MAP) estimator are constructed. For the mean squares estimator, we derive asymptotic normality in the sense of weak convergence and in the sense of strong approximation. The asymptotic normality is then used to derive error bounds. When the Markov chain is infrequently switching, we derive error bounds for MAP estimators. When the Markovian parameters are fast varying, we show that the averaged behavior of the parameter process can be derived from the stationary measure of the Markov chain and that can be estimated using empirical measures. Upper and lower error bounds on estimation errors are also established. [Copyright &y& Elsevier]

Abstract: Facing the pressing needs of many applications in network and control systems, this paper introduces a class of nonlinear systems with random time delays and derives conditions on moment exponential stability of the underlying systems. The system model is versatile and can accommodate a wide variety of situations. The stability analysis to date in the literature is mostly delay independent. To highlight the role of random delay for stability, this paper focuses on delay-dependent stability. Dependence of stability on random time delays introduces technical difficulties beyond the existing literature. We model the random time delays by a continuous-time Markov chain involving two-time scales defined by a small parameter . leading to a two-time scale framework. The random delays change their values with a fast varying mode and a slowly evolving effect. Under broad conditions, the stability of the system is studied using a limit system in the sense of weak convergence of probability measures. Using the limit system as a bridge, this paper establishes the Razumikhin-type criteria on the moment exponential stability. These criteria show that the mean of the random time delay with respect to the stationary distribution of the fast changing part of the Markov chain plays an important role in the moment exponential stability, which presents a novel feature of our work. In particular, we show that the overall system may be stabilized by the Markov switching even when some of the underlying subsystems are unstable, which shows that the Markov chain may serve as a stabilization factor. Explicit conditions for moment exponential stability are derived when the system is linear. Examples are given to illustrate our results. [Copyright &y& Elsevier]

Abstract: This work examines almost sure stability of a pure random delay system whose delay time is modeled by a finite state continuous-time Markov chain with two-time scales. The Markov chain contains a fast-varying part and a slowly-changing part. Using the properties of the weighted occupation measure of the Markov chain, it is shown that the overall systemʼs almost-sure-asymptotic stability can be obtained by using the “averaged” delay. This feature implies that even if some longer delay times may destabilize the system individually, the system may still be stable if their impact is balanced. In other words, the Markov chain becomes a stabilizing factor. Numerical results are provided to demonstrate our results. [Copyright &y& Elsevier]

Abstract: This paper is concerned with asymptotic properties of consensus-type algorithms for networked systems whose topologies switch randomly. The regime-switching process is modeled as a discrete-time Markov chain with a finite state space. The consensus control is achieved by using stochastic approximation methods. In the setup, the regime-switching process (the Markov chain) contains a rate parameter in the transition probability matrix that characterizes how frequently the topology switches. On the other hand, the consensus control algorithm uses a stepsize that defines how fast the network states are updated. Depending on their relative values, three distinct scenarios emerge. Under suitable conditions, we show that when , a continuous-time interpolation of the iterates converges weakly to a system of randomly switching ordinary differential equations modulated by a continuous-time Markov chain. In this case a scaled sequence of tracking errors converges to a system of switching diffusion. When , the network topology is almost non-switching during consensus control transient intervals, and hence the limit dynamic system is simply an autonomous differential equation. When , the Markov chain acts as a fast varying noise, and only its averaged network matrices are relevant, resulting in a limit differential equation that is an average with respect to the stationary measure of the Markov chain. Simulation results are presented to demonstrate these findings. [Copyright &y& Elsevier]

Abstract: This paper is concerned with persistent system identification for plants that are equipped with binary sensors whose unknown parameter is a random process represented by a Markov chain. We treat two classes of problems. In the first class, the parameter is a stochastic process modeled by an irreducible and aperiodic Markov chain with transition rates sufficiently faster than adaptation rates of identification algorithms. In this case, an averaged behavior of the parameter process can be derived from the stationary measure of the Markov chain and can be estimated with empirical measures. Upper and lower error bounds are established that explicitly show impact of unmodeled dynamics. In the second class of problems, the state switches values infrequently. A moving-window maximum a posterior (MAP) algorithm is introduced for tracking the time-varying parameters. Numerical results are presented to illustrate the tracking performance of the MAP algorithm and compare it with the widely used Viterbi algorithm. [Copyright &y& Elsevier]