Robust State Estimation for Linear Systems

1993 ◽  
Vol 115 (1) ◽  
pp. 193-196
Author(s):  
S. S. Garimella ◽  
K. Srinivasan
Keyword(s):  
Dynamic System ◽  
State Estimation ◽  
Real Time ◽  
Linear Systems ◽  
Upper Bound ◽  
Estimation Error ◽  
System Model ◽  
Linear Dynamic ◽  
Modeling Errors ◽  
System States

Real-time state estimation of a linear dynamic system using an observer, in the presence of modeling errors in the system model used by the observer and uncertainty in the initial system states, is considered here. A guideline for designing observers for multioutput systems is established, based on an expression for an upper bound on the norm of the state estimation error derived in this paper. An example is presented to illustrate the usefulness of this guideline.

scholarly journals Real-Time Hydraulic Interval State Estimation for Water Transport Networks: a Case Study

2017 ◽  
Author(s):  
Stelios G. Vrachimis ◽  
Demetrios G. Eliades ◽  
Marios M. Polycarpou
Keyword(s):  
State Estimation ◽  
Real Time ◽  
Water Distribution ◽  
Estimation Error ◽  
Distribution Networks ◽  
Water Levels ◽  
Water Distribution Networks ◽  
Unaccounted For Water ◽  
Tank Water

Abstract. Hydraulic state estimation in water distribution networks is the task of estimating water flows and pressures in the pipes and nodes of the network based on some sensor measurements. This requires a model of the network, as well as knowledge of demand outflow and tank water levels. Due to modeling and measurement uncertainty, standard state-estimation may result in inaccurate hydraulic estimates without any measure of the estimation error. This paper describes a methodology for generating hydraulic state bounding estimates based on interval bounds on the parametric and measurement uncertainties. The estimation error bounds provided by this method can be applied to estimate the unaccounted-for water in water distribution networks. As a case study, the method is applied to a transport network in Cyprus, using actual data in real-time.

Filtering of Linear Systems With Unknown Inputs

2003 ◽  
Vol 125 (3) ◽  
pp. 482-485 ◽  
Author(s):  
Hosam E. Emara-Shabaik
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Linear Systems ◽  
Gaussian Noise ◽  
Unknown Inputs ◽  
Fast Tracking ◽  
Disturbance Estimation ◽  
Simulation Results ◽  
System States ◽  
Unknown Disturbance

State estimation of linear systems under the influence of both unknown deterministic inputs as well as Gaussian noise is considered. A Kalman like filter is developed which does not require the estimation of the unknown inputs as is customarily practiced. Therefore, the developed filter has reduced computational requirements. Comparative simulation results, under the influence of various types of unknown disturbance inputs, show the merits of the developed filter with respect to a conventional Kalman filter using disturbance estimation. It is found that the developed filter enjoys several practical advantages in terms of accuracy and fast tracking of the system states.

Event-based finite horizon state estimation for stochastic systems with network-induced phenomena

2018 ◽  
Vol 41 (6) ◽  
pp. 1580-1589 ◽  
Author(s):  
Li Liu ◽  
Aolei Yang ◽  
Wenju Zhou ◽  
Xiaowei Tu ◽  
Gang Wang ◽  
...  
Keyword(s):  
State Estimation ◽  
Stochastic Systems ◽  
Estimation Error ◽  
Estimation Method ◽  
Finite Horizon ◽  
Drop Out ◽  
System Model ◽  
Transmission Delays ◽  
Error Covariance ◽  
Compensation Approach

This paper investigates a finite horizon state estimation problem for a class of discrete-time stochastic systems with random transmission delays and out-of-order packets of data. Employing an event-driven signal-choosing scheme of logic zero-order-holder (LZOH), a system model is established synthetically in a unified form considering the network-induced phenomena, to drop out-of-order packets and improve system performance. By virtue of the established system model, a novel minimum error covariance matrix for the augmented state-space is obtained from the estimated variance constraint. With the aid of a finite horizon, the upper boundary of estimation error covariance is introduced during the information transmission from sensor to estimator, and the appropriate filter parameters are probed. To improve the estimation performance and alleviate the computation burden, an estimation-based compensation approach for random transmission delays is proposed using the received valid signals. Finally, the effectiveness and applicability of the proposed state estimation method are illustrated by a numerical simulation.

scholarly journals Simultaneous Robust Fault and State Estimation for Linear Discrete-Time Uncertain Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Feten Gannouni ◽  
Fayçal Ben Hmida
Keyword(s):  
Convex Optimization ◽  
State Estimation ◽  
Discrete Time ◽  
Upper Bound ◽  
Optimization Problem ◽  
Estimation Error ◽  
Original System ◽  
Error Variance ◽  
Linear Matrix ◽  
Convex Optimization Problem

We consider the problem of robust simultaneous fault and state estimation for linear uncertain discrete-time systems with unknown faults which affect both the state and the observation matrices. Using transformation of the original system, a new robust proportional integral filter (RPIF) having an error variance with an optimized guaranteed upper bound for any allowed uncertainty is proposed to improve robust estimation of unknown time-varying faults and to improve robustness against uncertainties. In this study, the minimization problem of the upper bound of the estimation error variance is formulated as a convex optimization problem subject to linear matrix inequalities (LMI) for all admissible uncertainties. The proportional and the integral gains are optimally chosen by solving the convex optimization problem. Simulation results are given in order to illustrate the performance of the proposed filter, in particular to solve the problem of joint fault and state estimation.

scholarly journals Resilient State Estimation for Control Systems Using Multiple Observers and Median Operation

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Heegyun Jeon ◽  
Sungmin Aum ◽  
Hyungbo Shim ◽  
Yongsoon Eun
Keyword(s):  
State Estimation ◽  
Estimation Error ◽  
Point Of View ◽  
Design Stage ◽  
Necessary Condition ◽  
Computationally Efficient ◽  
Sensor Noise ◽  
Linear Dynamic Systems ◽  
True State ◽  
System States

This paper addresses the problem of state estimation for linear dynamic systems that is resilient against malicious attacks on sensors. By “resiliency” we mean the capability of correctly estimating the state despite external attacks. We propose a state estimation with a bank of observers combined through median operations and show that the proposed method is resilient in the sense that estimated states asymptotically converge to the true state despite attacks on sensors. In addition, the effect of sensor noise and process disturbance is also considered. For bounded sensor noise and process disturbance, the proposed method eliminates the effect of attack and achieves state estimation error within a bound proportional to those of sensor noise and disturbance. While existing methods are computationally heavy because online solution of nonconvex optimization is needed, the proposed approach is computationally efficient by using median operation in the place of the optimization. It should be pointed out that the proposed method requires the system states being observable with every sensor, which is not a necessary condition for the existing methods. From resilient system design point of view, however, this fact may not be critical because sensors can be chosen for resiliency in the design stage. The gained computational efficiency helps real-time implementation in practice.

scholarly journals Real-time hydraulic interval state estimation for water transport networks: a case study

2018 ◽  
Vol 11 (1) ◽  
pp. 19-24 ◽  
Author(s):  
Stelios G. Vrachimis ◽  
Demetrios G. Eliades ◽  
Marios M. Polycarpou
Keyword(s):  
State Estimation ◽  
Real Time ◽  
Water Distribution ◽  
Estimation Error ◽  
Distribution Networks ◽  
Water Levels ◽  
Water Distribution Networks ◽  
Unaccounted For Water ◽  
Tank Water

Abstract. Hydraulic state estimation in water distribution networks is the task of estimating water flows and pressures in the pipes and nodes of the network based on some sensor measurements. This requires a model of the network as well as knowledge of demand outflow and tank water levels. Due to modeling and measurement uncertainty, standard state estimation may result in inaccurate hydraulic estimates without any measure of the estimation error. This paper describes a methodology for generating hydraulic state bounding estimates based on interval bounds on the parametric and measurement uncertainties. The estimation error bounds provided by this method can be applied to determine the existence of unaccounted-for water in water distribution networks. As a case study, the method is applied to a modified transport network in Cyprus, using actual data in real time.

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