Simultaneous Output-Only Identification of Physical Parameters and Unknown Inputs for Linear Mechanical Systems

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 information 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. One numerical example is given to illustrate the procedure.

Formation-containment tracking for general linear multi-agent systems with a tracking-leader of unknown control input

In this paper an effective approach for the identification of stochastic structural systems from multiple-excitation multiple-response forced vibration data, is introduced. The proposed approach represents a novel extension of the method of Lee and Fassois (1990b), that enables it to: (a) Operate on either vibration displacement, velocity, or acceleration data records, and, (b) perform accurate analysis of the estimated structural model by using a currently introduced exact and physically meaningful Dispersion Analysis methodology. These new features, combined with its other important properties, make the proposed approach not only capable of overcoming the limitations of current techniques, but, also, a comprehensive procedure for multiple-excitation multiple-response stochastic structural dynamics identification. The excellent performance characteristics of the proposed approach are finally verified via numerical simulations with structural systems characterized by well-separated and closely-spaced modes, as well as data corrupted at various noise-to-signal ratios. Comparisons with the Eigensystem Realization Algorithm (ERA), through which the limitations of deterministic methods are illustrated, are also presented.

The robot localization problem is typically solved using state estimation techniques, where process and sensing inaccuracies are invariably present. Moreover, disturbances in the sensing and actuating mechanisms add to the uncertainties. Any system may degrade over time, and its parameter values may be ambivalently known. Cumulatively, all these sources of errors and uncertainties are considered as unknown inputs. This work aims to address the unknown inputs using a robust state (pose in the robot localization problem) estimator. The proposed robust state estimator deals with the unknown inputs such that the solution of the estimator is constrained in a way that warrants unbiased state estimates in the presence of the unknown inputs. This article explores the formulation of these constraints and the development of a constrained state estimator for a system, where the unknown inputs appear in both the state transition map (i.e., system model) and the state-output map (i.e., measurement model). The theoretical development of such a strategy stems from the localization problem of a wheeled mobile robot. The residuals of the constrained state estimator developed contain information about the unknown inputs. We conceive a recursive least squares strategy to estimate the unknown inputs simultaneously with the states using this information. Using simulations and experimental studies, we demonstrate the adequacy of our strategy for a differential drive robot.

The Dynamic Regulation of Linear Discrete-time Systems with Unknown Input (A Design Method Using Adaptive State Observer)

This paper extends previous work on robust two-stage Kalman filter (RTSKF) for systems with unknown inputs affecting both the system state and the output. By making use of an augmented known input model, an augmented unknown input model, an unknown input error dynamics model, and the previously proposed RTSKF, a unified extension of the RTSKF is further proposed to enhance the unknown input filtering performance. Through the global optimality analysis technique, the conditions under which the unknown input filter and the system state estimator of the RTSKF can both achieve the globally optimal filtering performances are provided. An application of this new RTSKF to functional filtering problem is addressed.

Using the theory of non-commutative rings , the delay identification problem of nonlinear time-delay systems with unknown inputs is studied. Necessary and sufficient conditions are proposed to judge the identifiability of the delay, where two different cases are discussed for the dependent and independent outputs, respectively. After that, necessary and sufficient conditions are given to analyze the causal and non-causal observability for nonlinear time-delay systems with unknown inputs .

Due to possible distortion contained in frequency-domain data, system identification methods based on data-matching alone do not guarantee stable models. This is a model of a linear system from its frequency response data. It is an improvement and an extension of previous work. The method first identifies a matrix-fraction description of the transfer function matrix of the system from data. Then, through forming a multivariable observable or controllable canonical form, the method separates and replaces the unstable subsystem by a stable subsystem having approximately the same frequency response. Finally, it calculates the Markov parameters of the resulting model and obtains a state-space model through the Eigensystem Realization Algorithm.

A robust three stage Kalman filtering problem is investigated in this article for non‐linear systems with stochastic non‐linearities, random faults and intermittent missing measurements. Therefore, a more general system model is governed in which unknown stochastic non‐linearities are considered in both the system state and measurement equations. The fault terms are included by stochastic coefficients. Also, the sensor measurements occur in a random behaviour that encounters stochastic missing of data for each sensor. Both faults and unknown inputs are covered in the proposed filter. Moreover, the robust features of the developed estimator resolve the problems arising from the need for accurate models of faults and unknown inputs. Furthermore, any predetermined knowledge about the statistical characteristics of the above factors is not required. The augmented filters are mostly used to provide the fault diagnosis features, however, in the current work, this filter is decoupled to reduce the computational volume attributed to this approach. It is proved that the estimation error is ultimately bounded despite different stochastic terms and inaccurate information about the fault and unknown inputs. Finally, an illustrative example is proposed to demonstrate the effectiveness of the developed method.

In this paper, we deal with residual vector generation for fault detection problems in linear systems via unknown input observer (UIO) when the so-called observer matching condition is not satisfied. Based on the relative degree between unknown input and output, a vector of the auxiliary output is introduced so that the observer matching condition is satisfied with respect to the vector. Auxiliary outputs are related to the derivatives of measured signals. However, differentiation leads to excessive amplification of measurement noise. A dynamically equivalent configuration of linear systems is developed using successive integrations to avoid differentiation. As such, auxiliary outputs are constructed without differentiation. Then, the equivalent dynamic system and its corresponding auxiliary outputs are used to generate the residual vector via an exponentially converging UIO. Fault detection in the generated residual vector is also investigated. Finally, the effectiveness of the proposed method is shown via numerical simulation.

Unknown input observers (UIO) are well-known in the literature for linear systems, in particular in the fault detection and identification area. Their particularity rests in the possibility of obtaining an exact asymptotic estimation of the state or a functional of it despite of completely unknown input disturbances. However, conditions for this to be possible are very restrictive, what reduces considerably the applicability and usefulness of UIOs. In the paper a method to reduce the severity of such conditions is proposed. The cause for the highly restrictive conditions for UIOs lies in the fact that the unknown input is assumed to be completely arbitrary, i.e. no knowledge about it is assumed. However, in practice some information about them is available, and one could use it to design an observer that is robust to such kinds of inputs. We propose the use of a linear model of the unknown inputs and an observer robust to such kinds of inputs is designed. This reduces the necessary conditions for its existence. It is intuitively clear that the more information on the disturbances is known the less restrictive the conditions for the existence of a robust observer are, as is shown in the paper.

The stability analysis of the adaptive three-stage Kalman filter

Galerkin approximation in modeling of controlled distributed-parameter flexible systems

In this paper, a differential neural network (DNN) implemented as a robust observer estimates the dynamics of perturbed uncertain nonlinear systems affected by exogenous unknown inputs. In the first stage, the identification error converges into a neighborhood around the origin. Then, the second-order sliding mode supertwisting algorithm implemented as a robust exact differentiator reconstructed the unknown inputs. The approach proposed in this paper can be applied in the case of full access to the state vector (identification problem) and in the case of partial access to the state vector (estimation problem). In the second case, the nonlinear system under study must have well-defined full relative degree with respect to the unknown input. Numerical examples showed the effectiveness of the proposed algorithm. The first example tested the DNN working as an identifier into a mathematical model describing the dynamics of a spatial minisatellite. The second example (with a DNN implemented as an observer) tested the methodology of this paper over a single link flexible robot manipulator represented in a canonical (Brunovsky) form. In both examples, the mathematical models served as data generators in the testing of the neural networks. Even when not exact mathematical description of both models was used in the input estimation, the accuracy obtained with the DNN is comparable with the case of applying a high-order differentiator with complete knowledge of the plant.

This brief investigates vortex formation control problem for linear multiagent systems with unknown leader input and external disturbances. This brief proposes a distributed control protocol with antisymmetric matrix which can adjust the interaction between agents to realize the vortex formation of multiagent system. Each agent only communicates with their neighbor agents through the communication topology without requiring the whole system to be fully connected, which makes the control protocol more suitable for large-scale systems. The unknown bounded external disturbance and the input information of leader that may be encountered in practical application are considered in the protocol design. A control term related to the symbolic function is introduced to deal with bounded external disturbances and unknown leader input signal, which can deal with more complex external environment and uncooperative leader in practical applications. Finally, a numerical example is presented to verify the proposed protocol.