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Observability of a hybrid system is defined as the ability to determine the continuous state of the system. Whether a hybrid system is observable or not depends on which events can be disabled, which events can be forced, and the connectivity of the discrete states, as well as its continuous dynamics. We model a hybrid system using a hybrid machine that takes into consideration both continuous variables and discrete events. We classify hybrid systems into four classes based on their discrete-event parts. For each class, conditions are derived to check observability. If a hybrid system is not observable, then we check if a weaker version of observability, called $B$ -observability, is satisfied. $B$ -observability requires that a hybrid system become observable after some finite occurrences of events. Conditions are derived to check $B$ -observability. These conditions involve both the discrete-event and continuous-variable parts of hybrid systems. If the continuous-variable part of a system has a constant- $A$ matrix, then the conditions for the continuous-variable part can be simplified. We illustrate the results by an example of a battery management system of an electric vehicle. [ABSTRACT FROM AUTHOR]

In this article, we investigate controllability of hybrid systems. We use hybrid machines to model such hybrid systems. The model consists of an automaton and a linear time-invariant system. The control goal is to drive the continuous state from any initial state to any final state. To achieve this goal, controls at both the discrete-event level and the continuous-variable level are used. Control at the discrete-event level can force some forcible events, and disable some controllable events. For the case that all events are controllable and forcible, and the graph of the automaton is strongly connected, a necessary and sufficient condition for controllability is obtained, using some existing results on controllability of switched linear systems. For three other cases, sufficient conditions are derived. If a hybrid system is not controllable, we design a supervisor to control the discrete-event part to ensure that the system becomes controllable after some finite transitions if possible. We find a necessary and sufficient condition for such a discrete-event control to exist. [ABSTRACT FROM AUTHOR]

Inspired by the subgradient push method developed recently by Nedić et al. we present a distributed dual averaging push algorithm for constrained nonsmooth convex optimization over time-varying directed graph. Our algorithm combines the dual averaging method with the push-sum technique and achieves an $O(1/ \sqrt{k})$ convergence rate. Compared with the subgradient push algorithm, our algorithm, first, addresses the constrained problems, and, second, has a faster convergence rate, and, third, simplifies the convergence analysis. We also generalize the proposed algorithm so that input variables of subgradient oracles have guaranteed convergence. [ABSTRACT FROM AUTHOR]

This note develops a distributed algorithm to solve a convex optimization problem with coupled constraints. Both coupled equality and inequality constraints are considered, where functions in the equality constraints are affine and functions in the inequality constraints are convex. Different from primal-dual subgradient methods with decreasing stepsizes for nonsmooth optimizations, our algorithm focuses on smooth problems and uses a fixed stepsize to find the exact optimal solution. Convergence analysis is derived with rigorous proofs. Our result is also illustrated by simulations. [ABSTRACT FROM AUTHOR]

This paper investigates the interaction between control and communications in networked systems by studying a class of stochastic approximation algorithms that accommodate random network topology switching processes, time-varying functions, nonlinear dynamics, additive and nonadditive noises, and other uncertainties. Interaction among control strategy and the multiple stochastic processes introduces critical challenges in such problems. By modeling the random switching as a discrete-time Markov chain and studying multiple stochastic uncertainties in a unified framework, it is shown that under broad conditions, the algorithms are convergent. The performance of the algorithms is further analyzed by establishing their rate of convergence and asymptotic characterizations. Simulation case studies are conducted to evaluate the performance of the procedures in various aspects. [ABSTRACT FROM AUTHOR]

Consensus conditions and convergence speeds are crucial for distributed consensus algorithms of networked systems. Based on a basic first-order average-consensus protocol with time-varying topologies and additive noises, this paper first investigates its critical consensus condition on network topology by stochastic approximation frameworks. A new joint-connectivity condition called extensible joint-connectivity that contains a parameter $\delta$ (termed the extensible exponent) is proposed. With this and a balanced topology condition, we show that a critical value of \delta$ for consensus is 1/2$ . Optimization on convergence rate of this protocol is further investigated. It is proved that the fastest convergence rate, which is the theoretic optimal rate among all controls, is of the order 1/t for the worst topologies, which are balanced and satisfy the extensible joint-connectivity condition. For practical implementation, certain open-loop control strategies are introduced to achieve consensus with a convergence rate of the same order as the fastest convergence rate. Furthermore, a consensus condition is derived for nonstationary and strongly correlated random topologies. The algorithms and consensus conditions are applied to distributed consensus computation of mobile ad-hoc networks; and their related critical exponents are derived from relative velocities of mobile agents for guaranteeing consensus. [ABSTRACT FROM PUBLISHER]

State observability and observer designs are investigated for linear-time-invariant systems in continuous time when the outputs are measured only at a set of irregular sampling time sequences. The problem is primarily motivated by systems with limited sensor information in which sensor switching generates irregular sampling sequences. State observability may be lost and the traditional observers may fail in general, even if the system has a full-rank observability matrix. It demonstrates that if the original system is observable, the irregularly sampled system will be observable if the sampling density is higher than some critical frequency, independent of the actual time sequences. This result extends Shannon's sampling theorem for signal reconstruction under periodic sampling to system observability under arbitrary sampling sequences. State observers and recursive algorithms are developed whose convergence properties are derived under potentially dependent measurement noises. Persistent excitation conditions are validated by designing sampling time sequences. By generating suitable switching time sequences, the designed state observers are shown to be convergent in mean square, with probability one, and with exponential convergence rates. Schemes for generating desired sampling sequences are summarized. [ABSTRACT FROM AUTHOR]

Focuses on the problem of continuous identification and adaptive stabilization of single input and single output discrete time-varying systems, as it relates to H... Findings of research on adaptive control; Observations about time-varying plants; Description of methodology used in conducting research.

Investigates the problem of identification of time-varying systems on the framework of worst-case identification and information-based complexity. Definition of basic notation and mathematics preliminaries; Persistent identification measures for linear time-invariant (LTI) systems; Persistent identification measures for slowly varying systems; Conclusions.

Optimization methods are essential and have been used extensively in a broad spectrum of applications. Most existing literature on optimization algorithms does not consider systems that involve unknown system parameters. This article studies a class of stochastic adaptive optimization problems in which identification of unknown parameters and search for the optimal solutions must be performed simultaneously. Due to a fundamental conflict between parameter identifiability and optimality in such problems, we introduce a method of adding stochastic dither signals into the system, which provide sufficient excitation for estimating the unknown parameters, leading to convergent adaptive optimization algorithms. Joint identification and optimization algorithms are developed and their simultaneous convergence properties of parameter estimation and optimization variable updates are proved. Under both noise-free and noisy observations, the corresponding convergence rates are established. The main results of this article reveal certain fundamental relationships and tradeoff among updating step sizes, dither magnitudes, parameter estimation errors, optimization accuracy, and convergence rates. Simulation case studies are used to illustrate the adaptive optimization algorithms and their main properties. [ABSTRACT FROM AUTHOR]

In this work, recursive identification algorithms are developed for Hammerstein systems under the conditions considerably weaker than those in the existing literature. For example, orders of linear subsystems may be unknown and no specific conditions are imposed on their moving average part. The recursive algorithms for estimating both linear and nonlinear parts are based on stochastic approximation and kernel functions. Almost sure convergence and strong convergence rates are derived for all estimates. In addition, the asymptotic normality of the estimates for the nonlinear part is also established. The nonlinearity considered in the paper is more general than those discussed in the previous papers. A numerical example verifies the theoretical analysis with simulation results. [ABSTRACT FROM PUBLISHER]

System identification extracts information from a system's operational data to derive a representative model for the system so that a decision can be made with desired accuracy and reliability. When resources are limited, especially for networked systems sharing data and communication power and bandwidth, identification must consider complexity as a critical limitation. Focusing on optimal resource allocation under a given reliability requirement, this paper studies identification complexity and its relations to decision making. Dynamic resource assignments are investigated. Algorithms are developed and their convergence properties are established, including strong convergence, almost sure convergence rate, and asymptotic normality. By a suitable design of resource updating step sizes, the algorithms are shown to achieve the CR lower bound asymptotically, and hence are asymptotically efficient. Illustrative examples demonstrate significant advantages of our real-time and individualized resource allocation methodologies over population-based worst-case strategies. [ABSTRACT FROM PUBLISHER]

This technical note presents new results on probabilistic characterization of identification errors in their relationships to data sizes and accuracy requirements. Employing the moderate deviations principle, this technical note shows that if the identification accuracy progressively increases with a suitable rate, the probability of an estimate going outside the precision bounds decays exponentially with the data size. The precise rate of the decaying probability is obtained. System identification under regular, binary, and quantized observations are considered. Impact of unmodeled dynamics is also investigated. [ABSTRACT FROM AUTHOR]

This paper develops stochastic consentability of linear multiagent systems with time delays and multiplicative noises. First, the stochastic stability for stochastic differential delay equations driven by multiplicative noises is examined, and the existence of the positive definite solution for a class of generalized algebraic Riccati equations (GAREs) is established. Then, sufficient conditions are deduced for the mean square and almost sure consentability and stabilization based on the developed stochastic stability and GAREs. Consensus protocols are designed for linear multiagent systems with undirected and leader-following topologies. It is revealed that multiagent consentability depends on certain characterizing system parameters, including linear system dynamics, communication graph, channel uncertainties, and time delay of the deterministic term. It is shown that a second-order integrator multiagent system is unconditionally mean square and almost surely consentable for any given noise intensities and time delay, and that the mean square and almost sure consensus can be achieved by carefully choosing the control gain according to certain explicit conditions. [ABSTRACT FROM PUBLISHER]