Dawei Shi

Event-triggered maximum likelihood state estimation

The event-triggered state estimation problem for linear time-invariant systems is considered in the framework of Maximum Likelihood (ML) estimation in this paper. We show that the optimal estimate is parameterized by a special time-varying Riccati equation, and the computational complexity increases exponentially with respect to the time horizon. For ease in implementation, a one-step event-based ML estimation problem is further formulated and solved, and the solution behaves like a Kalman filter with intermittent observations. For the one-step problem, the calculation of upper and lower bounds of the communication rates from the process side is also briefly analyzed. An application example to sensorless event-based estimation of a DC motor system is presented and the benefits of the obtained one-step event-based estimator are demonstrated by comparative simulations.

An event-triggered approach to state estimation with multiple point-and set-valued measurements

Abstract In this work, we consider state estimation based on the information from multiple sensors that provide their measurement updates according to separate event-triggering conditions. An optimal sensor fusion problem based on the hybrid measurement information (namely, point- and set-valued measurements) is formulated and explored. We show that under a commonly-accepted Gaussian assumption, the optimal estimator depends on the conditional mean and covariance of the measurement innovations, which applies to general event-triggering schemes. For the case that each channel of the sensors has its own event-triggering condition, closed-form representations are derived for the optimal estimate and the corresponding error covariance matrix, and it is proved that the exploration of the set-valued information provided by the event-triggering sets guarantees the improvement of estimation performance. The effectiveness of the proposed event-based estimator is demonstrated by extensive Monte Carlo simulation experiments for different categories of systems and comparative simulation with the classical Kalman filter.

On Set-Valued Kalman Filtering and Its Application to Event-Based State Estimation

Motivated by challenges in state estimation with event-based measurement updates, the properties of the exact and approximate set-valued Kalman filters with multiple sensor measurements for linear time-invariant systems are investigated in this work. First, we show that the exact and the proposed approximate set-valued filters are independent of the fusion sequence at each time instant. Second, the boundedness of the size of the set of estimation means is proved for the exact set-valued filter. For the approximate set-valued filter, if the closed-loop matrix is contractive, then the set of estimation means has a bounded size asymptotically; otherwise a nonsingular linear transform is constructed such that the size of the set of estimation means for the transformed states is asymptotically bounded. Third, the effect of set-valued measurements on the size of the set of estimation means is analyzed and conditions for performance improvement in terms of smaller size of the set of estimation means are proposed. Finally, the results are applied to event-based estimation, which allow the event-triggering conditions to be designed by considering requirements on performance and communication rates. The efficiency of the proposed results are illustrated by simulation examples and comparison with the approximate event-based MMSE estimator and the Kalman filter with intermittent observations.

Optimal Linear Cyber-Attack on Remote State Estimation

Recent years have witnessed the surge of interest of security issues in cyber-physical systems. In this paper, we consider malicious cyber attacks in a remote state estimation application where a smart sensor node transmits data to a remote estimator equipped with a false data detector. It is assumed that all the sensor data can be observed and modified by the malicious attacker and a residue-based detection algorithm is used at the remote side to detect data anomalies. We propose a linear deception attack strategy and present the corresponding feasibility constraint which guarantees that the attacker is able to successfully inject false data without being detected. The evolution of the estimation error covariance at the remote estimator is derived and the degradation of system performance under the proposed linear attack policy is analyzed. Furthermore, we obtain a closed-form expression of the optimal attack strategy among all linear attacks. Comparison of attack strategies through simulated examples are provided to illustrate the theoretical results.

Event-based state estimation of discrete-state hidden Markov models

The state estimation problem for hidden Markov models subject to event-based sensor measurement updates is considered in this work, using the change of probability approach. We assume the measurement updates are transmitted through wired or wireless communication networks. For the scenarios with reliable and unreliable communication channels, analytical expressions for the probability distributions of the states conditioned on all the past point- and set-valued measurement information are obtained. Also, we show that the scenario with a lossy channel, but without the event-trigger, can be treated as a special case of the reliable channel results. Based on these results, closed-form expressions for the estimated communication rates under the original probability measure are presented, which are shown to be the ratio between a weighted 1 -norm and the 1 -norm of the unnormalized conditional probability distributions of the states under the new probability measures constructed. Implementation issues are discussed, and the effectiveness of the results is illustrated by numerical examples and comparative simulations.

Event-based state estimation of linear dynamic systems with unknown exogenous inputs

In this work, an event-based optimal state estimation problem for linear-time varying systems with unknown inputs is investigated. By treating the unknown input as a process with a non-informative prior, the event-based minimum mean square error (MMSE) estimator is obtained in a recursive form. It is shown that for the general time-varying case, the closed-loop matrix of the optimal event-based estimator is exponentially stable and the estimation error covariance matrix is asymptotically bounded for each sample path of the event-triggering process. The results are also extended to the multiple sensor scenario, where each sensor is allowed to have its own event-triggering condition. The efficiency of the proposed results is illustrated by a numerical example and comparative simulation with the MMSE estimators obtained based on time-triggered measurements. The results are potentially applicable to event-based secure state estimation of cyber-physical systems.

Optimal periodic scheduling of sensor networks: A branch and bound approach

Abstract A periodic scheduling problem for sensor networks with communication constraints is considered for state estimation. The solvability of the problem is first discussed and a necessary and sufficient condition is presented based on the notion of periodic detectability. Since the calculation of the average prediction error variance requires the computation of the symmetric periodic positive-semidefinite stabilizing (SPPS) solutions to the periodic Riccati equations, a moving approximate cost function is proposed, which gradually converges to the exact cost function. Also, it is shown that the upper bound of the approximation error is independent of the SPPS solutions and converges to zero exponentially. Based on these results, a branch and bound based algorithm is proposed to compute the optimal periodic schedule, and the idea is to iteratively trim the set of schedules that are potentially robust optimal with respect to the approximation error. If the optimal schedule is unique, the algorithm solves the periodic scheduling problem by exploring a finite number of nodes. Moreover, given an arbitrary nonzero suboptimality specification, the algorithm results in a suboptimal schedule set containing all the optimal schedules at a manageable computation effort. A numerical example is presented to illustrate the proposed results.

Approximate optimal periodic scheduling of multiple sensors with constraints

A constrained periodic multiple-sensor scheduling problem is considered in this paper. For each sensor, constraints on dwell time and activation times are imposed. At each time instant, only one sensor can update its measurement with the estimator; and the objective is to minimize the average state estimation error. An approximation framework is proposed to calculate the objective function, which transforms the original scheduling problem into an Approximate Optimal Scheduling Problem (AOSP). An upper bound on the approximation error is presented to evaluate the performance of the framework. To solve the AOSP, a necessary condition is first proposed on the optimal schedules. When no constraints on activation times exist, a dynamic programming based algorithm is devised to identify the optimal schedule with polynomial computational complexity. When activation-time constraints exist, we show that the AOSPs can be solved by solving traveling salesman problems. Examples are provided to illustrate the proposed results.

Event-based state estimation of linear dynamical systems: Communication rate analysis

This work presents results on communication rate analysis for event-based state estimation schemes. An event-based estimator in the form of the Kalman filter with intermittent observations is first introduced, based on which time-varying upper and lower bounds on the expectation of the communication rate are developed. For stable systems, time-invariant upper and lower bounds are given. For sensors whose measurement values are scalars, the exact expression for the expectation of the communication rate is obtained. Numerical examples are presented to illustrate the results. It is shown that the developed results are rich enough to be generalized to recover existing results obtained for event-based minimum mean squared error estimates and estimates under more general event-triggering schemes.

Event-Based Robust Sampled-Data Model Predictive Control: A Non-Monotonic Lyapunov Function Approach

In this paper, two event-based robust sampled-data model predictive control (MPC) strategies are proposed based on the non-monotonic Lyapunov function approach for continuous-time systems with disturbances. Each event-triggering mechanism consists of the event-based MPC law and the triggering conditions. We show that although the proposed event-triggering conditions are only checked at the sampling instants and the control law is piecewise constant, the feasibility of the event-based sampled-data MPC algorithm and the stability of the closed-loop system are guaranteed in continuous time. Besides, the implementation issue is discussed, and we show that the proposed triggering conditions can be checked rapidly without obviously increasing the computational burden. Finally, an application to a nonholonomic robot system is provided to illustrate the effectiveness of the proposed results.