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Abstract: In this paper, a new method is introduced to enhance feedback robustness against communication gain uncertainties. The method employs a fundamental property in stochastic differential equations to add a scaled stochastic dither under which tolerable gain uncertainties can be much enlarged, beyond the traditional deterministic optimal gain margin. Algorithms, stability, convergence, and robustness are presented for first-order systems. Extension to higher-dimensional systems is further discussed. Simulation results are used to illustrate the merits of this methodology. [Copyright &y& Elsevier]

Abstract: Joint estimation of states and events in linear regime-switching systems is studied under irregular sampling schemes which stem from improved sampling and quantization methods for efficient utility of communication resources. Joint observability and sampling complexity are established, extending Shannon’s sampling theorem and our recent results on sampling complexity to joint estimation problems. Observer design and convergence analysis are conducted for systems under noisy observations. It is shown that our algorithms converge strongly with an error bound of the order . Simulation examples are included to illustrate potential usages of the algorithms. [Copyright &y& Elsevier]

Abstract: This paper focuses on state reconstruction problems for systems whose outputs are measured only by binary-valued sensors. A binary-valued sensor is characterized by its switching threshold or post-switching location and by its output that indicates only whether the system output is above or below the threshold. The traditional passive-type state reconstruction that does not require input design will fail in general, even if the system has a full-rank observability matrix. It is shown that under controllability conditions and bounded uncertainty on the initial state, it is always possible to construct a causal input that will cause the output to cross the sensor threshold in a designated time interval. Information on the time instants of threshold crossing is then used to reconstruct the initial state. It is proved that if the system is observable, such a reconstruction is always possible if the eigenvalues of the system are all real valued. If the eigenvalues of the system contain only purely imaginary and non-repeating values, it is sufficient that threshold crossing occurs within a relatively small time interval. In general without constraints on system eigenvalues, an input can always be randomized to ensure that the state can be reconstructed with probability one. These results lead to an active state reconstruction algorithm. [Copyright &y& Elsevier]

Abstract: This paper studies identification of systems in which only quantized output observations are available. An identification algorithm for system gains is introduced that employs empirical measures from multiple sensor thresholds and optimizes their convex combinations. Strong convergence of the algorithm is first derived. The algorithm is then extended to a scenario of system identification with communication constraints, in which the sensor output is transmitted through a noisy communication channel and observed after transmission. The main results of this paper demonstrate that these algorithms achieve the Cramér–Rao lower bounds asymptotically, and hence are asymptotically efficient algorithms. Furthermore, under some mild regularity conditions, these optimal algorithms achieve error bounds that approach optimal error bounds of linear sensors when the number of thresholds becomes large. These results are further extended to finite impulse response and rational transfer function models when the inputs are designed to be periodic and full rank. [Copyright &y& Elsevier]

Abstract: System identification of plants with binary-valued output observations is of importance in understanding modeling capability and limitations for systems with limited sensor information, establishing relationships between communication resource limitations and identification complexity, and studying sensor networks. This paper resolves two issues arising in such system identification problems. First, regression structures for identifying a rational model contain non-smooth nonlinearities, leading to a difficult nonlinear filtering problem. By introducing a two-step identification procedure that employs periodic signals, empirical measures, and identifiability features, rational models can be identified without resorting to complicated nonlinear searching algorithms. Second, by formulating a joint identification problem, we are able to accommodate scenarios in which noise distribution functions are unknown. Convergence of parameter estimates is established. Recursive algorithms for joint identification and their key properties are further developed. [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]