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This paper is devoted to numerically solving a class of optimal stopping problems for stochastic hybrid systems involving both continuous states and discrete events. The motivation for solving this class of problems stems from quickest event detection problems of stochastic hybrid systems in broad application domains. We solve the optimal stopping problems numerically by constructing feasible algorithms using Markov chain approximation techniques. The key tasks we undertake include designing and constructing discrete-time Markov chains that are locally consistent with switching diffusions, proving the convergence of suitably scaled sequences, and obtaining convergence for the cost and value functions. Finally, numerical results are provided to demonstrate the performance of the algorithms. [ABSTRACT FROM AUTHOR]

This paper establishes exponential convergence rates for a class of primal–dual gradient algorithms in distributed optimization without strong convexity. The convergence analysis is based on a carefully constructed Lyapunov function. By evaluating metric subregularity of the primal–dual gradient map, we present a general criterion under which the algorithm achieves exponential convergence. To facilitate practical applications of this criterion, several simplified sufficient conditions are derived. We also prove that although these results are developed for the continuous-time algorithms, they carry over in a parallel manner to the discrete-time algorithms constructed by using Euler's approximation method. [ABSTRACT FROM AUTHOR]

This paper studies mean-square (MS) convergent observers for estimating continuous states of randomly switched linear systems (RSLSs) with unobservable subsystems that are subject to stochastic output observation noises. When subsystems are unobservable and switching sequences are random, the classical Kalman–Bucy filters that are applied to observable sub-states are shown to be potentially divergent. It is also shown that unless the switching interval T can be selected to be sufficiently small from the outset, MS convergence may never be achieved, regardless of how the observers for the subsystems are designed. The critical threshold T m a x on T is derived for MS convergent observers to be achievable. Under the condition T < T m a x , this paper introduces design algorithms for subsystem observers to generate a globally MS convergent observer for the entire continuous state. A fundamental design tradeoff between convergence speeds and steady-state estimation errors is analyzed. This paper extends our recent new framework and algorithms for strong convergent observer design in RSLSs by including observation noises, considering multi-output systems, establishing new algorithms for MS convergence, and developing design tradeoff analysis. Examples and a practical case study are presented to illustrate the design procedures, main convergence properties, and error analysis. [ABSTRACT FROM AUTHOR]

Open circuit voltage (OCV), as a nonlinear function of state of charge (SoC) of lithium ion battery, commonly obtained through offline OCV test at certain ambient temperatures and aging stages. The OCV-SoC relationship may be inaccurate in real application due to the difference in operation conditions. In this paper, the OCV is identified by H infinity filter (HIF) in real operation conditions. Due to the no need to derive the jacobian matrices with unscented Kalman filter (UKF), the identified discrete OCV points are propagated to state estimation process instead of the traditional OCV-SoC nonlinear function. Additionally, the polarization voltage across the polarization capacitor is also passed to state estimation in the form of discrete data points. The experimental results demonstrate that the HIF-UKF can obtain the OCV and SoC in real time. [ABSTRACT FROM AUTHOR]

In this paper, we investigate active on-line diagnosis in discrete event systems. Active diagnosis can be used for fault detection, fault localization, fault-tolerant control, among others. Discrete event systems are general models for complex manmade systems. For the active on-line diagnosis, we do not construct the entire diagnostic automaton off-line. Instead, we look N steps ahead to determine active diagnosability and calculate diagnostic strategies. Thus, we define active N -diagnosability and investigate the relation between active diagnosability and active N -diagnosability. We also develop an algorithm to check active N -diagnosability. If a system is actively N -diagnosable, the algorithm will also give the control that diagnoses the system. We show that there are significant computational advantages for using the on-line approach. [ABSTRACT FROM AUTHOR]

This paper investigates identification of Wiener systems with quantized inputs and binary-valued output observations. By parameterizing the static nonlinear function and incorporating both linear and nonlinear parts, we begin by investigating system identifiability under the input and output constraints. Then a three-step algorithm is proposed to estimate the unknown parameters by using the empirical measure, input persistent patterns, and information on noise statistics. Convergence properties of the algorithm, including strong convergence and mean-square convergence rate, are established. Furthermore, by selecting a suitable transformation matrix, the asymptotic efficiency of the algorithm is proved in terms of the Cramér–Rao lower bound. Finally, numerical simulations are presented to illustrate the main results of this paper. [ABSTRACT FROM AUTHOR]

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 paper introduces identification algorithms for finite impulse response systems under quantized output observations and general quantized inputs. While asymptotically efficient algorithms for quantized identification under periodic inputs are available, their counterpart under general inputs has encountered technical difficulties and evaded satisfactory resolutions. Under quantized inputs, this paper resolves this issue with constructive solutions. A two-step algorithm is developed, which demonstrates desired convergence properties including strong convergence, mean-square convergence, convergence rates, asymptotic normality, and asymptotical efficiency in terms of the Cramér–Rao lower bound. Some essential conditions on input excitation are derived that ensure identifiability and convergence. It is shown that by a suitable selection of the algorithm’s weighting matrix, the estimates become asymptotically efficient. The strong and mean-square convergence rates are obtained. Optimal input design is given. Also the joint identification of noise distribution functions and system parameters is investigated. Numerical examples are included to illustrate the main results of this paper. [ABSTRACT FROM AUTHOR]

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 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: This work is concerned with system identification of plants using quantized output observations. We focus on relationships between identification space and time complexities. This problem is of importance for system identification in which data-flow rates are limited due to computer networking, communications, wireless channels, etc. Asymptotic efficiency of empirical measure based algorithms yields a tight lower bound on identification accuracy. This bound is employed to derive a separation principle of space and time complexities and to study sensor threshold selection. Insights gained from these understandings provide a feasible approach for optimal utility of communication bandwidth resources in enhancing identification accuracy. [Copyright &y& Elsevier]

Abstract: This work is concerned with identification of Wiener systems whose outputs are measured by binary-valued sensors. The system consists of a linear FIR (finite impulse response) subsystem of known order, followed by a nonlinear function with a known parametrization structure. The parameters of both linear and nonlinear parts are unknown. Input design, identification algorithms, and their essential properties are presented under the assumptions that the distribution function of the noise is known and the nonlinearity is continuous and invertible. It is shown that under scaled periodic inputs, identification of Wiener systems can be decomposed into a finite number of core identification problems. The concept of joint identifiability of the core problem is introduced to capture the essential conditions under which the Wiener system can be identified with binary-valued observations. Under scaled full-rank conditions and joint identifiability, a strongly convergent algorithm is constructed. The algorithm is shown to be asymptotically efficient for the core identification problem, hence achieving asymptotic optimality in its convergence rate. For computational simplicity, recursive algorithms are also developed. [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]

The essential issues of time complexity and probing signal selection are studied for persistent identification of linear time-invariant systems in a closed-loop setting. By establishing both upper and lower bounds on identification accuracy as functions of the length of observation, size of unmodeled dynamics, and stochastic disturbances, we demonstrate the inherent impact of unmodeled dynamics on identification accuracy, reduction of time complexity by stochastic averaging on disturbances, and probing capability of full rank periodic signals for closed-loop persistent identification. These findings indicate that the mixed formulation, in which deterministic uncertainty of system dynamics is blended with random disturbances, is beneficial to reduction of identification complexity. [Copyright &y& Elsevier]

This paper proposes a learning-based distributed optimization framework to enhance the resilience of distributed power system algorithms against communication failures. The autoregressive-moving-average (ARMA) model is used to estimate the missing states and control actions of neighboring agents during communication contingencies. The proposed framework allows agents to predict the future control actions of neighbors. Thus, even during complete loss of communication, agents can efficiently perform distributed optimization. We use the Distributed Optimal Frequency Control (DOFC) algorithm, which includes optimal power sharing to achieve frequency stability, as a benchmark application platform to show the effectiveness of the proposed framework. The theoretical findings are evaluated on two practical power systems. The results show that the ARMA-based DOFC algorithm can asymptotically reach the same convergence rate as the power system without communication interruptions. • Developing ARMA model to estimate the states and control actions of neighboring agents. • Embedding ARMA model into DOFC algorithm to mitigate communication failures. • Characterizing relationship between estimation errors and convergence rates of ARMA-based DOFC. • Developing a practical criterion for reliability of DOFC under communication uncertainties. • Illustrating the convergence rate of ARMA-based DOFC can asymptotically reach the CR lower bound. [ABSTRACT FROM AUTHOR]

This paper investigates the impact of communication packet loss on Distributed Optimal Frequency Control (DOFC) in Alternating Current (AC) electric energy systems, populated with multiple clusters of hybrid producer–consumer (prosumer) agents. The paper first establishes rigorous relationships between the communication packet delivery ratio and the convergence rate of the proposed DOFC algorithm. This provides a foundation for resource allocation on communication systems to enhance the convergence speed of distributed optimization and control algorithms, such as DOFC, under noisy and disrupted communication systems. The paper develops a systematic approach to identify the best possible convergence rate over all possible algorithms, by introducing an algorithm that can achieve asymptotically the Cramér-Rao (CR) lower bound. This fundamental result links the information contents of data to the best possible mean-square estimation error. Simulation studies on an electric energy system validate the theoretical results. [ABSTRACT FROM AUTHOR]

Motivated by the seminal work of Dupire (2009) on functional Itô formulas, this work investigates asymptotic properties of systems represented by stochastic functional differential equations (SFDEs). Stability of general delay-dependent SFDEs is investigated using degenerate Lyapunov functionals, which are only positive semi-definite rather than positive definite as used in the classical work. This paper first establishes boundedness and regularity of SFDEs by using degenerate Lyapunov functionals. Then moment and almost sure exponential stabilities are obtained based on degenerate Lyapunov functionals and the semi-martingale convergence theorem. As an application of the stability criteria, consentability of stochastic multi-agent systems with nonlinear dynamics is studied. [ABSTRACT FROM AUTHOR]

This paper proposes an architectural solution to enhance the resilience of distributed decision-making and control in microgrids and smart grids with respect to communication delays. The paper develops a resource allocation framework to optimally place the multiple-input multiple-output (MIMO) communication technology on critical channels to reduce the communication bottle neck and expedite the convergence speed of distributed online optimization algorithms, which require convergence in the cyber network before the solution can be implemented on the physical grid. The paper shows that optimal placement of the MIMO technology can decrease communication transmission delays, which in turn improves the reliability of power system operational protocols, such as distributed frequency regulation. Illustrative case studies using data from real-world power systems show that only upgrading the critical communication channels is sufficient to achieve system-wide performance improvement. • Proposing an architectural solution to enhance the resilience of distributed optimization in smart grids with respect to communication delays. • Determining an upper bound on the communication delays under different MIMO communication architectures. • Developing a resource allocation algorithm to optimally place the MIMO technology and to increase the resilience of communication networks. [ABSTRACT FROM AUTHOR]

The incremental capacity (IC) analysis method is widely used to analyze the aging origins and state of health (SOH) of lithium ion batteries. This paper analyzes the technical difficulties during the application of the IC analysis method at first. A universal capacity model based on charging curve is then proposed, which not only inherits the advantages of IC analysis method but also avoids the tedious data preprocessing procedure, to estimate SOH of lithium ion batteries. The feasibility and accuracy of the model are demonstrated. To verify the accuracy and flexibility of the proposed capacity model, it is applied on different types of lithium ion batteries including LiFePO 4 , LiNi 1 / 3 Co 1 / 3 Mn 1 / 3 O 2 , and Li 4 / 3 Ti 5 / 3 O 4 . Furthermore, the proposed capacity model is applied on the aged cells to validate the model accuracy during the whole life span of lithium ion batteries. The results show that the model error is less than 4% of the nominal capacity for each case. [ABSTRACT FROM AUTHOR]

This paper considers the problem of identifiability and parameter estimation of single-input–single-output, linear, time-invariant, stable, continuous-time systems under irregular and random sampling schemes. Conditions for system identifiability are established under inputs of exponential polynomial types and a tight bound on sampling density. Identification algorithms of Gauss–Newton iterative types are developed to generate convergent estimates. When the sampled output is corrupted by observation noises, input design, sampling times, and convergent algorithms are intertwined. Persistent excitation (PE) conditions for strongly convergent algorithms are derived. Unlike the traditional identification, the PE conditions under irregular and random sampling involve both sampling times and input values. Under the given PE conditions, iterative and recursive algorithms are developed to estimate the original continuous-time system parameters. The corresponding convergence results are obtained. Several simulation examples are provided to verify the theoretical results. [ABSTRACT FROM AUTHOR]

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 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]

This paper introduces distributed adaptive algorithms for optimal step size selection in a distributed constrained optimization problem that involves stochastic target variations and noisy observations. The limit behavior of the step size sequences reflects fundamental impact that must be balanced between tracking the target changes and attenuating observation noises. Algorithms for simultaneously estimating target variation, tracking the global optimal solution, and finding the optimal step size are derived, which are shown to achieve convergence on all the sequences simultaneously to their respective optimal values. [ABSTRACT FROM AUTHOR]

• A sufficient-necessary condition is given to design a delay controller for one area. • A criterion is established for simplifying delay control design in multi-area LFC. • Proposed method has better performance compared with conventional approaches. Load frequency control (LFC) has been considered as one of the most important frequency regulation mechanisms in modern power system. One of the inevitable problems involved in LFC over a wide area is communication delay. Not only can the delay deteriorate the system performance but also cause system instability. In this paper, an alternative design method is proposed to devise delay compensators for LFC in one or multiple control areas. For one-area LFC, a sufficient and necessary condition is given for designing a delay compensator. For multi-area LFC with area control errors (ACEs), it is demonstrated that each control area can have its delay controller designed as that in a one-area system if the index of coupling among the areas is below the threshold value determined by the small gain theorem. Effectiveness of the proposed method is verified by simulation studies on LFCs with communication delays in one and multiple interconnected areas with and without time-varying delays, respectively. [ABSTRACT FROM AUTHOR]

This paper provides a further step towards popularizing the proposed Butler-Volmer (BV) equation-based model and its implementation on state of power (SOP) prediction at various temperatures, which is based on the relationship between state of charge and state of useful charge. The actual 10 s SOP of battery is obtained using the constant current pulse when the restriction of voltage is exactly managed. The COMPLEX method is taken to determine the coefficients of the simplified form of BV equation, enabling online estimation of battery states. Robustness analysis of the proposed model and algorithm on SOP prediction over a large temperature range is analyzed and verified, showing their reliability and accuracy in estimating the terminal voltage and predicting power capability. [ABSTRACT FROM AUTHOR]

The constant polarization voltage is managed for battery heating to achieve a good tradeoff between short heating time and less damage to battery lifetime based on an electro-thermal coupled model. The optimal frequency for maximum heat generation rate at a certain temperature is determined, which is different from the frequency for minimum total impedance. Heating under variable frequency is almost the same as under a constant frequency in terms of heating time and efficiency. However, engineering realization for variable frequency is more difficult, implying that constant frequency heating is a more promising candidate. The optimal frequency during the overall heating process, which is always lower than that at the initial temperature, can be evaluated from the intermediate temperature with low computational effort. Experimental results demonstrate that the heating time at the optimal frequency, corresponding to the maximum heat generation during the overall heating process, is the shortest with high efficiency. The battery is heated from −15.4 °C to 5.6 °C within 338 s, an average temperature-rise rate of 3.73 °C/min with an essentially uniform temperature distribution. The proposed heating strategy, which is experimentally verified with no apparent detrimental effect on battery health, is of great potential for rapidly improving operating performance of electric vehicles in cold weather. [ABSTRACT FROM AUTHOR]

A low-temperature electro-thermal coupled model, which is based on the electrochemical mechanism, is developed to accurately capture both electrical and thermal behaviors of batteries. Activation energies reveal that temperature dependence of resistances is greater than that of capacitances. The influence of frequency on polarization voltage and irreversible heat is discussed, and frequency dependence of polarization resistance and capacitance is obtained. Based on the frequency-dependent equation, a reduced low-temperature electro-thermal coupled model is proposed and experimentally validated under different temperature, frequency and amplitude conditions. Simulation results exhibit good agreement with experimental data, where the maximum relative voltage error and temperature error are below 2.65% and 1.79 °C, respectively. The reduced model is demonstrated to have almost the same accuracy as the original model and require a lower computational effort. The effectiveness and adaptability of the proposed methodology for model reduction is verified using batteries with three different cathode materials from different manufacturers. The reduced model, thanks to its high accuracy and simplicity, provides a promising candidate for development of rapid internal heating and optimal charging strategies at low temperature, and for evaluation of the state of battery health in on-board battery management system. [ABSTRACT FROM AUTHOR]

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]