66,110 research outputs found
Comparing Kalman Filters and Observers for Power System Dynamic State Estimation with Model Uncertainty and Malicious Cyber Attacks
Kalman filters and observers are two main classes of dynamic state estimation
(DSE) routines. Power system DSE has been implemented by various Kalman
filters, such as the extended Kalman filter (EKF) and the unscented Kalman
filter (UKF). In this paper, we discuss two challenges for an effective power
system DSE: (a) model uncertainty and (b) potential cyber attacks. To address
this, the cubature Kalman filter (CKF) and a nonlinear observer are introduced
and implemented. Various Kalman filters and the observer are then tested on the
16-machine, 68-bus system given realistic scenarios under model uncertainty and
different types of cyber attacks against synchrophasor measurements. It is
shown that CKF and the observer are more robust to model uncertainty and cyber
attacks than their counterparts. Based on the tests, a thorough qualitative
comparison is also performed for Kalman filter routines and observers.Comment: arXiv admin note: text overlap with arXiv:1508.0725
Simultaneous Mode, Input and State Estimation for Switched Linear Stochastic Systems
In this paper, we propose a filtering algorithm for simultaneously estimating
the mode, input and state of hidden mode switched linear stochastic systems
with unknown inputs. Using a multiple-model approach with a bank of linear
input and state filters for each mode, our algorithm relies on the ability to
find the most probable model as a mode estimate, which we show is possible with
input and state filters by identifying a key property, that a particular
residual signal we call generalized innovation is a Gaussian white noise. We
also provide an asymptotic analysis for the proposed algorithm and provide
sufficient conditions for asymptotically achieving convergence to the true
model (consistency), or to the 'closest' model according to an
information-theoretic measure (convergence). A simulation example of
intention-aware vehicles at an intersection is given to demonstrate the
effectiveness of our approach.Comment: Submitted to SIAM Journal on Control and Optimizatio
Nonlinear Bayesian Estimation: From Kalman Filtering to a Broader Horizon
This article presents an up-to-date tutorial review of nonlinear Bayesian
estimation. State estimation for nonlinear systems has been a challenge
encountered in a wide range of engineering fields, attracting decades of
research effort. To date, one of the most promising and popular approaches is
to view and address the problem from a Bayesian probabilistic perspective,
which enables estimation of the unknown state variables by tracking their
probabilistic distribution or statistics (e.g., mean and covariance)
conditioned on the system's measurement data. This article offers a systematic
introduction of the Bayesian state estimation framework and reviews various
Kalman filtering (KF) techniques, progressively from the standard KF for linear
systems to extended KF, unscented KF and ensemble KF for nonlinear systems. It
also overviews other prominent or emerging Bayesian estimation methods
including the Gaussian filtering, Gaussian-sum filtering, particle filtering
and moving horizon estimation and extends the discussion of state estimation
forward to more complicated problems such as simultaneous state and
parameter/input estimation
Dynamic State Estimation under Cyber Attacks: A Comparative Study of Kalman Filters and Observers
Utilizing highly synchronized measurements from synchrophasors, dynamic state
estimation (DSE) can be applied for real-time monitoring of smart grids.
Concurrent DSE studies for power systems are intolerant to unknown inputs and
potential attack vectors --- a research gap we will fill in this work.
Particularly, we (a) present an overview of concurrent estimation techniques,
highlighting key deficiencies, (b) develop DSE methods based on cubature Kalman
filter and dynamic observers, (c) rigorously examine the strengths and
weaknesses of the proposed methods under attack-vectors and unknown inputs, and
(d) provide comprehensive recommendations for DSE. Numerical results and
in-depth remarks are also presented
The Unknown Input Observer and its Advantages with Examples
This brief memo reviews the theory of Unknown Input Observers (UIO) for state
estimation in systems subject to disturbance inputs that are not known a
priori. One main advantage of the UIO is that the observer structure naturally
decouples the plant inputs from the state estimation process. This advantage is
highlighted in three example dynamic systems commonly found in control theory.
It is shown that the estimation error for all three systems asymptotically
approaches zero by application of the UIO under the influence of dynamic
disturbances
An autoregressive (AR) model based stochastic unknown input realization and filtering technique
This paper studies the state estimation problem of linear discrete-time
systems with stochastic unknown inputs. The unknown input is a wide-sense
stationary process while no other prior informaton needs to be known. We
propose an autoregressive (AR) model based unknown input realization technique
which allows us to recover the input statistics from the output data by solving
an appropriate least squares problem, then fit an AR model to the recovered
input statistics and construct an innovations model of the unknown inputs using
the eigensystem realization algorithm (ERA). An augmented state system is
constructed and the standard Kalman filter is applied for state estimation. A
reduced order model (ROM) filter is also introduced to reduce the computational
cost of the Kalman filter. Two numerical examples are given to illustrate the
procedure.Comment: 14 page
A Gaussian process latent force model for joint input-state estimation in linear structural systems
The problem of combined state and input estimation of linear structural
systems based on measured responses and a priori knowledge of structural model
is considered. A novel methodology using Gaussian process latent force models
is proposed to tackle the problem in a stochastic setting. Gaussian process
latent force models (GPLFMs) are hybrid models that combine differential
equations representing a physical system with data-driven non-parametric
Gaussian process models. In this work, the unknown input forces acting on a
structure are modelled as Gaussian processes with some chosen covariance
functions which are combined with the mechanistic differential equation
representing the structure to construct a GPLFM. The GPLFM is then conveniently
formulated as an augmented stochastic state-space model with additional states
representing the latent force components, and the joint input and state
inference of the resulting model is implemented using Kalman filter. The
augmented state-space model of GPLFM is shown as a generalization of the class
of input-augmented state-space models, is proven observable, and is robust
compared to conventional augmented formulations in terms of numerical
stability. The hyperparameters governing the covariance functions are estimated
using maximum likelihood optimization based on the observed data, thus
overcoming the need for manual tuning of the hyperparameters by
trial-and-error. To assess the performance of the proposed GPLFM method,
several cases of state and input estimation are demonstrated using numerical
simulations on a 10-dof shear building and a 76-storey ASCE benchmark office
tower. Results obtained indicate the superior performance of the proposed
approach over conventional Kalman filter based approaches.Comment: Submitted to Mechanical Systems and Signal Processin
Simultaneous state and exogenous input estimation for nonlinear systems using boundary-layer sliding mode observers
While sliding mode observers (SMOs) using discontinuous relays are widely
analyzed, most SMOs are implemented computationally using a continuous
approximation of the discontinuous relays. This approximation results in the
formation of a boundary layer in a neighborhood of the sliding manifold in the
observer error space. Therefore, it becomes necessary to develop methods for
attenuating the effect of the boundary layer and guaranteeing performance
bounds on the resulting state estimation error. In this paper, a method is
proposed for constructing boundary-layer SMOs (BL-SMOs) with prescribed state
estimation error bounds. The BL-SMO formulation is then extended to
simultaneously estimate exogenous inputs (disturbance signals in the state and
output vector fields), along with the system state. Two numerical examples are
presented to illustrate the effectiveness of the proposed approach
Motion Planning of Uncertain Ordinary Differential Equation Systems
This work presents a novel motion planning framework, rooted in nonlinear programming theory, that treats uncertain fully and under-actuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it, and poor robustness and suboptimal performance result if it’s not accounted for in a given design. In this work uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach enables the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, the proposed framework allows the user to pose, and answer, new design questions related to uncertain dynamical systems.
Specifically, the new framework is explained in the context of forward, inverse, and hybrid dynamics formulations. The forward dynamics formulation, applicable to both fully and under-actuated systems, prescribes deterministic actuator inputs which yield uncertain state trajectories. The inverse dynamics formulation is the dual to the forward dynamic, and is only applicable to fully-actuated systems; deterministic state trajectories are prescribed and yield uncertain actuator inputs. The inverse dynamics formulation is more computationally efficient as it requires only algebraic evaluations and completely avoids numerical integration. Finally, the hybrid dynamics formulation is applicable to under-actuated systems where it leverages the benefits of inverse dynamics for actuated joints and forward dynamics for unactuated joints; it prescribes actuated state and unactuated input trajectories which yield uncertain unactuated states and actuated inputs.
The benefits of the ability to quantify uncertainty when planning the motion of multibody dynamic systems are illustrated through several case-studies. The resulting designs determine optimal motion plans—subject to deterministic and statistical constraints—for all possible systems within the probability space
Disturbance Observer-based Robust Control and Its Applications: 35th Anniversary Overview
Disturbance Observer has been one of the most widely used robust control
tools since it was proposed in 1983. This paper introduces the origins of
Disturbance Observer and presents a survey of the major results on Disturbance
Observer-based robust control in the last thirty-five years. Furthermore, it
explains the analysis and synthesis techniques of Disturbance Observer-based
robust control for linear and nonlinear systems by using a unified framework.
In the last section, this paper presents concluding remarks on Disturbance
Observer-based robust control and its engineering applications.Comment: 12 pages, 4 figure
- …