Unknown Exogenous Inputs Research Articles

SVD-Based Parameter Identification of Discrete-Time Stochastic Systems with Unknown Exogenous Inputs

This paper addresses the problem of parameter identification for discrete-time stochastic systems with unknown exogenous inputs. These systems form an important class of dynamic stochastic system models used to describe objects and processes under a high level of a priori uncertainty, when it is not possible to make any assumptions about the evolution of the unknown input signal or its statistical properties. The main purpose of this paper is to construct a new SVD-based modification of the existing Gillijns and De Moor filtering algorithm for linear discrete-time stochastic systems with unknown exogenous inputs. Using the theoretical results obtained, we demonstrate how this modified algorithm can be applied to solve the problem of parameter identification. The results of our numerical experiments conducted in MATLAB confirm the effectiveness of the SVD-based parameter identification method that was developed, under conditions of unknown exogenous inputs, compared to maximum likelihood parameter identification when exogenous inputs are known.

Parameter identification of the linear discrete-time stochastic systems with unknown exogenous inputs

The paper addresses a parameter identification problem for linear discrete-time stochastic systems with unknown exogenous inputs. Such systems are considered when solving practical problems related to the measurements processing in the case when it is impossible to do any assumptions about the evolution of unknown input signal or its statistical characteristics that can change over time. We consider a class of discrete time linear stochastic systems with unknown exogenous inputs, where an additional source of a priori uncertainty of the system model is introduced, namely, the unknown parameter, on the elements of which the system model matrices can depend. This formulation of the parameter identification problem under the conditions of unknown inputs and the presence of random noises describes a high degree of uncertainty of a discrete time linear stochastic system. We propose a novel solution to this problem based on the construction of a new instrumental identification criterion. Minimization of this criterion allows for evaluating the unknown system model parameters simultaneously with the estimating of the state vector and unknown exogenous inputs of the system. Numerical experiments confirm the validity and efficiency of the proposed parameter identification method.

On distributed fusion estimation with stochastic scheduling over sensor networks

The paper deals with the distributed fusion estimation for linear time-varying systems over sensor networks, in which stochastic sensor scheduling and unknown exogenous inputs are taken into account. In the stochastic sensor scheduling, expensive and cheap channels are used to respectively transmit the high-precision data and the low-precision quantized data. Based on the stochastic scheduling scheme, a recursive minimum mean square error (MMSE) estimator is proposed against the unknown inputs. Then, a distributed fusion estimator is presented by combining local estimates and covariances from all sensors, relying on the covariance intersection (CI) fusion rule. Sufficient conditions are established to ensure that the proposed fusion estimator is stable with the stochastically ultimately bounded estimation error. Finally, a target tracking example is given to show the effectiveness of the proposed method.

On controlled mode discernibility for nonlinear hybrid systems with unknown exogenous input

This paper considers the mode discernibility and controlled mode discernibility for nonlinear hybrid systems with unknown switchings and unknown exogenous input, motivated by its potential applications to fault detection and isolation, cyber-security, and robust control. We formally define the mode discernibility and controlled mode discernibility, and then characterize these properties from a geometric perspective. Specifically, we review and complement the concept of controlled invariance for nonlinear systems, based on which a new concept called strongly controlled invariance is proposed as a tool to characterize the controlled mode discernibility. Besides the general characterization of controlled mode discernibility, we discuss some commonly considered special nonlinearities, and demonstrate that the discerning control design problem can be formulated as a quadratic game for some cases.

Intensive care unit occupancy predictions in the COVID-19 pandemic based on age-structured modelling and differential flatness

The COVID-19 pandemic confronts governments and their health systems with great challenges for disease management. In many countries, hospitalization and in particular ICU occupancy is the primary measure for policy makers to decide on possible non-pharmaceutical interventions. In this paper a combined methodology for the prediction of COVID-19 case numbers, case-specific hospitalization and ICU admission rates as well as hospital and ICU occupancies is proposed. To this end, we employ differential flatness to provide estimates of the states of an epidemiological compartmental model and estimates of the unknown exogenous inputs driving its nonlinear dynamics. A main advantage of this method is that it requires the reported infection cases as the only data source. As vaccination rates and case-specific ICU rates are both strongly age-dependent, specifically an age-structured compartmental model is proposed to estimate and predict the spread of the epidemic across different age groups. By utilizing these predictions, case-specific hospitalization and case-specific ICU rates are subsequently estimated using deconvolution techniques. In an analysis of various countries we demonstrate how the methodology is able to produce real-time state estimates and hospital/ICU occupancy predictions for several weeks thus providing a sound basis for policy makers.

Output-feedback control of precision motion systems with uncertain nonlinearities

We propose output-feedback tracking control with an extended high-gain observer-based feedback control for a class of precision motion systems that include unknown rate-dependent hysteresis nonlinearities with linear dynamics. The proposed control system has a number of features; namely, (i) it can guarantee ultimate boundedness of the tracking error, where the ultimate bound can be made arbitrarily small, for any given initial conditions and for bounded unknown exogenous inputs and modeling parameters, (ii) it provides the possibility of shaping the transient response of the closed-loop system as desired, and (iii) the proposed technique is non-adaptive inversion free technique. To verify the effectiveness of these results, first simulation results are provided for an iron pendulum in a magnetic field system. Then, the output-feedback approach is also applied experimentally to a piezotube micropositioning actuator for a precision motion control.

Distributed consensus-based estimation with unknown inputs and random link failures

This paper focuses on the distributed state estimation problem for linear time-varying systems with unknown exogenous inputs and random link failures. The unknown inputs appear both in the system equation and the measurement equation, and no information of them is available. The communication links between sensor nodes are unreliable and suffer from random link failures governed by a set of independent Bernoulli processes. By modeling the unknown inputs as processes with non-informative priors, a novel minimum mean square error (MMSE) estimator is derived. Then, a distributed consensus-based estimation algorithm is developed by repeatedly fusing local information from the neighbors possessing the successful link communications, in the sense that each sensor exchanges the local information obtained by performing the local MMSE estimation with its neighbors. Further, sufficient conditions are given to guarantee the stability of the proposed distributed estimator, in which the estimation error in each sensor is uniformly bounded in mean square. Finally, numerical examples are provided to show the effectiveness of the proposed technique.

Event-triggered robust state estimation for systems with unknown exogenous inputs

An event-triggered robust state estimation problem for linear time-varying systems subject to Gaussian noises and non-stochastic unknown exogenous inputs is investigated in this work. To design the estimator, the state estimation problem is formulated as an optimization problem with a risk-sensitive cost function. This problem is solved by constructing a reference probability measure, under which the cost function has a simpler form and an information state can be developed. The obtained robust state estimator is shown to have a recursive form parameterized by a Riccati-type time-varying matrix equation. The effectiveness of the proposed event-based robust state estimator is illustrated with numerical examples.

Iterative learning control for semi‐linear distributed parameter systems based on sensor–actuator networks

In this study, the iterative learning control (ILC) method is considered for tracking control of a class of distributed parameter systems (DPSs) based on sensor-actuator networks (SANs) with the unknown exogenous input and the measurement noise, which are described by a semi-linear parabolic partial differential equation. The D-type ILC algorithm is presented to control DPSs with non-collocated SANs. When the unknown exogenous input and the measurement noise are bounded, the upper bounds of output errors are obtained via the Bellman-Gronwall lemma and semi-group theory, respectively. The authors prove that the output errors converge to zero in the absence of the unknown exogenous input and the measurement noise. Two examples are given to show the effectiveness of the proposed D-type ILC scheme.

Robust sensitive fault detection and estimation for single-rate and multirate nonlinear sampled-data systems

This paper investigates the problem of fault detection and estimation for nonlinear sampled-data systems in the presence of unknown exogenous inputs. Both cases of single-rate and multirate sampling are treated and general observer-based frameworks are provided using discrete-time approximation to estimate fault signals of any sources. We show that these frameworks are input-to-error stable with respect to the estimation error and can simultaneously enhance robustness against unknown inputs and sensitivity to faults in a mixed H−∕H∞ sense for the unknown exact discrete-time model of the plant. Our results are then applied to a class of Lipschitz nonlinear systems with a refined Euler approximate model to derive sampled-data fault estimation techniques where stability and H−∕H∞ optimization are ensured using linear matrix inequalities (LMIs). Simulation results of a flexible joint robot illustrate the effectiveness of the proposed methodologies.

State and unknown input observers for nonlinear systems with delayed measurements

The use of connected devices or humans-in-the-loop for measuring outputs of dynamical systems inevitably produces time-varying measurement delays. These delays can lead to instability or severe degradation of system performance. In this paper, linear matrix inequality-based sufficient conditions are proposed for the design of state and unknown input observers based on delayed measurements for a class of nonlinear systems, where the nonlinearities are characterized by incremental multiplier matrices. The proposed observer is guaranteed to perform at specified operational levels in the presence of unknown exogenous inputs acting on the states and measurement outputs. Sufficient conditions are also provided for the estimation of these unknown inputs to a specified degree of accuracy. The potential of the proposed approach is illustrated via estimation of enzyme kinetics.

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.

Dynamic modeling of neuronal responses in fMRI using cubature Kalman filtering

This paper presents a new approach to inverting (fitting) models of coupled dynamical systems based on state-of-the-art (cubature) Kalman filtering. Crucially, this inversion furnishes posterior estimates of both the hidden states and parameters of a system, including any unknown exogenous input. Because the underlying generative model is formulated in continuous time (with a discrete observation process) it can be applied to a wide variety of models specified with either ordinary or stochastic differential equations. These are an important class of models that are particularly appropriate for biological time-series, where the underlying system is specified in terms of kinetics or dynamics (i.e., dynamic causal models). We provide comparative evaluations with generalized Bayesian filtering (dynamic expectation maximization) and demonstrate marked improvements in accuracy and computational efficiency. We compare the schemes using a series of difficult (nonlinear) toy examples and conclude with a special focus on hemodynamic models of evoked brain responses in fMRI. Our scheme promises to provide a significant advance in characterizing the functional architectures of distributed neuronal systems, even in the absence of known exogenous (experimental) input; e.g., resting state fMRI studies and spontaneous fluctuations in electrophysiological studies. Importantly, unlike current Bayesian filters (e.g. DEM), our scheme provides estimates of time-varying parameters, which we will exploit in future work on the adaptation and enabling of connections in the brain.

Adaptive Regulation in Switched Bimodal Systems: An Experimental Evaluation

This paper presents experimental results on the adaptive exact output regulation in a switched bimodal mechanical system subject to unknown sinusoidal exogenous inputs representing reference or disturbance signals. The adaptive regulator design exploits the Q parameterization of regulators for the switched system, and where the Q parameter is tuned online to yield the desired regulator. The proposed adaptive regulator is evaluated on an experimental setup motivated by the flying height regulation problem in hard disk drives. In the experimental setup, the tip of a flexible beam is supposed to maintain a constant separation with respect to a surface with an unknown profile, while also being subject to an unknown disturbance force. The system exhibits a switching behaviour depending on whether contact takes place between the surface to be tracked and the tip of the beam. The experimental results successfully demonstrate the effectiveness of the proposed approach in achieving exact output regulation against unknown sinusoidal exogenous inputs and in the presence of switching in the system dynamics.

Identification of Unknown Exogenous Input to Stochastic Linear Systems via Pseudomeasurement Approach

Identification of Unknown Exogenous Input to Stochastic Linear Systems via Pseudomeasurement Approach

Observer-based Identification of Unknown Exogenous Input via Pseudomeasurement Approach

A novel approach to identify the unknown time and magnitude of exogenous stepwise input is proposed by introducing an idea of pseudomeasurement with regard to the unknown magnitude. The efficacy of the proposed approach is verified by simulation studies.

Sensor-Only Noncausal Blind Identification of Pseudo Transfer Functions

Motivated by passive health monitoring applications, we consider blind identification where only sensor measurements are available. The goal is to identify a pseudo transfer function (PTF) between two sensors in the presence of an unknown initial state and unknown exogenous input. For this problem, we choose one sensor to be the pseudo input to the system and we delay the second sensor, treating it as the pseudo output.We show that the order of the pseudo-transfer function is no larger than one higher than the order of the system. We demonstrate this method on a two-degree-of-freedom mass-spring-damper system and validate the identified PTFs by comparing them with analytical results.

Identification of Unknown Exogenous Input of Stochastic Linear Systems via Pseudomeasurement Approach

Identification of Unknown Exogenous Input of Stochastic Linear Systems via Pseudomeasurement Approach

擬似観測量の導入による線形確率システムの未知外生入力の同定

A joint method is proposed for estimating the systems state and identifying the unknown exogenous input to the stochastic dynamical systems by introducing an idea of pseudomeasurement. Both state estimation and parameter identification are processed by the Kalman filter, incorporating the pseudomeasurements. As unknown exogenous input, two kind of inputs-stepwise and impulse inputs-are investigated, and several simulation studies are presented in order to show the efficacy of introducing the pseudomeasurements.

Two-stage Kalman estimator with unknown exogenous inputs

This paper presents a two-stage estimator for bias and state filtering in discrete-time stochastic linear systems affected by unknown inputs or disturbances. We show that the state estimate can be expressed as X k/k= X ̃ k/k+β k/kb k/k where X ̃ k/k is a bias-free state estimate and b k/ k the optimal estimate of constant bias. The proposed two-stage estimator is based on an alternate derivation of the unbiased minimum variance estimator with unknown exogenous inputs developed by Darouach and Zasadzinski (1997, Automatica 33, 717–719).