Augmented State Vector Research Articles

Observer‐based fault reconstructions and fault‐tolerant control designs for uncertain switched systems with both actuator and sensor faults

This study considers the problems of the simultaneous estimations of the states, actuator and sensor faults and the design of observer-based fault-tolerant control (FTC) for a class of uncertain switched systems. First, by treating the system state, actuator fault and sensor fault as an augmented state vector, a descriptor system is constructed, where the output equation contains no faults in form. Second, the relationships between the preconditions of the original system and the descriptor system are investigated in detail, under which a reduced-order observer, which can estimate the original system states, actuator faults and sensor faults simultaneously without suffering from the influence of the disturbance, is developed. Third, based on the state estimations given by the reduced-order observer, a state-fault feedback fault-tolerant controller is designed based on an optimising H ∞ performance index and the gains are computed by linear matrix inequalities (LMIs). Finally, an electrical circuit example is given to show the effectiveness of the proposed methods.

Design of multiobserver for nonlinear systems represented by fuzzy T–S models with sensor faults

This paper deals with the estimation of sensor faults for nonlinear systems represented by a Takagi–Sugeno (T–S) fuzzy model. The basic idea is to introduce an augmented state vector which groups together the states of the fuzzy T–S model and the sensor faults. In order to ensure the robustness of the proposed multiobserver and guarantee the convergence conditions, analysis and stability study are based on the candidate Lyapunov function and the formulation of Linear Matrix Inequality (LMI). The impact of the derivation of sensor faults has been attenuated using the $$H_{\infty }$$ performance in the proposed multiobserver. To illustrate the validation of this observer, an academic example will be introduced in this work.

A Local Unscented Transform Kalman Filter for Nonlinear Systems

AbstractThis paper proposes an efficient data assimilation approach based on the sigma-point Kalman filter (SPKF). With a potential for nonlinear filtering applications, the proposed approach, designated as the local unscented transform Kalman filter (LUTKF), is similar to the SPKF in that the mean and covariance of the nonlinear system are estimated by propagating a set of sigma points—also referred to as ensemble members—generated using the scaled unscented transformation (SUT), while making no assumptions with regard to nonlinear models. However, unlike the SPKF, the LUTKF can reduce the influence of observations on distant state variables by employing a localization scheme to suppress spurious correlations between distant locations in the error covariance matrix. Moreover, while the SPKF uses the augmented state vector constructed by concatenating the model states, model noise, and measurement noise, the system state for the LUTKF is not augmented with the random noise variables, thereby providing an accurate state estimate with relatively few sigma points. In sensitivity experiments executed with a 40-variable Lorenz system, the LUTKF required only three sigma points to prevent filter divergence for linear/nonlinear measurement models. Comparisons of the LUTKF and the local ensemble transform Kalman filters (LETKFs) reveal the advantages of the proposed filter in situations that share common features with geophysical data assimilation applications. In particular, the LUTKF shows considerable benefits over LETKFs when assimilating densely spaced observations that are related nonlinearly to the model state and that have high noise levels—such as the assimilation of remotely sensed data from satellites and radars.

Stabilization of Interval Type-2 Fuzzy-Based Reliable Sampled-Data Control Systems.

This article investigates the stabilization problem of the Takagi-Sugeno (T-S) fuzzy-based interval type-2 (IT-2) reliable sampled-data control system. Different from the existing studies, the information for the entire sampling interval with a relation of the augmented state vectors is considered for designing the reliable sampled-data control of IT-2 T-S fuzzy systems. In this regard, we construct the suitable looped Lyapunov-Krasovskii functional (LKF) with the information of the fuzzy membership function that feeds back the time derivative of the membership function to derive sufficient conditions. These sufficient conditions are established in the form of linear matrix inequalities (LMIs), which ensure the global asymptotic stability of T-S fuzzy systems under the designed control technique. Finally, the applicability and superiority of developed reliable sampled-data control techniques were validated by three practical systems.

On discrete‐time LPV control using delayed Lyapunov functions

AbstractThis paper presents new stabilization conditions for discrete‐time linear parameter‐varying systems in the form of linear matrix inequalities. The use of Lyapunov functions with dependence on delayed scheduling parameters is introduced. In addition, a lifted condition based on a Lyapunov function with dependence on delayed scheduling parameters, constructed in terms of an augmented state vector that takes into account a generic number of higher‐order shifted states, is presented. Numerical examples are provided to illustrate the advantages of the proposed approach when compared to other techniques from the literature.

A Novel Approach to State and Unknown Input Estimation for Takagi–Sugeno Fuzzy Models With Applications to Fault Detection

In this paper, a novel approach is proposed for state and unknown input estimation of Takagi-Sugeno fuzzy systems. By introducing an augmented state vector, containing both system state and the unknown input, a functional observer is proposed to estimate this vector, and the proposed observer provides a highly flexible estimation output. Through casting the observer design problem into an equivalent solvability problem of a linear matrix equation with respect to the observer gains, the existence condition for the proposed observer is explicitly derived in terms of matrix rank. Furthermore, a parameterization methodology of the observer gain matrices is provided as well, which avoids directly solving the Sylvester equation. The proposed observer design scheme is further applied to the $H\_{}/H_\infty $ fault detection problem, and the effectiveness of the proposed approach is demonstrated by state and unknown input estimation for a tunnel diode circuit and fault detection for a continuously stirred tank reactor system.

Augmented zero equality approach to stability for linear systems with time-varying delay

This work focuses the delay-dependent stability problem for linear systems with time-varying delays. By composing a suitable augmented Lyapunov–Krasovskii functionals, using recent developed integral inequality and choosing newly states, a set of sufficient conditions for stability condition is induced within framework of linear matrix inequalities (LMIs). To enhance the feasible region of stability, single augmented zero equality is established with the augmented state vectors for the first time and the equality constraint is incorporated into a simple stability criterion by utilizing Finsler’s lemma. The comparison of maximum bounds of time-delay with various results proposed by recent studies will be conducted in numerical examples to demonstrate the superiority of the theorems presented by this paper.

Sensor-Fault-Estimation-Based Tolerant Control for Single-Phase Two-Level PWM Rectifier in Electric Traction System

This article presents a fault-estimation-based tolerant control strategy for single-phase two-level pulsewidth modulation rectifier subjected to catenary current sensor fault and dc-link voltage sensor fault. First, an augmented descriptor system is developed for the rectifier, whose augmented state vector consists of the state vector of original system as well as the sensor fault together with the measurement disturbance. Then, a linear reduced-order observer is designed for the descriptor plant. Accurate asymptotic estimation of the original state vector and the disturbed sensor fault are thus achieved simultaneously. Finally, the fault tolerant design method is addressed through sensor fault compensation, which allows the pre-design controller to continue to function normally even when both catenary current sensor and dc-link voltage sensor are faulty. Simulation and hardware-in-the-loop test results confirm the effectiveness of the proposed method.

Modification of Standard Kalman Filter Based on Augmented Input Estimation and Deadbeat Dissipative FIR Filtering

ABSTRACT This paper presents modification of standard Kalman filter (KF) based on augmented input estimation (AIE) and deadbeat dissipative FIR filtering (DDFF) for maneuvering target tracking. Although KF is a well-known tool in estimation and tracking but it has two weaknesses, disability in maneuvering motions and lack of robustness against temporary model uncertainty. For the first problem, the AIE is proposed to cover both the non-maneuvering and maneuvering parts of motion and so the maneuver detection procedure is eliminated. This model with an input estimation (IE) approach is a special augmentation in the state space model which considers both the state vector and the unknown input vector as a new augmented state vector. Also, KF is based on infinite impulse response (IIR) structure and cannot be robust against temporary model uncertainty. Unlike IIR, finite impulse response (FIR) filter is robust and stable against model uncertainty. So, for the second problem, an extra type of FIR filter named DDFF is introduced in this paper that not only has the intrinsic properties of FIR but also can improve these features by tuning some weighting parameters. In the last examples of the paper, the advantages of the proposed model against other models are shown.

Road profile estimation and half-car model identification through the automated processing of smartphone data

This paper proposes a robust road profile estimation method and vehicle parameter identification method through an optimization with an objective function and constraint conditions on estimated profiles. The methods require only vehicle response measurements, enabling easy and inexpensive, yet effective, road condition monitoring through the automated processing of smartphone data. A half-car (HC) model, representing both bouncing and pitching motions, is employed for the profile estimation. The road profiles at the front and rear tire locations are included as state variables in the augmented state vector and are estimated by combining the augmented Kalman filter (AKF), Robbins–Monro (RM) algorithm, and Rauch–Tung–Striebel (RTS) smoothing. The two independent state variables, however, correspond to a single physical profile, while their distance coordinates differ by the wheelbase. Therefore, the vehicle parameters are optimized through the minimization of the difference between the identified road profiles at the front and rear tire locations using a genetic algorithm. Three objective functions and three constraint conditions are proposed to automatically select the best vehicle parameters. With this HC model, the road profile is subsequently estimated by combining the AKF, RM, and RTS methods. Through numerical simulations, the accuracy of the profile estimation and validity of the parameter identification are clarified. The influences of different drive speeds and difference between the left and the right profiles are numerically investigated. Drive tests with three different vehicles and a reference laser profiler show that the algorithm can automatically compensate for differences among vehicles with different drive speeds and estimate profiles accurately.

Synthesis of one-stage signal processing algorithm for space radio navigation receiver

High requirements are imposed on modern user navigation apparatuses (UNA) of global navigation satellite systems (GNSS) in terms of the navigation support accuracy. As a rule, the UNA is built according to the scheme with two-stage signal processing. At the first stage, navigation signals are received and transferred to the intermediate frequency, signals are searched for and tracking of signal parameters (delay, phase, Doppler frequency shift) is performed. At the second stage, pseudo-ranges, pseudo-phases and pseudo-Doppler frequencies are measured, digital information is selected from the received radio signals and the navigation problem is solved, i.e. the coordinates and components of the user’s velocity vector are determined. The use of one-stage processing of navigation signals is one of the promising areas for further improving the navigational sighting accuracy in a UNA. In this case, all signals are processed in a single integrated filter with simultaneous solution of the navigation task. The article considers the synthesis of an optimal one-stage algorithm for processing GNSS signals using the theory of optimal filtering. This synthesis is aimed at providing the best accuracy in estimating the coordinates and components of the user’s velocity vector. The final algorithm implements vector tracking for the delays in received signals and their phases. Vector tracking loop includes a standard set of correlators, delay and phase discriminators and an integrated filter of the augmented state vector.

Stability analysis of discrete-time LPV switched systems

This paper addresses the stability problem for discrete-time switched systems under autonomous switching. Each mode of the switched system is modeled as a Linear Parameter Varying (LPV) system, the time-varying parameters can vary arbitrarily fast and are represented in a polytopic form. The Lyapunov theory is employed to get new conditions in the form of parameter-dependent LMIs. The constructed Lyapunov function takes advantage of using an augmented state vector with shifted states in its construction. In this sense, the Lyapunov function employed in this paper can be viewed as a discrete-time LPV switched Lyapunov function. Numerical experiments illustrate the efficacy of the technique in providing stability certificates.

Quadratic estimation for discrete time-varying non-Gaussian systems with multiplicative noises and quantization effects

This paper is concerned with the remote state estimation problem for a class of linear discrete time-varying non-Gaussian systems with multiplicative noises. Due to bandwidth constraints in digital communication networks, the measured outputs are quantized before transmission by a probabilistic uniform quantizer. Our attention is focused on the design of a recursive quadratic estimator that exploits the quadratic functions of the measurements. By introducing a proper augmented system which aggregates the original state vector and its second-order Kronecker power, we are able to transfer the quadratic estimation problem into a corresponding linear estimation problem of the augmented state vector. An upper bound is first established for the covariance of the estimation error that is expressed in terms of the solutions to certain matrix difference equations, and such an upper bound is then minimized by designing the filter parameters in an iterative manner. Subsequently, we discuss the monotonicity of the optimized upper bound with respect to the quantization accuracy. A numerical example is provided to verify the effectiveness of the proposed filtering algorithm.

An Improved Kalman Filter With Adaptive Estimate of Latency Probability

In this brief, an improved Kalman filter is proposed for a linear system with one-step randomly delayed measurement and unknown latency probability. The measurement likelihood function which is a weighted sum of two Gaussian distributions is transformed into an exponential multiplication form via importing a discrete Bernoulli random variable. Then, an hierarchical Gaussian form of the state-space model is established. Finally, an improved Kalman filter is deduced to estimate jointly the augmented state vector and the unknown parameters employing the variational Bayesian and state augmentation approaches. Simulation study indicates that the improved method has superior performance in estimation accuracy than the existing methods on the basis of accurate estimation of the unknown and time-varying latency probability.

Fault-tolerant output feedback sliding mode control with event-triggered transmission and signal quantization

In this paper, the problem of event-triggered-based sliding mode control for a class of continuous-time system with actuator failures and signal quantization via output feedback is investigated. The classical dynamic uniform quantization strategy is employed for data quantization in both sensor-controller side and controller-actuator side. A new event-triggered adaptive dynamic output feedback sliding mode control scheme is proposed to stabilize the fault closed-loop systems, where the event-triggered condition is established based on quantized augmented state vector that includes output measurement vector and dynamic compensator state vector. Sufficient conditions for the existence of controller gain matrices are formulated in terms of linear matrix inequalities (LMIs). The reachability of the proposed sliding surface can be ensured by the designed control scheme. Moreover, the existence of the minimal inter–event time and sufficient conditions under which the zeno behavior can be avoided is analyzed and presented. Finally, an example is provided to demonstrate the effectiveness of the proposed new design techniques

State Estimation With Trajectory Shape Constraints Using Pseudomeasurements

In this paper, a trajectory shape constraint on target motion is investigated, and the corresponding state estimation method is presented. This type of constraint occurs when only the shape of the target trajectory is known a priori , without any other necessary information to exactly describe the specific trajectory. For example, one may only know that the target moves along a straight line. This prior knowledge of trajectory can be considered as a constraint to improve tracking performance. To describe the shape constraint arising from the straight line assumption, the state vector is augmented by the states at previous time steps. This facilitates the description of the shape constraint using the components of the state vector. Pseudomeasurements are then constructed based on these relationships to incorporate the constraint into an estimation process to improve the performance. The redundancy of the complete set of pseudomeasurements for a given augmented state vector is analyzed, and the minimal set of pseudomeasurements, which describes the constraint exactly, is proposed. The time evolution equation for the augmented state and the measurement equation using the minimal pseudomeasurement set are formulated. A trajectory shape constraint Kalman filter (TSCKF) is then proposed for simultaneous filtering and smoothing. Since both the measurement vector and the state vector are high dimensional, the cubature Kalman filter is used in the proposed TSCKF to deal with the strong nonlinearity in this problem. Monte Carlo simulations illustrate the effectiveness of the proposed TSCKF and the improvement in both filtering and smoothing accuracies by incorporating the trajectory shape constraint.

Adaptive disturbance attenuation for a class of uncertain nonlinear systems: A double-gain nonlinear observer method

This paper is concerned with the problem of adaptive disturbance attenuation for a class of nonlinear systems. The traditional adaptive methods are almost impossible to compensate the time-varying unknown disturbance by designing parameter adaptive laws without a priori knowledge about the bounds of external disturbances. To solve the problem, a new strategy is proposed by constructing an augmented system where the external disturbance is considered as another component of the augmented state vector. Based on this, a double-gain nonlinear observer is employed to estimate the state of the augmented nonlinear system. Further, an output feedback control strategy is designed, and it is proved that the proposed strategy ensures that all the signals are bounded and the tracking error exponentially converges to an adjustable compact set. Finally, an example is performed to demonstrate the validity of the proposed scheme.

Simultaneous spatiotemporal bias and state estimation for asynchronous multi‐sensor system

Elimination of spatiotemporal bias of asynchronous multiple sensors is the foundation of accurate multi-sensor data fusion. In this article, a sequential processing simultaneous spatiotemporal bias and state estimation algorithm for asynchronous multi-sensor system is proposed. The spatiotemporal bias is combined with target state to obtain an augmented state vector, and the augmented state model is formulated. For asynchronous multi-sensor with known but different sampling periods, a sequential processing method is proposed to handle the multiple measurements. The relationship of sensor measurements, target state and spatiotemporal bias is analysed, and the corresponding measurement model is formulated. A novel algorithm, in which the unscented Kalman filter is used to handle the nonlinearity between the augmented measurement and state vectors, is proposed to jointly estimate the spatiotemporal bias and target state. Simulation results verify the effectiveness of the proposed algorithm.

Optimal reduced‐order LQG synthesis: Nonseparable control and estimation design

SummaryThe optimal linear‐quadratic‐Gaussian synthesis design approach and the associated separation principle are investigated for the case where the observer design model is a reduced model of the underlying system model. Performance of the resulting reduced‐order controller in the full‐state system environment is formulated in terms of an augmented state vector consisting of the system state vector and the reduced model state vector. Considering explicitly separated linear control and estimation laws, a calculus of variations/Hamiltonian approach is used to determine the necessary conditions for the optimal controller and observer gains for the simplified algorithms. Results show that the optimal gains are not separable, ie, the optimal controller and observer gains are coupled and cannot be computed independently. Numerical examples of an infinite‐horizon and finite‐horizon control and estimation large‐scale multiagent system problem clearly show the advantages of using the nonseparable coupled solutions.

On stability of neutral-type linear stochastic time-delay systems with three different delays

We study in this paper the mean square exponential stability of neutral-type linear stochastic time-delay systems with three different delays by using the Lyapunov–Krasovskii functionals (LKFs) based approach. First, for a specified augmented state vector, a complete augmented LKF is constructed to contain all possible integrals so that its time-derivatives (understood in the deterministic sense) can be written as a linear function of the augmented vector. The redundant variables in the LKF are eliminated so as to reduce the computational burden. Moreover, the absolute value requirement of certain terms in the constructed LKFs are removed by analyzing carefully the complex relationship among these three different time delays. Then, for ten different cases of time delays, sufficient stability conditions in terms of linear matrix inequalities are obtained with the help of the Ito formula and properties of stochastic integrals. The degenerated cases that the delays satisfy some equalities are also discussed. A numerical example is employed to illustrate the effectiveness of the proposed approach.