Unknown Input Observer Design Research Articles

Unknown input observer design for uncertain nonlinear systems with time-varying delay: application to online fault estimation

This paper recommends an unknown input observer (UIO) for uncertain nonlinear time-delay dynamics that enables online fault estimation. The main novelty of this paper is designing UIO to fault estimation for nonlinear systems that include time-varying delays in states and time-varying uncertainties in all matrices of the system. The other advantage of the proposed method is that both abrupt and incipient faults are considered. Furthermore, the state and output disturbances, as well as actuator and sensor faults, are considered. The Lyapunov–Krasovskii concept is used to guarantee the stability of the augmented closed-loop system. Calculating observer gains and stabilisation of estimation error dynamics are accomplished by utilising a new linear matrix inequality (LMI). Finally, an uncertain continuous-stirred tank reactor (CSTR) with a time-varying delay is used to evaluate the performance of the suggested technique.

Data-driven reduced-order unknown-input observers

In this paper we propose a data-driven approach to the design of reduced-order unknown-input observers (rUIOs). We first recall the model-based solution, by assuming a problem set-up slightly different from those traditionally adopted in the literature, in order to be able to easily adapt it to the data-driven scenario. Necessary and sufficient conditions for the existence of a reduced-order unknown-input observer, whose matrices can be derived from a sufficiently rich set of collected historical data, are first derived and then proved to be equivalent to the ones obtained in the model-based framework. Finally, a numerical example is presented, to validate the effectiveness of the proposed scheme.

Proportional multi-integral observer design for Takagi–Sugeno systems with unmeasurable premise variables: Conservatism reduction via polyquadratic Lyapunov function

In this paper, we present the design of a new unknown-input observer for Takagi–Sugeno fuzzy systems with unmeasurable premise variables. The work proposes an improvement of the simultaneous state and unknown-input observer. The main idea is to consider a non-quadratic Lyapunov function in order to reduce the conservatism of its quadratic counterpart. Moreover, the mean value theorem is used to express the error dynamics in a way that reduces the conservatism of the bounded terms assumptions. The stability conditions are formulated as Bilinear Matrix Inequalities. To address these, we propose an iterative algorithm based on linear matrix inequalities, which transforms the Bilinear form into a sets of linear matrix inequalities. Finally, two examples are given to highlight the performance of the proposed observer.

A dissipativity-based robust fault diagnosis approach for clusters of small satellites

This study explores distributed fault diagnosis strategies for clusters of diverse small satellites, encompassing variations in Lipschitz-based non-linear dynamic systems and environmental factors. The investigation focuses on identifying rapid time-varying fault magnitudes and profiles across cluster agents interconnected by a directed graph. The analysis acknowledges uncertainties linked with state-coupled disturbances in the system model. Utilizing satellite communication topologies, a comprehensive augmented vector is formulated for individual satellites to diagnose both their states and faults, along with the states and faults of entire satellite clusters. Integrating an Unknown Input Observer (UIO) effectively untangles error dynamics from state-coupled disturbances. The UIO design is approached under two distinct conditions: one satisfying the case-matching criterion and the other that does not. The computation of observer gains employs the application of Linear Matrix Inequalities (LMIs). Furthermore, an adaptive robust fault estimator is proposed for scenarios where the matching condition is not met. This approach integrates dissipativity principles and is benchmarked against the H∞ framework. Simulation outcomes demonstrate the effectiveness of the proposed methodology. Specifically, the results show fault estimation across three clusters comprising seven small satellites. Notably, observers can be strategically positioned within select satellites rather than all, thereby mitigating the computational load for clusters with numerous satellites. This approach retains diagnostic efficacy while enhancing computational efficiency.

Unknown input observer for Takagi-Sugeno implicit models with unmeasurable premise variables

<p>Recent years have seen a great deal of interest in implicit nonlinear systems, which are used in many different engineering applications. This study is dedicated to presenting a new method of fuzzy unknown inputs observer design to estimate simultaneously both non-measurable states and unknown inputs of continuous-time nonlinear implicit systems defined by Takagi-Sugeno (T-S) models with unmeasurable premise variables. The suggested observer is based on the singular value decomposition approach and rewritten the continuous-time T-S implicit models into an augmented fuzzy system, which gathers the unknown inputs and the state vector. The exponential convergence condition of the observer is established by using the Lyapunov theory and linear matrix inequalities are solved to determine the gains of the observer. Finally, the effectiveness of the suggested method is then assessed using a numerical application. It demonstrates that the estimated variables and the unknown input converge to the real variables accurately and quickly (less than 0.5 s).</p>

Design of unknown input observer for discrete-time Markov jump systems with unknown input in both state equation and output equation

The problem of unknown input observer design for discrete-time nonlinear generalized Markov jump systems is studied. First, like a normal system, the whole nonlinear system is transformed into a local linear system, and then a large number of linear system theories can be applied to solve related problems. Second, in the observer design of general discrete-time Markov jump systems, only the unknown input in the state equation is usually considered. In this paper, the unknown input is considered in both the state equation and the output equation. The state estimation error system is derived by defining the error. The non-uniform Lyapunov functional is selected to stabilize the estimation error system using the Lyapunov theory. The sufficient conditions for the stability of the system are obtained and transformed into the feasibility problem of linear matrix inequality. The problem of unknown input observer design for discrete-time nonlinear generalized Markov jump systems is solved using MATLAB software. Finally, a numerical example of two rules and two modes is used to verify the effectiveness and feasibility of the proposed unknown input observer.

Unknown Input Observer Design for a Class of Semilinear Hyperbolic Systems With Dynamic Boundary Conditions

The problem of unknown input observer design is considered for coupled PDE/ODE systems subject to incremental sector bounded nonlinearities and unknown boundary inputs. Assuming available measurements at the boundary of the distributed domain, the synthesis of the unknown input observer is based on Lyapunov methods and recast in terms of some matrix inequalities. Numerical simulations support and confirm the theoretical findings, illustrating the robust estimation performances of the proposed nonlinear unknown input observer.

Design of linear unknown input observers for sensor fault estimation in nonlinear systems

A systematic method for the design of linear unknown input observers (UIO) for sensor fault estimation in nonlinear systems is developed. Necessary and sufficient conditions for the existence of linear UIOs for nonlinear systems are derived. As long as these conditions are satisfied, we obtain explicit design formulas for the observer. The method is applied to a non-isothermal chemical reactor (CSTR) subject to a concentration sensor fault.

Unknown input observers for time-varying delay Takagi–Sugeno fuzzy systems with unmeasured nonlinear consequents

This paper investigates the problem of unknown input observer (UIO) design for Takagi–Sugeno (TS) fuzzy systems with time-varying delay. For observer design, all the unmeasured nonlinearities are isolated in the nonlinear consequent parts of TS fuzzy systems. This allows dealing with the well-known issue related to unmeasured premise variables for TS fuzzy observer design in a more effective fashion via the mean value theorem. Using the unknown input (UI) decoupling technique, no a priori information on the UI is needed for the proposed TS fuzzy observer design, which can guarantee the asymptotic estimations of both the system state and the unknown input. Employing a fuzzy Lyapunov–Krasovskii functional with a suitable augmented vector, the effect of time-varying delay on the estimation error dynamics is taken into account in the observer design. Numerical examples are presented to demonstrate the effectiveness of the proposed fuzzy UIO design method for nonlinear time-varying delay systems.

Design of unknown input observer for discrete-time Takagi Sugeno implicit systems with unmeasurable premise variables

In this study, an unknown input observer (UIO) is developed in explicit form to estimate unmeasurable states and unknown inputs (UIs) for nonlinear implicit systems represented by the discrete-time Takagi-Sugeno implicit systems (DTSIS) in the case of unmeasurable premise variables. The method employed is based on singular value decomposition (SVD) and augmenting the state vector, which is formed partly by the system state and partly by the UIs. The convergence of the augmented state estimation error is provided by a Lyapunov function ending with solving the linear matrix inequalities (LMI). An application to a model of the rolling disc is considered to evaluate the effectiveness of the developed approach. It appears that estimated variables converge to the true variables quickly and accurately.

Prescribed-Time Unknown Input Observers Design by Using Periodic Delayed Output With Application to Fault Estimation

This article considers the design of prescribed-time unknown input observers (PTUIOs) for linear systems, i.e., observers that estimate the state of a linear system with unknown inputs at a prescribed finite time. To this end, the generalized inverse is used first to transform a form amenable for observer design. Then, PTUIOs are designed by using the periodic delayed output so that their estimation errors converge to zero at a prescribed time. Both full-order and reduced-order PTUIOs are considered. For the reduced-order observer design, an alternative approach is also adopted, based on a transformation to a generalization of the normal form. In addition, the proposed PTUIOs are applied to estimate faults. Finally, two examples are given to illustrate the effectiveness of the proposed approaches.

Unknown input observer design for T-S fuzzy systems with time-varying bounded delays

Unknown input observer design for T-S fuzzy systems with time-varying bounded delays

LPV Unknown Input Observer-Based Estimation of Driver Intervention Torque and Vehicle Dynamics for Human-Machine Shared Driving

This paper presents an unknown input observer (UIO)-based method to jointly estimate the vehicle dynamics and the driver torque within the framework of human-machine shared driving. To deal with the time-varying vehicle longitudinal speed, the vehicle dynamics is represented as a linear parameter-varying (LPV) model. Based on an unknown input (UI) decoupling technique, an LPV observer is designed, which can guarantee an asymptotic estimation performance of both the vehicle dynamics and the driver torque. Via Lyapunov stability theory, we propose sufficient conditions, expressed in terms of linear matrix inequalities, for LPV unknown input observer design. High-fidelity Simulink-CarSim co-simulations are carried out to show the effectiveness of the proposed LPV UIO-based estimation method for driver-automation shared driving dynamics. Moreover, a comparative study is performed with a recent LPV method to highlight the practical interest of the new estimation solution.

Unknown input observer design for T-S fuzzy systems with time-varying bounded delays

Unknown input observer design for T-S fuzzy systems with time-varying bounded delays

Unknown input observer design for linear time-invariant multivariable systems based on a new observer normal form

In various applications in the field of control engineering, the estimation of the state variables of dynamic systems in the presence of unknown inputs plays an important role. Existing methods require the so-called observer matching condition to be satisfied, rely on the boundedness e variables or exhibit an increased observer order of at least twice the plant order. In this article, a novel observer normal form for strongly observable linear time-invariant multivariable systems is proposed. In contrast to classical normal forms, the proposed approach also takes the unknown inputs into account. The proposed observer normal form allows for the straightforward construction of a higher-order sliding mode observer, which ensures global convergence of the estimation error within finite time even in the presence of unknown bounded inputs. Its application is not restricted to systems which satisfy the aforementioned limitations of already existing unknown input observers. The proposed approach can be exploited for the reconstruction of unknown inputs with bounded derivative and robust state-feedback control, which is shown by means of a tutorial example. Numerical simulations confirm the effectiveness of the presented work.

Towards Kinematics From Motion: Unknown Input Observer and Dynamic Extension Approach

This letter addresses an unknown input observer design to estimate simultaneously the 3D depth of a tracked image feature and the camera linear velocity using a low cost monocular camera and inertial sensor. The camera kinematic model is at first, augmented via the dynamic extension approach then described as a quasi-Linear Parameter Varying (qLPV) model. Further, the qLPV system is transformed into Takagi-Sugeno (T-S) form with unmeasured premise variables. The error convergence analysis is performed based on Lyapunov theory and Input to State Stability (ISS) property to ensure the boundedness of the state estimation error. Gains that guarantee the asymptotic stability of the estimation error can be properly computed by means of Linear Matrix Inequalities (LMIs). Finally the proposed approach is validated using synthetic data.

Aggressive maneuver oriented integrated fault-tolerant control of a 3-DOF helicopter with experimental validation

In this paper, an integrated fault-tolerant control (FTC) strategy is proposed for unmanned helicopter system under aggressive maneuvers. In order to handle the effect of strong nonlinearities caused by large pitch angle, linear parameter varying (LPV) technique is adopted in the helicopter system modeling. Then, LPV model-based unknown input observer (UIO) design is conducted to simultaneously realize actuator faults and system state estimation, based on which an active fault-tolerant controlleris also constructed. Considering bi-directional robustness interactions between fault as well as state observer and active fault-tolerant controller, an integrated fault-tolerant controller design is further developed. Besides, actuator saturation is also considered in LPV modeling as well as integrated fault-tolerant controller design of the helicopter system. In order to guarantee the robust performance of proposed integrated fault tolerant controller design of helicopter system, energy-to-energy strategy is adopted. And the linear matrix inequality (LMI) toolbox is utilized for gain calculation. Finally, comparative experimental tests are carried out to show the effectiveness and advantages of the proposed FTC strategy.

Discrete-time LPV Systems with Inexact Scheduling Parameters: an Unknown Input Observer Design approach

In this paper, a novel unknown input observer (UIO) design for discrete-time linear parameter-varying (LPV) with inexact scheduling parameters is addressed. The proposed approach is particularly relevant as most LPV design conditions require that the time-varying parameters of the system are completely known and real-time available. Therefore, such strategies do not present adequate formulations to deal with such types of uncertainty. Moreover, UIOs have significant applications in different areas, such as fault detection and isolation problems. Existence conditions for the UIO are provided in order to properly handle the mismatch along with the presence of unknown inputs in the LPV system. The design conditions are based on an input-to-state stability approach obtained from a parameter-dependent Lyapunov function and are cast in the form of Linear Matrix Inequalities. The effectiveness of the proposed methods is illustrated using a numerical example.

Design of unknown input observer for discrete time nonlinear generalized Markov jump systems under fault conditions

In this paper, the design problem of unknown input observer for a class of nonlinear discrete time Markov jump systems has been studied. The state equation of the system with unknown input and actuator faults is considered. The unknown input observer has a relatively novel structure and can be applied to nonlinear discrete time Markov jump systems to estimate the system state and fault at the same time. Second, the design feasibility conditions of the unknown input observer based on Lyapunov function are given. Furthermore, the conditions are transformed into a set of linear matrix inequality conditions, which can be used to solve the parameters easily by using the related software toolbox. Finally, an example of nonlinear tunneling diode circuit is given to verify the feasibility and effectiveness of the proposed method.

Unknown input observer design for vehicle lateral dynamics described by Takagi–Sugeno fuzzy systems

AbstractThis article discusses the problem of an unknown input observer for nonlinear lateral dynamic systems. Takagi–Sugeno fuzzy models have been used to represent the vehicle lateral system with parameters uncertain. The observer used is well suited to estimate the vehicle state and actuator/sensor faults, simultaneously. By using Finsler's lemma, the conditions obtained are expressed through linear matrix inequality constraints. Finally, the results of the simulation clearly show the importance and effectiveness of the proposed approaches.