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This article aims to enlarge the applicability of event-triggered control for stochastic systems, and is particularly concerned with event-triggered stabilization for stochastic systems with control-dependent diffusion term. Roughly treating stochastic noises as unfavorable factors for system stability, the related works are based on Lyapunov-type conditions for ISS property with respect to sampling error as those in the nonstochastic context. The conditions imply the existence of a twice-differentiable Lyapunov function with negative-definite infinitesimal under continuous-time control, and indeed exclude many familiar stochastic systems with control-dependent diffusion term which are continuously stabilizable while no such Lyapunov function exists. As the main contribution of this article, an enlarged framework of event-triggered stabilization is established for stochastic systems with control-dependent diffusion term, starting from the system stability under continuous-time control, rather than from Lyapunov-type conditions for ISS property. Specifically, with moment exponential stability assumed under continuous-time control, elementary event-triggering mechanisms are proposed with an enforced minimum inter-execution interval, under which the event-triggered controller can render the system exponentially stable both in the sense of expectation and in the almost sure sense. Particularly, a distinctive analysis of closed-loop stability is performed via delicate comparison between the solutions under the event-triggered, and continuous-time controls. Within the framework, inclusive Lyapunov-type conditions incorporating the underlying positive effects of stochastic noises are presented for event-triggered exponential stabilization of the stochastic systems, where the candidate Lyapunov function involved is weakened to be nondifferentiable at the origin and, even, to allow non-negative infinitesimal under continuous-time control. [ABSTRACT FROM AUTHOR]

Recently, Thompson sampling has been shown to achieve good theoretical performance guarantees for stochastic control problems with parameter uncertainty when the state, control, and parameter spaces are all finite. Much less is known however about the performance of Thompson sampling when applied to continuous or more general spaces, which constitutes an important class of problems in practice. In this paper, we study Thompson sampling when applied to a broad class of average cost stochastic control problems where the state, control, and parameter spaces are all general measurable spaces. The main contributions of our paper are establishing theoretical performance guarantees for Thompson sampling as measured by: first, expected posterior sampling error; and second, average per period regret. [ABSTRACT FROM AUTHOR]

This paper addresses the event-triggered tracking for a class of uncertain nonlinear systems. Essentially different from the related works, the nonlinear systems allow serious (parametric) uncertainties, while no further a priori information, excepting some coarse information, is required on the reference signal to be tracked. This makes event-triggered control more challenging, partially because the sampling error cannot be precisely bounded any more. As main contributions of this paper, new adaptive event-triggered tracking schemes are proposed for the systems in two event-triggering architectures with different roles of the event-triggering mechanism on the information transmitting and control computing/updating. Much importantly, a dynamic gain is incorporated in either scheme not only to counteract the serious uncertainties, but also to overcome the bad influence of the sampling error. Based on the dynamic gain, two adaptive event-triggered controllers are designed with distinct event-triggering mechanisms, respectively. Particularly, to ensure application flexibility, one of the triggering mechanisms is rendered relatively independent of the controller signal. The designed event-triggered controllers are shown to achieve the practical tracking for the systems, that is, the prespecified arbitrary tracking accuracy can be guaranteed (a comparable objective to that via continuous-time control), while avoiding infinitely fast sampling/execution. [ABSTRACT FROM AUTHOR]

Devising efficient algorithms to solve continuously-varying strongly convex optimization programs is key in many applications, from control systems to signal processing and machine learning. In this context, solving means to find and track the optimizer trajectory of the continuously-varying convex optimization program. Recently, a novel prediction–correction methodology has been put forward to set up iterative algorithms that sample the continuously-varying optimization program at discrete time steps and perform a limited amount of computations to correct their approximate optimizer with the new sampled problem and predict how the optimizer will change at the next time step. Prediction–correction algorithms have been shown to outperform more classical strategies, i.e., correction-only methods. Typically, prediction–correction methods have asymptotical tracking errors of the order of $h^2$ , where $h$ is the sampling period, whereas classical strategies have order of $h$. Up to now, prediction–correction algorithms have been developed in the primal space, both for unconstrained and simply constrained convex programs. In this paper, we show how to tackle linearly constrained continuously-varying problem by prediction–correction in the dual space and we prove similar asymptotical error bounds as their primal versions. [ABSTRACT FROM AUTHOR]

This note presents new results on the design of the process noise covariance matrix in Kalman filtering. The proposed design belongs to the realm of worst case methods: the optimal covariance is sought such as to maximize an upper bound on the estimation error matrix under a total budget constraint. Optimality conditions are derived along with a numerical algorithm for iterative approximation of the optimal solution. The optimal solution features a few time points and the associated covariances. Broadly speaking, the process noise is only “active” at the time points that enhance its controllability. The importance of the method is that it bounds from above the performance of any Kalman filter with a different design. Monte Carlo simulations on a double harmonic system numerical example illustrate the good convergence, performance, and low sensitivity to initial guesses of the proposed method. Moreover, in terms of estimation accuracy, the Kalman filter with the optimal design outperforms a robust $H_2$ filter designed to cope with an equivalent uncertainty. [ABSTRACT FROM AUTHOR]

This paper concentrates on the integration of relative localization and the formation control over leader–follower networks. First, we develop a consensus-like relative localization scheme for each agent to estimate the real-time relative positions of its neighbors by merely using velocity as well as distance-related measurements and local communications under the assumption that the local frames of all agents share a common orientation. It is shown that the relative position estimate exponentially converges to its true value under a persistent excitation condition on relative velocity between the two agents. Second, an integrated relative localization and a leader–follower formation control are developed by combining the proposed relative localization scheme and a complex Laplacian-based formation control scheme. It is proven that the integrated system globally asymptotically converges to a stationary similar formation in the case of error-free initial relative position estimates while globally uniformly bounds in a neighborhood of the prescribed formation in the case with initial relative position estimation errors. Furthermore, based on the two degrees of freedom of similar formation on translation, the integrated scheme is also generalized to achieve moving similar formation control. Finally, simulations are presented to illustrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents novel modifications to a predictor-based model reference adaptive controller (PMRAC) to compensate for input delays in uncertain nonlinear systems. A delay-dependent stability condition, derived using a Lyapunov–Krasovskii functional, indicates that there exists a time delay margin, below which the asymptotic stability of the tracking and estimation errors as well as the input-to-state stability of the closed-loop system are guaranteed. Numerical experiments are carried out with comparisons to the original PMRAC and to a finite spectrum assignment scheme to validate the theoretical claims. The results also illustrate the effectiveness of the proposed delay compensation formulation and the asymptotic behaviors of the tracking and estimation errors. [ABSTRACT FROM AUTHOR]

This paper considers the secure state estimation problem for noisy systems in the presence of sparse sensor integrity attacks. We show a fundamental limitation, that is, $2\rho$ -detectability is necessary for achieving bounded estimation errors, where $\rho$ is the number of attacks. This condition is weaker than the $2\rho$ -observability condition typically assumed in the literature. Conversely, we propose a real-time state estimator that achieves the fundamental limitation. The proposed state estimator is inspired by robust control and fault detection and isolation, that is, it consists of local Luenberger estimators, local residual detectors, and a global fusion process. We show its performance guarantees for $\mathcal H_2$ , $\mathcal H_\infty$ , and $\ell _1$ systems. Finally, numerical examples show that it has relatively low estimation errors among existing algorithms and average computation time for systems with a sufficiently small number of compromised sensors. [ABSTRACT FROM AUTHOR]

Inspired by the interesting findings regarding the hierarchy and coordination of pigeons in Nagy et al.  [Nature, 2010], we revisit the discrete-time leader–follower consensus problem with switching topologies. The purpose of this paper is to investigate the impact of hierarchical topologies and followers’ self-loops on the convergence performance of leader–follower consensus, including the convergence rate and robustness to switching topologies. We first study the fixed topology case, and show that the followers converge to the leader's state in finite time if and only if each follower has no self-loops and the topology is hierarchical. However, we show via counterexample, that leader–follower consensus may not be achieved when some followers have no self-loops and the topology is switching; even if each interaction graph has a spanning tree rooted at the leader. With the aid of binary relation theory, we further develop a new approach to present a novel sufficient condition for leader–follower consensus with switching topologies and with some followers having no self-loops. We prove that when no followers have self-loops and the same hierarchical organization is kept under the switching topologies, then the fastest rate of convergence in leader–follower consensus can be achieved; even in the presence of complex dynamic topologies. This is consistent with the natural phenomena found in pigeons by Nagy et al. [ABSTRACT FROM AUTHOR]

In this paper, we consider the properties for Kalman filtering in a multi-hop network. A time-homogeneous Markov chain is used to characterize the stochastic packet delay and loss phenomenon of each relay. Since, after several relays, the average expected estimation error covariance at the terminal is difficult to calculate, we derive lower and upper bounds for the average value. Using these bounds, it is found that the stability is related to one special entry in the channel's transition probability matrix, from which we obtain a necessary and sufficient condition for the stability of the single-hop case and extend the result to the multihop one. [ABSTRACT FROM AUTHOR]

We consider output feedback control of linear discrete-time systems subject to bounded additive disturbances and measurement noise. The goal is to stabilize the system while ensuring the satisfaction of hard constraints on the state and input. For this purpose, we present a novel output-feedback model predictive control (MPC) scheme based on set-valued estimation. The main feature of the scheme is that the number of past measurements used in order to obtain the set-valued estimate depends on the particular time step in the prediction horizon for which the estimate is required. In particular, we employ fewer measurements for prediction steps that are farther in the future, which is a key point in establishing recursive feasibility. The resulting optimal control problem is of bounded complexity, which is a priori known, and is a linearly constrained convex optimization problem under additional assumptions. We demonstrate in a numerical example that the proposed MPC scheme allows an enlargement of the feasible set beyond what is possible with earlier schemes using only linear estimators. [ABSTRACT FROM AUTHOR]

Quantum Hamiltonian identification (QHI) is important for characterizing the dynamics of quantum systems, calibrating quantum devices, and achieving precise quantum control. In this paper, an effective two-step optimization (TSO) QHI algorithm is developed within the framework of quantum process tomography. In the identification method, different probe states are input into quantum systems and the output states are estimated using the quantum state tomography protocol via linear regression estimation. The time-independent system Hamiltonian is reconstructed based on the experimental data for the output states. The Hamiltonian identification method has computational complexity $O(d^6)$ , where $d$ is the dimension of the system Hamiltonian. An error upper bound $O(\frac{d^3}{\sqrt{N}})$ is also established, where $N$ is the resource number for the tomography of each output state, and several numerical examples demonstrate the effectiveness of the proposed TSO Hamiltonian identification method. [ABSTRACT FROM AUTHOR]

In this note, a switching-type delay-adaptive predictor feedback controller is proposed to globally stabilize linear systems with unknown input delay. The idea of our method is to take advantage of the robustness of feedback laws to delay estimate error that is sufficiently small. We first prove that, when the delay estimate is sufficiently close to the true delay, there is a Lyapunov–Krasovskii functional that is strictly decreasing, and asymptotic regulation is achievable. Then, with the help of the Lyapunov–Krasovskii functional as a supervisor, the switching logic plays the role of adjusting the estimated delay online to make it sufficiently close to the true delay. The result of this note shows that, global adaptive stabilization of linear systems with unknown input delay is achievable, with a logic-based switching control law. [ABSTRACT FROM PUBLISHER]

This paper presents an approach for the design of globally exponentially stable hybrid attitude and gyro-bias observers on SO(3) \times \mathbb R^3 . First, we propose a hybrid observer developed in a generic manner involving a generic family of potential functions with specific properties. Thereafter, we present a design method for such potential functions via an appropriate angular warping transformation applied to a new potential function on $SO(3)$. This results in a hybrid observer that uses directly body-frame measurements of known inertial vectors. [ABSTRACT FROM AUTHOR]

Descent algorithms based on the gradient, conjugate gradient, and Newton methods are investigated to perform optimization in moving horizon state estimation for discrete-time linear and nonlinear systems. Conditions that ensure the stability of the estimation error are established for single and multi iteration schemes with a least-squares cost function that takes into account only a batch of most recent information. Simulation results show the effectiveness of the proposed approaches also in comparison with techniques based on the Kalman filter. [ABSTRACT FROM AUTHOR]

In this note we construct minimax observers for linear stationary Differential-Algebraic Equations (DAE)s with bounded uncertain inputs, given noisy measurements. We prove a new duality principle and show that a finite (infinite) horizon minimax observer exists if and only if the DAE is $\ell$ -impulse observable ($\ell$ -detectable). Remarkably, the regularity of the DAE is not required. [ABSTRACT FROM AUTHOR]

In addition to being observable, systems composed of interconnected subsystems must typically exhibit a particular subsystem structure, if their state is to be estimated successfully by a partition-based moving horizon estimator (PMHE). Suitable subsystem structures—also called system partitionings—can be unknown, may not be desirable for a particular application, or may not exist at all. In this contribution, we present the first PMHE without any restrictions on the system partitioning. We analyze the convergence of its iterations at each time step and the stability of its estimation error dynamics. The benefits of our solution are illustrated on a numerical example. [ABSTRACT FROM AUTHOR]

The fundamental limits of remote estimation of autoregressive Markov processes under communication constraints are presented. The remote estimation system consists of a sensor and an estimator. The sensor observes a discrete-time autoregressive Markov process driven by a symmetric and unimodal innovations process. At each time, the sensor either transmits the current state of the Markov process or does not transmit at all. The estimator estimates the Markov process based on the transmitted observations. In such a system, there is a trade-off between communication cost and estimation accuracy. Two fundamental limits of this trade-off are characterized for infinite horizon discounted cost and average cost setups. First, when each transmission is costly, we characterize the minimum achievable cost of communication plus estimation error. Second, when there is a constraint on the average number of transmissions, we characterize the minimum achievable estimation error. Transmission and estimation strategies that achieve these fundamental limits are also identified. [ABSTRACT FROM AUTHOR]

The paper proposes a technique to estimate the angular velocity of a rigid body from single vector measurements. Compared to the approaches presented in the literature, it does not use attitude information nor rate gyros as inputs. Instead, vector measurements are directly filtered through a nonlinear observer estimating the angular velocity. Convergence is established using a detailed analysis of a linear-time varying dynamics appearing in the estimation error equation. This equation stems from the classic Euler equations and measurement equations. As is proven, the case of free-rotation allows one to relax the persistence of excitation assumption. Simulation results are provided to illustrate the method. [ABSTRACT FROM PUBLISHER]

A novel type of iterative partition-based moving horizon estimators (PMHE) is proposed, the estimates of which approach those of a centralized moving horizon estimator as the number of iterations increases. It uses a deterministic setting and can handle known inputs as well as bounds on the estimated state. We derive conditions on the system, its partitions, and the scalar regularization parameter, which guarantee convergence towards the optimal centralized state estimate as well as stability of the estimation error dynamics, even with a finite number of iterations at each time step. Finally, numerical simulations demonstrate both the features and competitive estimation quality of the proposed method. [ABSTRACT FROM AUTHOR]

State estimation is of great importance in various applications based on wireless networked control systems. Wireless sensor node usually forwards its data to a remote receiver through a series of relay nodes in order to save its limited energy. In this technical note, we investigate the data forwarding strategy design for accurate remote state estimation in multi-hop wireless networks. Based on different computational capability of relay nodes, we first propose two relay strategies, namely, Direct Forwarding Strategy (DFS) and Local Processing and Forwarding Strategy (LFS). Stability condition, estimation performance and energy efficiency of both the two strategies are theoretically analyzed. We further propose an Event-triggered Forwarding Strategy (EFS) which is able to balance the estimation accuracy and relay energy consumption. Numerical examples are employed to demonstrate the effectiveness of our design. [ABSTRACT FROM AUTHOR]

A fault-tolerant observer design methodology is proposed. The aim is to guarantee a minimum level of closed-loop performance under all possible sensor fault combinations while optimizing performance under the nominal, fault-free condition. A novel approach is proposed to tackle the combinatorial nature of the problem, which is computationally intractable even for a moderate number of sensors, by recasting the problem as a robust performance problem, where the uncertainty set is composed of all combinations of a set of binary variables. A procedure based on an elimination lemma and an extension of a semidefinite relaxation procedure for binary variables is then used to derive sufficient conditions (necessary and sufficient in the case of one binary variable) for the solution of the problem which significantly reduces the number of matrix inequalities needed to solve the problem. The procedure is illustrated by considering a fault-tolerant observer switching scheme in which the observer outputs track the actual sensor fault condition. A numerical example from an electric power application is presented to illustrate the effectiveness of the design. [ABSTRACT FROM PUBLISHER]

The integer order differentiation by integration method based on the Jacobi orthogonal polynomials for noisy signals was originally introduced by Mboup, Join and Fliess. We propose to extend this method from the integer order to the fractional order to estimate the fractional order derivatives of noisy signals. Firstly, two fractional order differentiators are deduced from the Jacobi orthogonal polynomial filter, using the Riemann–Liouville and the Caputo fractional order derivative definitions respectively. Exact and simple formulae for these differentiators are given by integral expressions. Hence, they can be used for both continuous-time and discrete-time models in on-line or off-line applications. Secondly, some error bounds are provided for the corresponding estimation errors. These bounds allow to study the design parameters' influence. The noise error contribution due to a large class of stochastic processes is studied in discrete case. The latter shows that the differentiator based on the Caputo fractional order derivative can cope with a class of noises, whose mean value and variance functions are polynomial time-varying. Thanks to the design parameters analysis, the proposed fractional order differentiators are significantly improved by admitting a time-delay. Thirdly, in order to reduce the calculation time for on-line applications, a recursive algorithm is proposed. Finally, the proposed differentiator based on the Riemann–Liouville fractional order derivative is used to estimate the state of a fractional order system and numerical simulations illustrate the accuracy and the robustness with respect to corrupting noises. [ABSTRACT FROM AUTHOR]

Tackling large approximate dynamic programming or reinforcement learning problems requires methods that can exploit regularities of the problem in hand. Most current methods are geared towards exploiting the regularities of either the value function or the policy. We introduce a general classification-based approximate policy iteration (CAPI) framework that can exploit regularities of both. We establish theoretical guarantees for the sample complexity of CAPI-style algorithms, which allow the policy evaluation step to be performed by a wide variety of algorithms, and can handle nonparametric representations of policies. Our bounds on the estimation error of the performance loss are tighter than existing results. [ABSTRACT FROM AUTHOR]

This paper presents a new approach to event-triggered control for nonlinear uncertain systems by using the notion of input-to-state stability (ISS) and the nonlinear small-gain theorem. The contribution of this paper is threefold. First, it is proved that infinitely fast sampling can be avoided if the system is input-to-state stabilizable with the sampling error as the external input and the corresponding ISS gain is locally Lipschitz. No assumption on the existence of known ISS-Lyapunov functions is made in the discussions. Moreover, the forward completeness problem with event-triggered control is studied systematically by using ISS small-gain arguments. Second, the proposed approach gives rise to a new self-triggered sampling strategy for a class of nonlinear systems subject to external disturbances. If an upper bound of the external disturbance is known, then the closed-loop system can be designed to be robust to the external disturbance, and moreover, the system state globally asymptotically converges to the origin if the external disturbance decays to zero. Third, a new design method is developed for event-triggered control of nonlinear uncertain systems in the strict-feedback form. It is particularly shown that the ISS gain with the sampling error as the input can be designed to satisfy the proposed condition for event-triggered control and self-triggered control. [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 note addresses Distributed State Estimation (DSE) over sensor networks. Two existing consensus approaches for DSE, i.e., consensus on information (CI) and consensus on measurements (CM), are combined to provide a novel class of hybrid consensus filters (named Hybrid CMCI) which enjoy the complementary benefits of CM and CI. Novel theoretical results, limitedly to linear systems, on the guaranteed stability of the Hybrid CMCI filters under collective observability and network connectivity are proved. Finally, the effectiveness of the proposed class of consensus filters is evaluated on a target tracking case study with both linear and nonlinear sensors. [ABSTRACT FROM AUTHOR]

We propose new game theoretic approaches to estimate a binary random variable based on sensor measurements that may have been corrupted by a cyber-attacker. The estimation problem is formulated as a zero-sum partial information game in which a detector attempts to minimize the probability of an estimation error and an attacker attempts to maximize this probability. While this problem can be solved exactly by reducing it to the computation of the value of a matrix, this approach is computationally feasible only for a small number of sensors. The two key results of this paper provide complementary computationally efficient solutions to the construction of the optimal detector. The first result provides an explicit formula for the optimal detector but it is only valid when the number of sensors is roughly smaller than two over the probability of sensor errors. In contrast, the detector provided by the second result is valid for an arbitrary number of sensor. While it may result in a probability of estimation error that is $\epsilon$ above the minimum achievable, we show that this error $\epsilon$ is small when the number of sensors is large, which is precisely the case for which the first result does not apply. [ABSTRACT FROM AUTHOR]

This technical note considers remote state estimation subject to limited sensor-estimator communication rate. We propose a stochastic online sensor scheduler for remote state estimation with time-out condition. The decision rule under which the sensor sends data is based on its measurements and a finite-state holding time between the present and the most recent sensor-to-estimator communication instance. This decision process is formulated as an optimization problem, relaxed and solved using generalized geometric programming optimization techniques with a low computational complexity. Moreover, the proposed scheduler is easy to execute, and provides a guaranteed performance which is shown to outperform the optimal offline scheduler. Numerical examples are provided to illustrate the proposed scheduler. [ABSTRACT FROM AUTHOR]

This paper addresses the stability of a Kalman filter when measurements are intermittently available due to constraints in the communication channel between the sensor and the estimator. We give a necessary condition and a sufficient condition, with a trivial gap between them, for the boundedness of the expected value of the estimation error covariance. These conditions are more general than the existing ones in the sense that they only require the state matrix of the system to be diagonalizable and the sequence of packet losses to be a stationary finite order Markov process. Hence, we extend the class of systems for which these conditions are known in two directions, namely, by including degenerate systems, and by considering network models more general than i.i.d. and Gilbert-Elliott. We show that these conditions recover known results from the literature when evaluated for non-degenerate systems under the assumption of i.i.d. or Gilbert-Elliott packet loss models. [ABSTRACT FROM PUBLISHER]

This technical note proposes local exponential observers for systems on linear Lie groups. We study two classes of systems. In the first class, the full state of the system evolves on a linear Lie group and is available for measurement. In the second class, only part of the system's state evolves on a linear Lie group and this portion of the state is available for measurement. In each case, we propose two different observer designs. We show that, depending on the observer chosen, local exponential stability of one of the two observation error dynamics, left- or right-invariant error dynamics, is obtained. For the first class of systems these results are developed by showing that the estimation error dynamics are differentially equivalent to a stable linear differential equation on a vector space. For the second class of system, the estimation error dynamics are almost linear. We illustrate these observer designs on an attitude estimation problem. [ABSTRACT FROM PUBLISHER]