Search

This paper presents a distributed event-based high gain feedback design for the cooperative global practical output regulation problem of nonlinear multi-agent systems with unit relative degree subject to the general nonlinear leader system. We first convert global practical output regulation problem into global practical stabilization problem, then prove the input-to-state stability of the closed-loop system by regarding the sampling error and the steady-state of the actuator together as the external input. Based on the high gain feedback technique, the input-to-state gain function can be made sufficiently small, and hence the tracking error can converge to an arbitrary predefined small residual set around the origin. A distinguishing feature of our result is that, our controller is static and purely digital, thus, giving rise to quite a simple structure. [ABSTRACT FROM AUTHOR]

In this paper, we develop an upper bound for the SPARSEVA (SPARSe Estimation based on a VAlidation criterion) estimation error in a general scheme, i.e., when the cost function is strongly convex and the regularized norm is decomposable for a pair of subspaces. We show how this general bound can be applied to a sparse regression problem to obtain an upper bound of the estimation error for the traditional l 1 SPARSEVA problem. Numerical results are used to illustrate the effectiveness of the suggested bound. [ABSTRACT FROM AUTHOR]

In this work, we consider the optimal sensory data scheduling of multiple process. A remote estimator is deployed to monitor S independent linear time-invariant processes. Each process is measured by a sensor, which is capable of computing a local estimate and sending its local state estimate wrapped up in packets to the remote estimator. The lengths of the packets are different due to different dynamics of each process. Consequently, it takes different time durations for the sensors to send the local estimates. In addition, only a portion of all the sensors are allowed to transmit at each time due to bandwidth limitation. We are interested in minimizing the sum of the average estimation error covariance of each process at the remote estimator under such packet transmission and bandwidth constraints. We formulate the problem as an average cost Markov decision process (MDP) over an infinite horizon. We first study the special case when S = 1 and find that the optimal scheduling policy always aims to complete transmitting the current estimate. We also derive a sufficient condition for boundedness of the average remote estimation error. We then study the case for general S . We establish the existence of a deterministic and stationary policy for the optimal scheduling problem. We find that the optimal policy has a consistent property among the sensors and a switching type structure. A stochastic algorithm is designed to utilize the structure of the policy to reduce computation complexity. Numerical examples are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, robust Kalman filtering problem is investigated for a class of two-dimensional (2-D) shift-varying uncertain systems with both additive and multiplicative noises over a finite horizon. The measurement outputs suffer from randomly occurring degradations obeying certain probabilistic distributions, and the norm-bounded parameter uncertainties enter into both the state and the output matrices. The main aim of this paper is to design a robust Kalman filter such that, in the presence of parameter uncertainties and degraded measurements, certain upper bound of the generalized estimation error variance is locally minimized in the trace sense at each shift step. Recursion of the generalized estimation error variances for the addressed 2-D system is first established via the introduction of a 2-D identity quadratic filter, based on which an upper bound of the generalized estimation error variance is obtained. Subsequently, such an upper bound is minimized in the trace sense by properly designing the filter parameters. The design scheme of the robust Kalman filter is presented in terms of two Riccati-like difference equations which can be recursively computed for programmed applications. Finally, a numerical example is provided to demonstrate effectiveness of the proposed filter design method. [ABSTRACT FROM AUTHOR]

This brief paper provides a comparison of methods for enclosing a given zonotope within another of lower complexity, commonly called order reduction . These techniques are essential for maintaining efficiency in recursive computations with zonotopes and are widely used in set-based estimation, hybrid systems verification, and fault detection. We first review existing methods and provide a new theoretical analysis of the method recently introduced by Scott et al. (2016). We then compare methods in terms of computational cost and overestimation error, and investigate the effects of zonotope dimension, initial order, and reduced order on these metrics. These results provide valuable guidance for the design of robust estimation and control algorithms that more effectively balance accuracy with computational cost. [ABSTRACT FROM AUTHOR]

This paper studies the distributed state estimation problem for a class of discrete time-varying systems over sensor networks. Firstly, it is shown that the gain parameter optimization in a networked Kalman filter requires a centralized framework. Then, a sub-optimal distributed Kalman filter (DKF) is proposed by employing the covariance intersection (CI) fusion strategy. It is proven that the proposed DKF is of consistency, that is, an upper bound of error covariance matrix can be provided by the filter in real time. The consistency also enables the design of adaptive CI weights for better filter precision. Furthermore, the boundedness of covariance matrix and the convergence of the proposed filter are proven based on the strong connectivity of directed network topology and the global observability which permits the sub-system with local sensor’s measurements to be unobservable. Meanwhile, to keep the covariance of the estimation error bounded, the proposed DKF does not require the system matrix to be nonsingular at each moment, which seems to be a necessary condition in the main DKF designs under global observability. Finally, simulation results of two examples show the effectiveness of the algorithm in the considered scenarios. [ABSTRACT FROM AUTHOR]

Many recently developed data-driven fault estimation methods are restricted to minimum-phase systems so that their practical applications are limited. In this paper, the data-driven fault estimation for non-minimum phase (NMP) systems is studied, for which the main difficulty is that the unstable zeros of an NMP system will result in a growing fault-estimation error. To deal with this problem, the inverse of an NMP system is equivalently formulated as a mixed causal and anti-causal system, and the proposed fault estimator is the sum of a stable causal filter and a stable anti-causal filter. The proposed fault estimator is shown to be asymptotically unbiased and its performance is demonstrated by numerical simulations. [ABSTRACT FROM AUTHOR]

Pricing strategy for power systems is an important and challenging problem, due to the difficulties in predicting the demand and the reactions of customers to the price accurately. Any prediction errors may result in higher costs to the supplier. To address this issue, in this paper, we propose a novel, practical closed-loop pricing algorithm (PCPA). Using the closed-loop control to well coordinate the customers and the supplier, the power system can run more efficiently, resulting in both cost saving for customers and higher profit for the supplier. We prove the convergence of PCPA, i.e., a stable price can be achieved. We provide sufficient conditions to guarantee the win-win solution for both the customers and the supplier, and an upper bound of the gain. We also provide a necessary and sufficient condition of that the highest win for both the customers and the supplier can be achieved. Extensive simulations have shown that PCPA can outperform the existing prediction-based pricing algorithms. It shows that the profit gain of the proposed algorithm can up to 100% when the total demand can be fixed to the optimal demand. [ABSTRACT FROM AUTHOR]

This paper considers optimal attack attention allocation on remote state estimation in multi-systems. Suppose there are M independent systems, each of which has a remote sensor monitoring the system and sending its local estimates to a fusion center over a packet-dropping channel. An attacker may generate noises to exacerbate the communication channels between sensors and the fusion center. Due to capacity limitation, at each time the attacker can exacerbate at most N of the M channels. The goal of the attacker side is to seek an optimal policy maximizing the estimation error at the fusion center. The problem is formulated as a Markov decision process (MDP) problem, and the existence of an optimal deterministic and stationary policy is proved. We further show that the optimal policy has a threshold structure, by which the computational complexity is reduced significantly. Based on the threshold structure, a myopic policy is proposed for homogeneous models and its optimality is established. To overcome the curse of dimensionality of MDP algorithms for general heterogeneous models, we further provide an asymptotically (as M and N go to infinity) optimal solution, which is easy to compute and implement. Numerical examples are given to illustrate the main results. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of state estimation for single-output linear systems. Under some structural properties of the system matrices it is possible to design a hybrid observer capable of estimating the state of the system exactly and in a finite time. Moreover, the proposed hybrid observer provides fixed-time convergence of the state estimation error, i.e. there exists a convergence time that is bounded and such a bound is independent of the initial estimation error. The robustness properties of the hybrid observer are analyzed for the linear system with unknown inputs, and the linear system with unknown inputs and parametric uncertainty. Some simulation results illustrate the effectiveness of the proposed hybrid observer. [ABSTRACT FROM AUTHOR]

We provide a new sequential predictors approach for the exponential stabilization of linear time-varying systems. Our method circumvents the problem of constructing and estimating distributed terms in the control laws, and allows arbitrarily large input delay bounds, pointwise time-varying input delays, and uncertainties. Instead of using distributed terms, our approach to handling longer delays is to increase the number of predictors. We obtain explicit formulas to find lower bounds for the number of required predictors. The formulas involve bounds on the delays and on the derivatives of the delays. We illustrate our method in three examples. [ABSTRACT FROM AUTHOR]

This article deals with the problem of fault prognosis in timed stochastic discrete event systems. For that purpose, partially observed stochastic Petri nets are considered to model the system with its sensors. The model represents both healthy and faulty behaviors of the system. Using a timed measurement sequence issued from the sensors, an approach denoted ( ρ , δ ) - prognosis is proposed to estimate the probability of a future fault occurrence. The method is based on two input parameters: the error bound ρ and the prognosis horizon δ . The main contribution is to bound the estimation error by ρ when the prognosis horizon does not exceed δ . An example is presented to illustrate the results. [ABSTRACT FROM AUTHOR]

A filter based on characteristic functions is developed in this paper, to fit to a class of non-Gaussian dynamical systems, which state models and measurement models are all nonlinear and multi-dimensional. The new filter overcomes limitations and expands the application of this kind of filter, which is proved to just fit to one special kind of systems with multi-dimensional linear state models and one-dimensional nonlinear measurement models. Firstly, the filter using characteristic function is introduced and its limitation is analysed. Then, we design the new filter to fit to nonlinear states and multi-dimensional measurements. Thirdly, the matrix format of performance index is presented to match to the new filter gain, and the weighting function vector is given to ensure the uniform boundedness of such a performance index. Finally, the new filter gain can be obtained by minimizing this performance index, and the process of filtering design is accomplished. Simulation examples are given to illustrate the effectiveness of the proposed filter design scheme. [ABSTRACT FROM AUTHOR]

We design state observers for nonlinear networked control systems (NCS) implemented over FlexRay. FlexRay is a communication protocol used in the automotive industry, which has the feature to switch between two scheduling rules during its communication cycles. These switches induce technical difficulties when modeling, designing and analyzing observers for such systems compared to standard NCS. We present a solution based on the emulation approach. Given an observer in the absence of communication constraints, we implement it over the network and we provide sufficient conditions on the latter, to preserve the stability property of the observer. In particular, we provide explicit bounds on the maximal allowable transmission intervals, which adapt to the lengths of the segment associated to each scheduling rule. We assume that the plant dynamics and measurements are affected by noise and we guarantee an input-to-state stability property for the corresponding estimation error system. The overall system is modeled as a hybrid system and the analysis relies on the use of a novel hybrid Lyapunov function. [ABSTRACT FROM AUTHOR]

We consider the problem of link activation for distributed estimation with power constraint. To satisfy the requirement of power consumption, we propose a stochastic link activation scheme, where each sensor equipped with a distributed estimator sends data to its neighboring sensors according to different probabilities. First, we design the optimal estimator gain of each sensor to minimize the state estimation error covariance. Then, we find an upper bound of the expected state estimation error covariance and provide a sufficient condition to guarantee the stability of the proposed estimator. Finally, we formulate the link activation problem as an optimization problem, and convert it to a convex optimization. [ABSTRACT FROM AUTHOR]

The problem of differentiating a function with bounded second derivative in the presence of bounded measurement noise is considered in both continuous-time and sampled-data settings. Fundamental performance limitations of causal differentiators, in terms of the smallest achievable worst-case differentiation error, are shown. A robust exact differentiator is then constructed via the adaptation of a single parameter of a linear differentiator. It is demonstrated that the resulting differentiator exhibits a combination of properties that outperforms existing continuous-time differentiators: it is robust with respect to noise, it instantaneously converges to the exact derivative in the absence of noise, and it attains the smallest possible—hence optimal—upper bound on its differentiation error under noisy measurements. For sample-based differentiators, the concept of quasi-exactness is introduced to classify differentiators that achieve the lowest possible worst-case error based on sampled measurements in the absence of noise. A straightforward sample-based implementation of the proposed linear adaptive continuous-time differentiator is shown to achieve quasi-exactness after a single sampling step as well as a theoretically optimal differentiation error bound that, in addition, converges to the continuous-time optimal one as the sampling period becomes arbitrarily small. A numerical simulation illustrates the presented formal results. [ABSTRACT FROM AUTHOR]

In this paper, a unified H ∞ dynamic observer (UO) is proposed for a class of linear systems in the presence of unknown inputs and disturbances. It generalizes the existing results on the proportional observer (PO), the proportional integral observer (PIO) and the dynamic observer (DO). The design approach of the UO is derived from the solution of the linear matrix inequality (LMI), based on the new dynamic observer formulation and the solution of the algebraic constraints obtained from the unbiased estimation error. A numerical example is provided to show the applicability and the performance of our results. [ABSTRACT FROM AUTHOR]

In this paper, the recursive state estimation problem is investigated for an array of discrete time-varying coupled stochastic complex networks with missing measurements. A set of random variables satisfying certain probabilistic distributions is introduced to characterize the phenomenon of the missing measurements, where each sensor can have individual missing probability. The Taylor series expansion is employed to deal with the nonlinearities and the high-order terms of the linearization errors are estimated. The purpose of the addressed state estimation problem is to design a time-varying state estimator such that, in the presence of the missing measurements and the random disturbances, an upper bound of the estimation error covariance can be guaranteed and the explicit expression of the estimator parameters is given. By using the Riccati-like difference equations approach, the estimator parameter is characterized by the solutions to two Riccati-like difference equations. It is shown that the obtained upper bound is minimized by the designed estimator parameters and the proposed state estimation algorithm is of a recursive form suitable for online computation. Finally, an illustrative example is provided to demonstrate the feasibility and effectiveness of the developed state estimation scheme. [ABSTRACT FROM AUTHOR]

Robust implementable output regulator design approaches are studied for linear continuous-time systems with periodically sampled measurements, consisting of both the regulation errors and extra measurements that are generally non-vanishing in steady state. A digital regulator is first developed via the conventional emulation-based approach, rendering the regulation errors asymptotically bounded with a small sampling period. We then develop a hybrid design framework by incorporating a generalized hold device, which transforms the original problem into the problem of designing an output feedback controller fulfilling two conditions for a discrete-time system, given any (large) non-pathological sampling period. In our hybrid design framework, we show that such a controller can always be obtained by designing a discrete-time internal model, a discrete-time washout filter, and a discrete-time output feedback stabilizer. As a result, the regulation errors are shown to be globally exponentially convergent to zero. This design framework is further developed for a multi-rate digital regulator with a large sampling period of the measurements and a small control execution period. [ABSTRACT FROM AUTHOR]

For the purpose to estimate the state of nonlinear continuous-time systems, we focus on the increasing-gain observer regarded as generalization of the well-known high-gain observer. As compared with the previous results on increasing-gain observers, the assumptions under which the global asymptotic stability of the estimation error is proved are relaxed. The stability analysis is drawn by using a more general type of Lyapunov functional, where design parameters can be tuned to set the time-varying gain. A new design method based on such a Lyapunov functional is proposed to construct the observer. Simulation results affirm the effectiveness of the increasing-gain approach as compared with the high-gain observer. [ABSTRACT FROM AUTHOR]

This paper studies the event-triggered control problem for nonlinear systems with partial state and output feedback. We first consider the control systems that are transformable into an interconnection of two input-to-state stable (ISS) subsystems with the sampling error as the external input. It is shown that infinitely fast sampling can be avoided and asymptotic stabilization can be achieved by appropriately choosing the decreasing rate of the threshold signal of the event-trigger. Then, we focus on the event-triggered output-feedback control problem for nonlinear uncertain systems in the output-feedback form. The key idea is to introduce a novel nonlinear observer-based control design and to transform the control system into the form of interconnected ISS systems. ISS small-gain methods are used as a fundamental tool in the discussions. [ABSTRACT FROM AUTHOR]

This paper is concerned with the finite-horizon estimation problem of randomly occurring faults for a class of nonlinear systems whose parameters are all time-varying. The faults are assumed to occur in a random way governed by two sets of Bernoulli distributed white sequences. The stochastic nonlinearities entering the system are described by statistical means that can cover several classes of well-studied nonlinearities. The aim of the problem is to estimate the random faults, over a finite horizon, such that the influence from the exogenous disturbances onto the estimation errors is attenuated at the given level quantified by an H ∞ -norm in the mean square sense. By using the completing squares method and stochastic analysis techniques, necessary and sufficient conditions are established for the existence of the desired finite-horizon H ∞ fault estimator whose parameters are then obtained by solving coupled backward recursive Riccati difference equations (RDEs). A simulation example is utilized to illustrate the effectiveness of the proposed fault estimation method. [ABSTRACT FROM AUTHOR]

This paper addresses the stability analysis problem for a class of linear hyperbolic systems with distributed controllers sampled in space and time. First, the considered system is recast in an equivalent form with a continuous time control loop and operators representing the discretization errors (spatio-temporal sampling errors). Then with the help of the Lyapunov–Razumikhin approach, the R ɛ -stability of the proposed linear hyperbolic systems of balance laws is verified via sufficient conditions. At last, the proposed method is illustrated numerically. [ABSTRACT FROM AUTHOR]

Abstract: Finite data and moving horizon estimation schemes are increasingly being used for a range of practical problems. However, both schemes suffer from potential conceptual difficulties. In the case of finite data, most of the methods in common use, excluding Bayesian strategies, depend upon asymptotic results. On the other hand, in the case of moving horizon estimation, there are two associated problems, namely (i) estimation error quantification is typically not available as a part of the solution and (ii) one needs to provide some form of prior state estimate (the so-called arrival cost). The current paper proposes a combined MAP–Bayesian scheme which, inter alia, addresses the finite data and moving horizon problems described above. The scheme combines MAP and Bayesian strategies. The efficacy of the method is illustrated via numerical examples. [Copyright &y& Elsevier]

Abstract: This paper studies the identification of finite impulse response (FIR) systems with binary-valued observations. Combining with the stochastic gradient algorithm and statistical property of the system noise, a recursive projection algorithm is proposed to estimate the unknown system parameters. Under some mild conditions on the a priori knowledge of the unknown parameters and inputs, the algorithm is proved to be convergent in the almost sure and mean square sense. Furthermore, the almost sure and mean square convergence rates of estimation errors are also obtained. A numerical example is given to demonstrate the effectiveness of the algorithm and the main results obtained. [Copyright &y& Elsevier]

Abstract: Recently the problem of estimating the initial state of some linear infinite-dimensional systems from measurements on a finite interval was solved by using the sequence of forward and backward observers Ramdani, Tucsnak, and Weiss (2010). In the present paper, we introduce a direct Lyapunov approach to the problem and extend the results to the class of semilinear systems governed by wave and beam equations with boundary measurements from a finite interval. We first design forward observers and derive Linear Matrix Inequalities (LMIs) for the exponential stability of the estimation errors. Further we obtain simple finite-dimensional conditions in terms of LMIs for an upper bound on the minimal time, that guarantees the convergence of the sequence of forward and backward observers on for the initial state recovering. This represents also an upper bound on the observability time. For observation times bigger than , these LMIs give upper bounds on the convergence rate of the iterative algorithm in the norm defined by the Lyapunov functions. In our approach, is found as the minimal dwelling time for the switched exponentially stable (forward and backward estimation error) systems with the different Lyapunov functions (Liberzon, 2003). The efficiency of the results is illustrated by numerical examples. [Copyright &y& Elsevier]

Abstract: The Kalman filter and smoother are optimal state estimators under certain conditions. The Kalman filter is typically presented in a predictor/corrector format, but the Kalman smoother has never been derived in that format. We derive the Kalman smoother in a predictor/corrector format, thus providing a unified form for the Kalman filter and smoother. We also discuss unbiased finite impulse response (UFIR) filters and smoothers, which can provide a suboptimal but robust alternative to Kalman estimators. We derive two unified forms for UFIR filters and smoothers, and we derive lower and upper bounds for their estimation error covariances. [Copyright &y& Elsevier]

Abstract: This paper is devoted to the design of interval observers for Linear Time Varying (LTV) systems and a class of nonlinear time-varying systems in the output canonical form. An interval observer design is feasible if it is possible to calculate the observer gains making the estimation error dynamics cooperative and stable. It is shown that under some mild conditions the cooperativity of an LTV system can be ensured by a static linear transformation of coordinates. The efficiency of the proposed approach is demonstrated through numerical simulations. [Copyright &y& Elsevier]

Abstract: This paper presents a novel approach to design estimators for nonlinear systems. The approach is based on a combination of linear Moving Horizon Estimation (MHE) and Direct Virtual Sensor (DVS) techniques, and allows the design of estimators with guaranteed stability, which can account for convex constraints on the variables to be estimated. It is also shown that the designed estimators are optimal, in the sense that they give minimal worst-case estimation error, on the basis of the available finite number of noise-corrupted data, with respect to an ideal MHE filter (obtained by assuming exact knowledge of the system dynamics and of the global solution of the related nonlinear program). The approach is tested on a nonlinear mass–spring–damper system. [Copyright &y& Elsevier]

This paper addresses the event-triggered output-feedback stabilization for a class of uncertain nonlinear systems. Essentially different from the related literature, the systems under investigation allow large uncertainties (whose size is unknown) coupling to unmeasurable states, which requires to integrate a comprehensive output-feedback compensation mechanism into the event-triggered philosophy and would bring substantial challenges to the event-triggered control. To solve the problem, a novel scheme of adaptive event-triggered output-feedback control is established for the systems. Specifically, an adaptive dynamic gain is introduced not only to counteract the large uncertainties but also to cope with the execution/sampling error. Then, an adaptive event-triggered output-feedback controller based on dynamic-gain observer is constructed to guarantee global convergence for the resulting closed-loop system while reducing execution/sampling. Particularly, the event-triggering mechanism involved is delicately designed by fully exploiting the dynamic gain, to enable the negative influence of the gain through the execution error to be counteracted (no matter how large the gain becomes) while precluding infinitely fast execution which violates the implementation of event-triggered controller in practice. Correspondingly, a distinctive analysis pattern is implemented for the closed-loop performance, due to the coupling of the dynamic-gain compensation mechanism and the event-triggering mechanism. Moreover, for more efficient resource saving, we further show the feasibility of adaptive dynamic event-triggering mechanism for the desired stabilization. [ABSTRACT FROM AUTHOR]