Augmented State Vector Research Articles

Observer-based output feedback control for switched T–S fuzzy systems with local nonlinear segments by using past output measurements

This paper researches the observer-based exponential stabilization problem for switched Takagi–Sugeno (T–S) fuzzy systems with unmeasurable premise variables and local nonlinearities. The local nonlinear parts that satisfy the incremental quadratic constraint exist in the systems and observers, which have the merit of being able to contain many common nonlinearities in a unified framework. Because the premise variables are not measurable, the performance of the observers in estimation is critical. Different from existing observer-based control strategies, the strategy of this paper not only depends on the current outputs of the systems but also relates to the past outputs of the systems which can provide a way to improve performance. In order to tackle the difficulties caused by introducing the past outputs and design a set of non-fragile fuzzy controllers to stabilize the systems, a new augmented state vector is constructed. Then, the conditions for designing the observer-based controller are derived by using auxiliary scalars, projection Lemma and S-procedure. Finally, the effectiveness of the control strategy obtained in this paper is proved by two examples.

Harnessing membership function dynamics for stability analysis of T-S fuzzy systems

The main goal of this paper is to develop a new less conservative linear matrix inequality (LMI) condition for the asymptotic stability of continuous-time Takagi-Sugeno fuzzy systems. A key advantage of this new condition is its independence from the bounds on the time-derivatives of the membership functions (MFs), a requirement that presents in the existing approaches. This is achieved by introducing a novel fuzzy Lyapunov function that incorporates an augmented state vector. Notably, this augmented state vector includes MFs and allows their dynamics to be integrated into the proposed LMI condition. This inclusion of additional information about MFs reduces the conservativeness of the suggested stability condition. Finally, examples are given to demonstrate the effectiveness of the proposed method.

Path integration solutions for stochastic systems with Markovian jumps

A path integration method for solving Markovian jump stochastic dynamical systems is presented. The Markovian jump process and the state vector of the system are combined into a new augmented state vector. The randomness of the Markovian jump is modeled by a stochastic process, which is merged with the stochastic perturbations to form the stochastic source affecting the evolution of the augmented system. Then a probability mapping is constructed, mapping the probability space of the stochastic source to the short-time transition probability density function of the augmented system. By solving this probability mapping, the short-time transition probability density function of the path integration method is obtained, thus a path integration method is customized for Markovian jump stochastic systems. Finally, a hydraulic relief valve system is used as an application example to demonstrate the availability of the path integration algorithm. The results suggest that the pre-compression parameters and coefficient of restitution of the plug can induce stochastic P-bifurcation phenomena. When the above two parameters are small, the system becomes unstable with the parameters taken in this example. Monte Carlo simulations prove that the proposed method effectively captures the transient and stationary responses of Markovian jump systems.

Improved results for T-S fuzzy systems with two additive time-varying delays via an extended binary quadratic function negative-determination lemma

This paper is concerned with the stability and stabilization problems for T-S fuzzy systems with two additive time-varying delays. Firstly, a novel Lyapounov-Krasovskii functional (LKF) is constructed by delay-product-type functional method together with the state vector augmentation. In order to handle time-delay square terms introduced into the derivative of LKF, an extended binary quadratic function negative-determination lemma is proposed. A less conservative delay-dependent stability condition is developed since not only some new bounding technologies are employed to deal with integral terms, but also the proposed lemma is employed to dispose nonlinear time-delay terms in derivative of constructed function. Then, the corresponding controller design method for closed-loop delayed fuzzy system is derived based on parallel distributed compensation scheme. Finally, four numerical examples are given to illustrate the superiority and effectiveness of the proposed criteria.

[formula omitted] performance analysis for aperiodic sampled-data systems via a matrix-injection method

This study proposes a matrix-injection method to complete the H∞ performance analysis of linear systems under aperiodic sampled data. First of all, an augmented looped-functional is constructed by combining the looped-functional method with state vector augmentation. To make use of sampling period-related information in this augmented functional, sampling period-dependent quadratic terms are kept in the derivative of the functional. Then, to deal with the aforementioned quadratic terms, a matrix-injection method is developed. This method introduces two free matrices, which allows for a reduction in the conservativeness of the results. A sufficient condition with less conservatism is provided using these techniques. Finally, three examples are given to demonstrate the superiority of the presented approach.

Simultaneous Spatiotemporal Bias Compensation and Data Fusion for Asynchronous Multisensor Systems

Bias estimation of sensors is an essential prerequisite for accurate data fusion. Neglect of temporal bias in general real systems prevents the existing algorithms from successful application. In this paper, both spatial and temporal biases in asynchronous multisensor systems are investigated and two novel methods for simultaneous spatiotemporal bias compensation and data fusion are presented. The general situation that the sensors sample at different times with different and varying periods is explored, and unknown time delays may exist between the time stamps and the true measurement times. Due to the time delays, the time stamp interval of the measurements from different sensors may be different from their true measurement interval, and the unknown difference between them is considered as the temporal bias and augmented into the state vector to be estimated. Multisensor measurements are collected in batch processing or sequential processing schemes to estimate the augmented state vector, results in two spatiotemporal bias compensation methods. In both processing schemes, the measurements are formulated as functions of both target states and spatiotemporal biases according to the time difference between the measurements and the states to be estimated. The Unscented Kalman Filter is used to handle the nonlinearity of the measurements and produce spatiotemporal bias and target state estimates simultaneously. The posterior Cramer-Rao lower bound (PCRLB) for spatiotemporal bias and state estimation is presented and simulations are conducted to demonstrate the effectiveness of the proposed methods.

UAV Path Optimization for Angle-Only Self-Localization and Target Tracking Based on the Bayesian Fisher Information Matrix.

In this paper, new path optimization algorithms are developed for uncrewed aerial vehicle (UAV) self-localization and target tracking, exploiting beacon (landmark) bearings and angle-of-arrival (AOA) measurements from a manoeuvring target. To account for time-varying rotations in the local UAV coordinates with respect to the global Cartesian coordinate system, the unknown orientation angle of the UAV is also estimated jointly with its location from the beacon bearings. This is critically important, as orientation errors can significantly degrade the self-localization performance. The joint self-localization and target tracking problem is formulated as a Kalman filtering problem with an augmented state vector that includes all the unknown parameters and a measurement vector of beacon bearings and target AOA measurements. This formulation encompasses applications where Global Navigation Satellite System (GNSS)-based self-localization is not available or reliable, and only beacons or landmarks can be utilized for UAV self-localization. An optimal UAV path is determined from the optimization of the Bayesian Fisher information matrix by means of A- and D-optimality criteria. The performance of this approach at different measurement noise levels is investigated. A modified closed-form projection algorithm based on a previous work is also proposed to achieve optimal UAV paths. The performance of the developed UAV path optimization algorithms is demonstrated with extensive simulation examples.

A Bayesian model calibration framework for stochastic compartmental models with both time-varying and time-invariant parameters

We consider state and parameter estimation for compartmental models having both time-varying and time-invariant parameters. In this manuscript, we first detail a general Bayesian computational framework as a continuation of our previous work. Subsequently, this framework is specifically tailored to the susceptible-infectious-removed (SIR) model which describes a basic mechanism for the spread of infectious diseases through a system of coupled nonlinear differential equations. The SIR model consists of three states, namely, the susceptible, infectious, and removed compartments. The coupling among these states is controlled by two parameters, the infection rate and the recovery rate. The simplicity of the SIR model and similar compartmental models make them applicable to many classes of infectious diseases. However, the combined assumption of a deterministic model and time-invariance among the model parameters are two significant impediments which critically limit their use for long-term predictions. The tendency of certain model parameters to vary in time due to seasonal trends, non-pharmaceutical interventions, and other random effects necessitates a model that structurally permits the incorporation of such time-varying effects. Complementary to this, is the need for a robust mechanism for the estimation of the parameters of the resulting model from data. To this end, we consider an augmented state vector, which appends the time-varying parameters to the original system states whereby the time evolution of the time-varying parameters are driven by an artificial noise process in a standard manner. Distinguishing between time-varying and time-invariant parameters in this fashion limits the introduction of artificial dynamics into the system, and provides a robust, fully Bayesian approach for estimating the time-invariant system parameters as well as the elements of the process noise covariance matrix. This computational framework is implemented by leveraging the robustness of the Markov chain Monte Carlo algorithm permits the estimation of time-invariant parameters while nested nonlinear filters concurrently perform the joint estimation of the system states and time-varying parameters. We demonstrate performance of the framework by first considering a series of examples using synthetic data, followed by an exposition on public health data collected in the province of Ontario.

Robust T‐S fuzzy‐model‐based nonfragile sampled‐data control for cyber‐physical systems with stochastic delay and cyber‐attacks

AbstractThis work addresses the nonfragile sampled‐data control (SDC) of the Takagi‐Sugeno (T‐S) fuzzy model for cyber‐physical systems (CPSs) subject to cyber‐attacks (CAs). The sets of random variables satisfying the Bernoulli distribution are utilized to depict the probability of the data transmitted by the network being subjected to stochastic delay and CAs. Then, the information for the entire sampling interval to with a relation of the augmented state vectors is considered for designing the SDC of the T‐S fuzzy systems (TSFSs). In this regard, the fractional delayed state looped functional (LF) approach is presented to handle the formulated Lyapunov‐Krasovskii functional. Based on the LF method, new criteria are acquired to design SDC such that the proposed CPS is asymptotically stable in terms of linear matrix inequalities. It is worth noting that the proposed control strategy for the TSFSs guarantees stable performance while dealing with the attacks in the numerical section. Also, for the various attacking strengths of periodic and non‐periodic nature, the TSFSs have been simulated to show the efficiency of the proposed control method. Additionally, three numerical models have been performed to validate the less conservatism and superiority of the derived results over the existing ones.

Robust Optimal Parallel Tracking Control Based on Adaptive Dynamic Programming.

This article focuses on a novel robust optimal parallel tracking control method for continuous-time (CT) nonlinear systems subject to uncertainties. First, the designed virtual controller facilitates the transformation of the original nonlinear system into an affine system with an augmented state vector, which promotes the introduction of the optimal parallel tracking control problem. Then, this article generates fresh insight into counteracting the effects of uncertainty by developing a novel parallel control system that invokes the formulated virtual control law and an auxiliary variable obtained from the relationship between the solutions of the optimal control problems for the uncertain system and the nominal one. Next, critic neural networks (NNs) approximate the Hamilton-Jacobi-Bellman (HJB) equations' solution to implement the proposed robust optimal control method via adaptive dynamic programming (ADP). Finally, simulation experiments demonstrate the proposed method's remarkable effectiveness.

Fault Diagnosis of PEM Fuel Cells: An Assessment of two Bayes’ Filters

In this paper a comparative performance assessment of two Bayes’ Filters, the square root unscented Kalman filter (SRUKF) and the particle filter (PF), is conducted in terms of detecting the failure events of flooding and catalytic degradation. The Bayes’ filters operate within a multiple model fault diagnosis framework, where the models are distinguished by an augmented state vector incorporating a system parameter, namely the mass transfer coefficient of the gas diffusion layer or the exchange current density. To achieve a solid comparison, a multi-scale PEMFC degradation model is derived and used in the simulation study to better emulate the behaviour of the PEMFC in the case of catalytic degradation. Simulation results demonstrate that the early detection of flooding and catalytic degradation can be achieved by both the SRUKF based and the PF based multiple model fault diagnosis system, with a slight performance superiority for the SRUKF.

Temperature enhanced early detection of internal short circuits in lithium-ion batteries using an extended Kalman filter

Fuel shortages and environmental concerns primarily drive the recent growth in electrification. Lithium-ion batteries are the preferred power source for electric vehicles and other applications due to their high energy and power densities. Among potential issues that can affect Li-ion batteries, thermal runaway is a significant concern, believed to be primarily caused by internal short circuits. Therefore, early internal short circuit detection has become a critical task for any Li-ion battery-powered engineering system prioritizing safety. This paper presents a novel online internal short circuit detection method based on the state vector augmentation of an extended Kalman filter with: (i) voltage and surface temperature observations, (ii) a hysteresis state, and (iii) a state related to the internal short circuit. The proposed method is assessed numerically, mimicking an electrical vehicle battery working cycle. The framework allows for an online estimation of the internal short circuit state while remaining computationally lean, thus potentially allowing for implementation into commercial BMSs, and it is proven to capture the internal short circuit occurrence within safety limits. Additionally, the advantages of including both voltage and surface temperature observations have been highlighted. Future work envisaged towards field implementation of the technique in BMS is eventually and briefly discussed.

Robust Kalman Filter for Systems With Colored Heavy-Tailed Process and Measurement Noises

In this paper, we consider the robust state estimation for a linear system with colored heavy-tailed process and measurement noises. We employ the state augmentation and measurement differencing methods to whiten the colored noise and use the Student’s t distribution to model the heavy-tailed property, which makes a new state space model with the augmented state vector. The posterior estimation of the system state, inaccurate scale matrices, and auxiliary parameters are jointly inferred with the variational Bayes method by constructing the hierarchical Gaussian forms of the prediction and likelihood probability density functions and selecting the proper prior distributions of the scale matrices and auxiliary parameters. A typical target tracking simulation is given to confirm the performance of the proposed robust Kalman filter.

Observer-based fuzzy integral sliding mode control for bilateral teleoperation systems with time-varying delays

This paper aims to examine the stability and tracking performance of a bilateral teleoperation system. The Takagi–Sugeno fuzzy method is utilized, through which the nonlinear master–slave dynamics is converted as a fuzzy-based system. The state observers are designed for the linearized fuzzy teleoperation systems, and the corresponding estimation errors are formulated. Importantly, a novel observer-based fuzzy integral sliding mode control is developed by deliberately introducing the delay term into the sliding surfaces. As such, advanced delay-product type of Lyapunov–Krasovskii functionals are constructed for the augmented state vectors, in order to acquire the additional delay information. In addition, the Wirtinger-based integral inequality along with an extended reciprocally convex matrix inequality is applied to the Lyapunov derivatives to establish the delay-dependent stability conditions. Numerical results are provided to demonstrate efficacy of the developed control mechanism.

State augmentation method for buffeting responses of wind-sensitive structures in wind environments with large turbulence intensity

Recent studies have shown that wind fields with large turbulence intensity are frequently observed in non-synoptic winds such as typhoons and hurricanes. The quadratic terms of the fluctuating wind speed are important for calculating buffeting responses of wind-sensitive structures under high turbulence. In this study, a moment-based method, which is called the state augmentation method, is used to obtain high-order response moments and avoid the large computational cost of the high-order frequency domain method. First, the buffeting force formula with nonlinear velocity terms is established, and the Non-Gaussian buffeting force is further approximated as a polynomial of the Ornstein–Uhlenbeck (OU) process. Then, an augmented state vector is introduced to express the relationship between the statistical moments of each order, and the 1st to 4th response moments can be solved sequentially by a particular set of linear equations. Finally, the extreme responses of a single-degree-of-freedom (SDOF) tower and a long-span suspension bridge are calculated as engineering examples. By comparing the computation results with the frequency method, it is proven that this moment-based method has a sufficient accuracy in analysing quadratic terms. The calculation results also show that quadratic terms under high turbulence significantly amplify the non-Gaussian peak factor and extreme responses.

Joint parameter-input estimation for digital twinning of the Block Island wind turbine using output-only measurements

This paper presents a recursive Bayesian inference framework for digital twinning of an offshore wind turbine (OWT) in the Block Island Wind Farm (BIWF), the first commercial offshore wind farm in the U.S. with jacket substructure. The framework employs a window-based extended Kalman filter (EKF) to jointly estimate the dynamic input loads and unknown model parameters of the finite element (FE) model of the turbine using sparse output-only measurements. The estimation of input loads on the OWT is critical for fatigue life estimation, foundation monitoring and control strategy. In the proposed joint estimation algorithm, unknown input time histories are divided into overlapping windows and the current window of inputs is concatenated with uncertain model parameters to form an augmented state vector. To account for the uncertainty about wind direction and misalignment between wind direction and the turbine yaw angle, two independent horizontal wind load time histories in X and Y directions are estimated at the nacelle level. A numerical validation study is first performed in which wind loads of the OWT are simulated using the multi-physics platform FAST, and structural vibration responses are generated using the FE model in OpenSees. The window-based EKF is implemented using the simulated measurements, and the estimations of structural stiffness as the updating model parameter and input loads are observed to have high accuracy. The proposed algorithm is then validated using in-situ measurements on one of the OWT in BIWF. To investigate the effectiveness and robustness of the method under different environmental and operational conditions, four cases are considered in which the turbine is operating at the rated rotor speed (region 3 of power generation), below the rated rotor speed (region 2), idling rotor state (region 1 or no power), and region 4 beyond cut-out wind speed. Accurate predictions of acceleration and strain data are obtained using the proposed algorithm, and the estimations of model parameter are consistent and close to their nominal value under different conditions. These results from numerical and experimental studies validate the proposed window-based EKF for joint parameter-input estimation and digital twinning for long-term structural health monitoring of the OWT.

Filtering of Noisy Nonlinear Buck Converter with CPL Using Carleman Linerization

The paper includes a novel approach for filtering of nonlinear Buck converter with Constant Power Load in noisy environment based on the Carleman linearization approach. The procedure starts with the modeling of Buck converter with Constant Power Load using Hamiltonian framework resulting in the deterministic model of network i.e., a finite dimensional system of ordinary differential equations. To evaluate the effect of noise on it, a Gaussian noise is embedded in the network through switch, which results in the development of stochastic state model and noise present at measurement terminals is considered for measurement equations. Using Carleman linearization approach, the finite-dimensional nonlinear model is transmuted into a bilinear model of infinite-dimension which can be approximated for any chosen order. As a result, we arrive at the finite-dimensional bilinear model of Buck converter with augmented state vector of higher dimension than the original system. State estimation of stochastic dynamical systems in the presence of noisy measurements is an interesting problem and hence, filtering technique is adopted here. The filtering equations in Itô setting are derived for bilinear systems using probabilistic approach for state estimation. The superiority of the proposed bilinear filtering technique over the benchmark EKF is demonstrated by the numerical simulations.

State Compensation for Maritime Autonomous Surface Ships’ Remote Control

With the development of emerging techniques, maritime autonomous surface ships (MASS) have attracted much attention, and the remote control ships’ future seems promising. However, due to communication issues, ship–shore transmission faces the challenge of time delay. The use of the transmitted information without compensation could reduce the effectiveness of controlling or could cause the remote control to be unstable. To eliminate the negative effects of uncertain delays during navigation, an Augmented State Cubature Kalman Filter (AS-CKF) is proposed. First, the uncertainty of the transmission delays is modeled using a probability density function (PDF). Second, the ship’s states are updated and estimated using the delayed observed data, and then the real state of the ship is simultaneously corrected in the augmented state vector. In this way, the delay compensation problem becomes a one-step prediction problem. To test the proposed AS-CKF for MASS, we simulate scenarios with the remote control ship under different communication time delays. The results show improvements compared to the traditional CKF, EKF, or AS-EKF, which indicates the potential of the proposed methods in remote control MASS.

Mean-square stability of discrete-time switched systems under modeled random switching

This paper studies the mean-square stability of discrete-time linear switched systems with random switching, where the switching signal is the output of a logic dynamical switching model driven by an independent and identically distributed (i.i.d.) process. This class of switching is referred to as the modeled random switching. By regarding the switching model as a part of the system, a combined switched system with i.i.d. switching is obtained, which is of a hybrid nature, that is, the augmented state vector has both logic and continuous components. The semi-tensor product of matrices and the vector representation of logic are applied to merge the logic and the continuous components of the state. The equivalence between the mean-square stability of the original switched system and that of the merged switched system under i.i.d. switching is proved. By deriving the dynamics of the column-stacking form of the covariance matrix, necessary and sufficient conditions of mean-square stability for discrete-time linear switched systems with modeled random switching are obtained. An illustrative example is provided to demonstrate the usage of the proposed results.

Fusion steady‐state robust filtering for uncertain multisensor networked systems with application to autoregressive moving average signal estimates

AbstractThis article is concerned with the centralized fusion (CF) robust steady‐state Kalman filtering problem for a class of multisensor networked systems with mixed uncertainties including state‐dependent and noise‐dependent multiplicative noises, missing measurements, packet dropouts, and uncertain noise variances. By using a model transformation approach, the initial multisensor system under study is transformed into a multi‐model multisensor system only with uncertain noise variances. By introducing an augmented state vector, the CF system is obtained. In the light of the minimax robust estimation method, and based on the worst‐case fusion system with conservative upper bounds of uncertain noise variances, the CF robust steady‐state Kalman estimators (predictor, filter, and smoother) are proposed in a unified form. By means of the permutation matrices and Lyapunov equation method, the robustness of CF estimators is proved. The accuracy relations among the robust local and fusion steady‐state estimators are proved. An example applied to autoregressive moving average signal estimation is put forward, and the robust CF steady‐state signal estimators are proposed. Simulation experiment shows the correctness of the proposed approach.