Presence Of Unknown Inputs Research Articles

An adaptive three-stage extended Kalman filter for nonlinear discrete-time system in presence of unknown inputs

Considering the performances of conventional Kalman filter may seriously degrade when it suffers stochastic faults and unknown input, which is very common in engineering problems, a new type of adaptive three-stage extended Kalman filter (AThSEKF) is proposed to solve state and fault estimation in nonlinear discrete-time system under these conditions. The three-stage UV transformation and adaptive forgetting factor are introduced for derivation, and by comparing with the adaptive augmented state extended Kalman filter, it is proven to be uniformly asymptotically stable. Furthermore, the adaptive three-stage extended Kalman filter is applied to a two-dimensional radar tracking scenario to illustrate the effect, and the performance is compared with that of conventional three stage extended Kalman filter (ThSEKF) and the adaptive two-stage extended Kalman filter (ATEKF). The results show that the adaptive three-stage extended Kalman filter is more effective than these two filters when facing the nonlinear discrete-time systems with information of unknown inputs not perfectly known.

Strong detectability and unknown input observer design for a class of networks of systems

Abstract Detectability is the key property which underlies the design of any convergent observer. In this paper a method for analyzing the detectability for a class of networks of systems with unknown inputs is presented, exploiting the definition of indistinguishable trajectories and the structure of the underlying network graph. This analysis yields sufficient conditions for the sensor location in order to ensure the system’s strong detectability in presence of unknown inputs. Based on this analysis a simple (reduced order) unknown-input observer with explicit convergence conditions in terms of system parameters and the sensor locations is proposed and tested in numerical simulations for an illustrative case example of a Markov-chain based epidemic spreading model in a scale-free network with N = 103 nodes.

Unknown Input Observers for Hybrid Linear Systems with State Jumps

This paper investigates the problem of constructing an observer that asymptotically estimates a linear function of the state of a linear plant with state jumps in the presence of unknown inputs. Suitable geometric notions are introduced and discussed in order to deal with this problem. A complete characterization of its solvability, together with a procedure for constructing the observer, is given in geometric terms. A sufficient solvability condition that can be practically checked by a simple procedure is also illustrated. Under mildly restrictive hypothesis, the necessary and sufficient solvability conditions can be practically checked and the observer can be practically constructed.

Prediction of States of Discrete Systems with Unknown Input of the Model Using Compensation

The problem of state prediction for linear dynamic systems with discrete time is considered in the presence of unknown input and inaccurately specified parameters in the model. An algorithm with compensation for the constant component and estimation of the unknown variable input component by the least squares method is suggested. Results of statistical simulation are presented. The algorithm can be used for solving problems of processing information obtained as a result of observations over physical processes.

미지 입력을 가진 기계 시스템을 위한 비선형 관측기 설계

This paper presents the design methodology of an unknown input observer for Lipschitz nonlinear systems with unknown inputs in the framework of convex optimization. We use an unknown input observer (UIO) to consider both nonlinearity and disturbance. By deriving a sufficient condition for exponential stability in the linear matrix inequality (LMI) form, existence of a stabilizing observer gain matrix of UIO will be assured by checking whether the quadratic stability margin of the error dynamics is greater than the Lipschitz constant or not. If quadratic stability margin is less than a Lipschitz constant, the coordinate transformation may be used to reduce the Lipschitz constant in the new coordinates. Furthermore, to reduce the maximum singular value of the observer gain matrix elements, an object function to minimize it will be optimally designed by modifying its magnitude so that amplification of sensor measurement noise is minimized via multi-objective optimization algorithm. The performance of UIO is compared to a nonlinear observer (Luenberger-like) with an application to a flexible joint robot system considering a change of load and disturbance. Finally, it is validated via simulations that the estimated angular position and velocity provide true values even in the presence of unknown inputs.

Reduced‐order observer design for one‐sided Lipschitz time‐delay systems subject to unknown inputs

This study addresses the observer design problem for a class of one-sided Lipschitz time-delay systems in the presence of unknown inputs. The non-linearities are assumed to satisfy the one-sided Lipschitz and quadratically inner-bounded conditions; hence, a wider class of non-linear systems is investigated in this work. A novel approach for the non-linear observer design problem subject to time delays and disturbances is proposed. Both H ∞ observer design and asymptotic observer design with reduced-order are introduced. To deal with the time-delay issue, Wirtinger-based integral inequality, which encompasses the Jensen inequality, is employed to derive less conservative synthesis conditions in linear matrix inequalities form. Two numerical examples are given to illustrate the effectiveness and the edge of the authors' results over other relevant works in the literature.

Application of Input and State Multiple Model Adaptive Estimator for Aircraft Airspeed Approximation

This paper addresses the problem of state estimation in the presence of unknown inputs if the system is dependent on an uncertain parameter. Multiple Model Adaptive Estimation is applied to state and unknown input observers. The theory is evaluated on an aircraft airspeed estimator algorithm. The developed algorithm is based-on linear time invariant (LTI) models of an aircraft linearized at distinct airspeed values. Separate Kalman Filters are designed for aircraft LTI models, run parallel, and the airspeed estimate is the weighted sum of the airspeed estimates provided by the Kalman Filters. Linear and nonlinear test simulations without and with measurement noise proved that the developed algorithm is able to provide accurate airspeed estimates.

New unified [formula omitted] dynamic observer design for linear systems with unknown inputs

In this paper, a unified H∞ dynamic observer (UO) is proposed for a class of linear systems in the presence of unknown inputs and disturbances. It generalizes the existing results on the proportional observer (PO), the proportional integral observer (PIO) and the dynamic observer (DO). The design approach of the UO is derived from the solution of the linear matrix inequality (LMI), based on the new dynamic observer formulation and the solution of the algebraic constraints obtained from the unbiased estimation error. A numerical example is provided to show the applicability and the performance of our results.

The stability analysis of the adaptive three-stage Kalman filter

An adaptive three-stage Kalman filter, which can track the fault and unknown inputs, is proposed by extending the special linear models of fault and unknown inputs to two general linear models without requirement of matrices ranks. It can be used when the fault and unknown inputs are not perfectly known. In this paper, the detailed stability analysis of the adaptive three-stage Kalman filter, which is applied for state and fault estimation of linear systems in the presence of unknown inputs, is investigated. Furthermore, an illustrative example is given to apply this filter and the performances of this filter are also verified by simulation.

Observers design for switched discrete-time singular time-delay systems with unknown inputs

This paper addresses the state estimation problem for a class of switched discrete-time singular systems simultaneously subject to state delays, unknown inputs (UIs) and arbitrary switching sequences. A mode-dependent observer is constructed, and, in view of the observation performance and the realizability, two class of design methods are proposed. The first class is based on the principle of exact decoupling, which allows the observer to perfectly reconstruct the system state regardless the presence of UIs under stringent rank conditions. The second one, with the aid of introducing L2-attenuation of UIs to the state estimation error, relaxes the rank constraints required in the first class method while permitting the observer to give an unknown input approximately decoupled state estimation. In both methods, by defining an appropriate switched Lyapunov function and using the linear matrix inequality technique, sufficient conditions for the existence of the observer are given, and the convergence rate of the state estimation error is proved to be exponential. Finally, two numerical examples are given to show the effectiveness of the developed theoretical results.

Exact State Estimation for Linear Systems with Unbounded Disturbances

A finite-time observer is designed for linear invariant systems in the presence of unknown inputs or disturbances with unavailable upper bound. The main condition for designing the observer is strongly detectability. Geometric control theory is used to decompose the given system into two parts: strongly observable subsystem and strongly detectable subsystem. Through a series of transformations, the former can be partitioned into two parts: affected and unaffected by unknown inputs (UI-free and UI-dependent), and then the states can be exactly estimated via time-delayed observer in pre-defined time. The nonstrongly observable subsystem can be observed asymptotically. Without the upper bound of disturbances, the observer ensures that the convergence time can be set arbitrarily. A numerical example illustrates the effective of the proposed estimation schemes.

State Estimation for Linear Discrete Systems with Unknown Input Using Compensations

The problem of construction of state estimations for linear systems with discrete time is considered in the presence of unknown input in the model of the object. A modification of the Kalman filter algorithm using compensation for the constant component and estimation of the unknown changing input component by the least squares method is suggested. Results of statistical simulation are presented. The algorithm can be used for solving problems of processing of information obtained as a result of observations over physical processes.

Attitude Control of Chaotic Satellite with Unknown Input and uncertainties based on Sliding Control

attitude control of missiles, spacecraft and satellites is essential; in order to remain them fixed in space to perform their missions accurately. The attitude equation of a satellite is a six- dimensional nonlinear system which includes some types of nonlinear behavior such as periodic trajectory, chaotic dynamics. In this paper, a sliding mode control design method for stabilization of the attitude chaotic satellites with unknown inputs and uncertainties. Using Lyapunov theory, the stability control system is proven. Simulation results show that the proposed controller can be chaotic satellite attitude in the presence of unknown inputs and uncertainties will converge to the unstable equilibrium points. In this section, the satellite system and the chaotic dynamics are studied. In (16) the problem of satellite attitude control with redundant thrusters, and in (17) satellite attitude control with an uneven inertia distribution has been investigated. However, given that the satellite attitude motion under external disturbances becomes chaotic mode, the control satellite system will be very complex. So, be very careful satellite control system is designed. In (13) and (14) satellite attitude control of chaotic behavior has been investigated. The orientation of the satellite at a given point can be locally described in terms of three angles

Hybrid sliding mode observer for switched linear systems with unknown inputs

This paper addresses the state observation and unknown input estimation of a class of switched linear systems with unknown inputs. This class of systems may have modes in which the state is not fully observable. A state transformation allows implementing two suitable reduced-order observers. The first one, based on second order sliding mode techniques, is proposed to reconstruct the discrete state in the presence of unknown inputs. The second one, based on gathering partial information from individual modes of the switched system and on higher order sliding mode techniques, is introduced to estimate the continuous state. Then, the observer injection signal of the first second order sliding mode observer is used to estimate the unknown inputs. Simulation results highlight the efficiency of the proposed method.

High-order sliding mode observers for nonlinear autonomous switched systems with unknown inputs

The state observation and unknown input identification problems are studied for a class of nonlinear autonomous switched systems. A bank of observers are designed using the high-order sliding mode techniques. The robustness of the high-order sliding mode observers is exploited to provide exact reconstruction of the continuous state and the discrete state even in the presence of unknown inputs. The value of the equivalent injection is used for identification of unknown inputs. Simulation results support the proposed method.

Fault, State, and Unknown Input Reconstruction in Nonlinear Systems Using Sliding Mode Observers

In this paper, a new approach to estimation of unknown inputs and faults in a class of nonlinear systems is presented. The approach is based on the design of a cascade connection of two sliding mode observers. The first observer is used for the estimation of state and unknown inputs and the second is used for the fault detection and isolation. An important feature of the proposed approach is that the state trajectories do not leave the sliding manifold even in the presence of unknown inputs and faults. This allows for faults and unknown inputs to be completely reconstructed based on the information retrieved from the equivalent output injection signals. The proposed approach is tested on a nonlinear model of single link flexible joint robot system.

Sensor Fault Detection and Diagnosis of a Process Using Unknown Input Observer

In this paper, a robust sensor fault detection and isolation (FDI) method based on the unknown input observer (UIO) approach is presented. The basic principle of unknown input observers is to decouple disturbances from the state estimation error. A single full-order observer is designed to detect sensor faults in the presence of unknown inputs (disturbances). By doing so, we generate a residual, a weighted output of the state estimation error, decoupled from disturbances. The resulting robust (in the sense of disturbances) residual can be used for fault detection. Although this scheme has successful fault detection, using one observer is not successful in fault isolation. Therefore, a robust sensor fault isolation observer scheme is proposed. In order to evaluate its ability, the presented method is adopted to detect and isolate sensor faults of a highly nonlinear dynamic system. The faulty behavior of output sensors in a jacketed continuous stirred tank reactor (CSTR), around operating point, is investigated. Simulation results show that model uncertainties and disturbances can be distinguished from a response to a sensor fault.

Design of Nonlinear Unknown Input Observer for Process Fault Detection

The objective of this paper is to design a robust fault detection scheme for nonlinear systems. A novel procedure for the design of a nonlinear unknown input observer (UIO) is proposed. The basic principle of unknown input observers is to decouple disturbances from the state estimation error. In the proposed method, the linear UIO design algorithm is extended to nonlinear systems and then observer gain is obtained using unscented transformation (UT). To illustrate the efficiency of the proposed method, it is adopted to detect sensor faults of a highly nonlinear dynamic system. The faulty behavior of output sensors in a jacketed continuous stirred tank reactor (CSTR) is investigated. A single full-order observer is designed to detect sensor faults in the presence of unknown inputs (disturbances). Simulation results show that disturbances and, therefore, a certain degree of model uncertainties can be distinguished from a response to a sensor fault.

Identification and Fuzzy Controller Design for Nonlinear Uncertain Systems with Input Time-Delay

This paper considers the identification and fuzzy controller design for nonlinear uncertain systems in presence of unknown input time-delay. Firstly, a time-delay Takagi-Sugeno-Kang (TSK) type fuzzy neural system (TDFN) is proposed to identify a class of nonlinear input time-delay systems. The input- output signals of nonlinear systems are used to identify the system dynamics and unknown time-delay, and then construct the system in the form TSK-fuzzy time-delay model. Each fuzzy rule has a corresponding linear system with an input time-delay as the consequent part. Based on parallel distribution compensation (PDC) approach, the Smith predictor compensation and dominate pole assignment technique are then adopted to design the fuzzy PID controller. Several simulations are shown to demonstrate the effectiveness and control performance of the proposed approach.

Finite-Time Converging Jump Observer for Linear Switched Systems with Unknown Inputs

Abstract The observation problem for linear switched systems with unknown inputs is addressed and solved via sliding mode technique. The proposed observer provides a finite time converging estimate of the state vector despite the presence of unknown inputs. The design procedure, which requires the knowledge of the discrete state of the switched system, is based on the principles of disturbance decoupling and hierarchical observer output injection. In order to cope with the switching nature of the plant under observation, state jumps in the observer state space are enforced intentionally. The implementation of an additional observer allows the reconstruction of the unknown inputs, which may be important in the framework of fault detection. A numerical example illustrates the effectiveness of the suggested technique.