Extended State Vector Research Articles

Extended state space for describing renormalized Fock spaces in QFT

We revisit the non-perturbative renormalization of a class of simple polaron models with resting fermions. The considered dispersion relations and form factors are allowed to be highly singular, such that infinite self-energies and wave function renormalizations may occur and the diagonalizing dressing transformations might not be implementable on Fock space. Instead of taking cutoffs, we rigorously interpret the self-energies and wave function renormalizations as elements of suitable vector spaces, as well as a field extension of the complex numbers. Moreover, we define two extended state vector spaces (ESSs) over this field extension, which contain a dense subspace of Fock space, but also incorporate non-square-integrable wave functions. Elements of these ESSs can be seen as states of virtual particles, described in a mathematically rigorous way. The Hamiltonian without cutoffs, formally infinite counterterms, and the dressing transformation can then be defined as linear operators between certain subspaces of the two Fock space extensions. This way, we obtain a renormalized Hamiltonian which can be realized as a densely defined self-adjoint operator on Fock space.

Filtr Kalmana jako alternatywa dla rozszerzonego obserwatora stanu w algorytmie regulacji ADRC

The article presents a modified Active Disturbance Rejection Control (ADRC) algorithm that uses the Kalman Filter (KF) for the estimation of extended state vector. The Kalman filter replaced the Extended State Observer (ESO) used in its basic form. The purpose of this modification was to improve the system robustness under conditions of stochastic measurement disturbances. The method of the control system synthesis and the Kalman filter gains selection, ensuring control efficiency, as well as their impact on the system operation, were presented. The experiments were carried out on a laboratory setup – the Ball Balancing Table (BBT). Control quality was assessed based on time plots of signals and integral performance indices for various algorithm gains configurations and different noise levels. As a result of the conducted research, the advantage of using the Kalman filter over the ESO in terms of sensitivity to measurement noises was demonstrated. Implementation of the Kalman filter as the ESO determined a positive impact on control quality and the ability to reject internal disturbance also in a deterministic system.

Collision-free automatic berthing of maritime autonomous surface ships via safety-certified active disturbance rejection control

This paper addresses the automatic berthing of a maritime autonomous surface ship operating in a confined water environment subject to static obstacles, dynamic obstacles, thruster constraints, and space constraints due to shorelines. A safety-certified active disturbance rejection control (ADRC) method is proposed for achieving the automatic berthing task of an MASS in the presence of model uncertainties and ocean disturbances. An extended state observer (ESO) based on a second-order robust exact differentiator (RED) is employed to estimate an extended state vector consisting of internal model uncertainties and external ocean disturbances. With the aid of the RED-based ESO, a nominal ADRC law is designed to achieve the position and heading stabilization. To avoid collisions with static obstacles, dynamic obstacles, and shorelines, input-to-state safe high-order control barrier functions are used to guarantee safety. Optimized control signals are obtained based on a constrained quadratic programming (QP) problem within safety constraints. In order to translate the control signals into the individual thruster command, a constrained QP problem is further used to search for optimized commands in real time. It is proven that the closed-loop automatic berthing system is input-to-state stable. By using the proposed method, the MASS is able to reach the desired position and heading with collision avoidance. Simulation results verify the effectiveness of the proposed safety-certified ADRC method for automatic berthing.

Hydrodynamics of transient processes in a well with an electric submersible pump

The relevance. Associated with the problem of increase in efficiency of algorithms for monitoring and controlling the dynamic operation modes of wells equipped with an electric submersible pump with adjustable supply. The result summarizes and develops the previously published solution on the design of a dynamic well model, through the transition from linearized correlations to quadratic relationships between states at key points of a lift. These points properly reflect the observed forms of behavior in transient and equilibrium operating modes at full start-stop control ranges. The main aim. Updated description of a comprehensive quadratic barometric model of the «reservoir–lift–electric pump–well head» type well, focused on the tasks of automatic control and regulation in real time. Objects. Well with frequency-regulated submersible pump. Methods. Material balance, percolation, hydrostatics, quadratic kinetics of friction losses, numerical modeling of differential equations, finite-dimensional description of the complex hydrodynamics of the well, taking into account the potential and kinetic head losses in the lift. Results: (1) Updated mathematical description of the hydrodynamics of the well with an electric submersible pump creates the basis for: more reliable solution of inverse problems of parametric model support according to the data of field control, refined assessment of the adjustment potential, predicting the dynamics of a possible system output beyond the boundaries of functional stability, technologies of numerical and analytical design of optimal solutions when selecting the parameters of arrangement and laws of operational regulation, synthesis of dynamic observers of an extended state vector synchronously operating with the dynamics of controlling well-head and deep pressure. (2) The results of the computational analysis demonstrate a complex behavior that does not match the graph of the inflow and pump supply, when changing the frequency and wellhead pressure. This explains the observed effect of the multi-tempoity of transient processes during starts and stops and possible instability of the supply with a sharp decrease in frequency. (3) Estimates of discrepancy between the solutions for a quadratic model and a linearized prototype indicate an increase in errors of linearized analysis with strong deviations of operating modes from the equilibrium-calculated states. The refinements in dynamically disturbed operating modes delivered by the updated model are important for improving the reliability of operational control systems and parametric estimation for data control mode states.

Analysis of methods for modeling human daily thermometry data

Abstract. Mathematical and computer modeling of daily thermometry allows to study processes of human thermal homeostasis more deeply. In practice, thermometry data is obtained using a digital thermometer, which autonomously reads the temperature of human skin in certain time intervals. The aim of present work is to analyse the methods of modeling and processing of human daily thermometry data. The first method consists in applying linear discrete stochastic models in the state space with Gaussian noises and known vector of input actions, while the estimation of the state vector is performed by discrete covariance Kalman filter. The second method assumes that the vector of input actions is unknown, and the S. Gillijns and B.D. Moor algorithm is used to process daily thermometry data. An alternative option is to use a model with an extended state vector and a Kalman filtering algorithm. The third method takes into account the presence of anomalous measurements (outliers) in the measurement data, and correntropy filter is proposed for their effective filtering. Numerical experiments for modeling and processing of daily thermometry data in MATLAB were carried out in order to compare the quality of discrete filtering algorithms. Modeling of thermometry data was carried out using a three-dimensional model 3dDRCM (3-dimension Discrete-time Real-valued Canonical Model). The results obtained can be used in the study of human daily thermometry processes, for example, to study the reaction of the athlete’s body to the received load.

Compensation of output external disturbances for a class of linear systems with control delay

The paper considers the problem of the output external unknown disturbance compensation under unmeasurable state vector for a class of linear systems with the control channel delay. It is assumed that the disturbance is the output of an autonomous linear generator. A special observer was built to estimate the disturbance. A system with an extended state vector is formed on the base of the observer’s estimates. A controller that provides disturbance compensation is proposed. An algorithm for the output external disturbances compensation for a class of linear systems with input delay is presented. This method does not require identification of disturbance parameters. The performance of the proposed algorithm was confirmed using computer simulation in the MATLAB Simulink software. The developed algorithm can be effectively applied to a class of problems related to rocking compensation in ship systems, control of robotic complexes various kinds, etc.

Simultaneous interval state and fault estimation for continuous-time switched systems

This paper deals with simultaneous interval state and fault estimation for continuous-time switched systems subject to unknown but bounded state disturbances. By taking the actuator fault vector as a part of an extended state vector, the original system is transformed into an augmented descriptor system. Under this augmented descriptor form, and by using a new structure of interval observers, the conservatism of observer gain matrices can be significantly reduced. The effect of disturbances is attenuated based on an L∞ approach. Then, the interval observer gains are computed by solving Linear Matrix Inequalities (LMIs) derived from a common Lyapunov function. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.

Iterative State Estimation With Weight Tuning and Pseudo-Measurement Generation

The proliferation of distributed generation (DG) in the power system at low and medium voltage levels is creating challenges to the operation and control of the network and its protection system. Recent studies focus on using smart methods to deal with these challenges. These methods require access to information that can be provided by distribution network state estimation. However, state estimation in the distribution network is hindered by limited network observability and increased uncertainty due to the presence of DGs. With the threat of false data injection attacks, the security of state estimation is also a concern. To this end, this article proposes an iterative state estimation that uses: 1) an extended state vector that includes DG outputs; 2) pseudo-measurement generation based on DG characteristics and static voltage control modes; and 3) a weight updating algorithm that incorporates bad data detection. Simulations on a 44-node test distribution network show that the proposed iterative method improves the estimation of the status and outputs of the DGs and subsequently increases the accuracy of the fault current calculation.

INCREASING THE ROUGHNESS OF THE PROCEDURE FOR EVALUATING A VECTOR OF THE CONDITION OF OBJECTS TO THE INFLUENCE OF UNCERTAINTY FACTORS

Algorithms for increasing the roughness of the procedure for assessing the state vector of control objects to the influence of uncertainty factors are given. Expressions are obtained for extended state vectors and observations. Stable inversion algorithms are given for a nondegenerate block matrix with the allocation of its left and right zero divisors of maximum rank. The presented stable computational procedures allow us to regularize the problem of synthesis of algorithms for estimating the parameters of regulators in adaptive control systems with a customizable model and to improve the quality indicators of control processes under conditions of parametric uncertainty

Towards Simultaneous Actuator and Sensor Faults Estimation for a Class of Takagi-Sugeno Fuzzy Systems: A Twin-Rotor System Application.

The paper is devoted to the problem of estimating simultaneously states, as well as actuator and sensor faults for Takagi–Sugeno systems. The proposed scheme is intended to cope with multiple sensor and actuator faults. To achieve such a goal, the original Takagi–Sugeno system is transformed into a descriptor one containing all state and fault variables within an extended state vector. Moreover, to facilitate the overall design procedure an auxiliary fault vector is introduced. In comparison to the approaches proposed in the literature, a usual restrictive assumption concerning fixed fault rate of change is removed. Finally, the robust convergence of the whole observer is guaranteed by the so-called quadratic boundedness approach which assumes that process and measurement uncertainties are unknown but bounded within an ellipsoid. The last part of the paper portrays an exemplary application concerning a nonlinear twin-rotor system.

H∞ switching fuzzy control of solar power generation systems with asymmetric input constraint

AbstractThis paper aims at presenting a maximum power point tracking (MPPT) controller for photovoltaic (PV) systems subject to asymmetric input constraint. Indeed, the output voltage of the DC‐DC converter used for adjusting the photovoltaic output power can be controlled by means of variation of duty ratio limited between 1 and 0. The control design goal is to improve the efficiency of PV systems under asymmetric saturation of duty ratio. To achieve this goal, first, a Takagi‐Sugeno (T‐S) fuzzy model is used to represent the nonlinear behavior of the PV system. A T–S reference model is employed to give the ideal state direction which must be followed. To achieve a good steady state tracking, the integral of the state tracking error is used to define an extended system state vector. Second, the input characteristic is partitioned into several regions. In each region, the asymmetric saturation function can be considered as a symmetric saturation function. Furthermore, H∞ stabilization conditions for the resulting switching fuzzy control of the PV system under actuator saturation are formulated in term of linear matrix inequalities (LMI) using the Lyapunov approach. Simulation results are exhibited to demonstrate the effectiveness of the proposed design method.

Highly computationally efficient state filter based on the delta operator

SummaryThe Kalman filter is not suitable for the state estimation of linear systems with multistate delays, and the extended state vector Kalman filtering algorithm results in heavy computational burden because of the large dimension of the state estimation covariance matrix. Thus, in this paper, we develop a novel state estimation algorithm for enhancing the computational efficiency based on the delta operator. The computation analysis and the simulation example show the performance of the proposed algorithm.

Improved Robust Constrained Model Predictive Control Design for Industrial Processes Under Partial Actuator Faults

Focusing on industrial processes under uncertainties and partial actuator faults, a new robust constrained model predictive control (MPC) strategy is developed. To enhance the corresponding control performance, a new state-space model in which an extended state vector is constructed by combining the state variables and the tracking error is introduced for the proposed MPC algorithm. As a consequence, there are extra degrees of freedom for the subsequent controller design by adjusting the output tracking error and the state variables separately, and the enhanced control performance is anticipated. Note that the state variables cannot be tuned in the robust MPC design that utilizes the traditional state space model so that its control performance may be limited because of the restricted degrees of freedom. Finally, the validity of the proposed robust MPC strategy is evaluated on the injection velocity control under uncertainties and partial actuator failures.

Population extremal optimization-based extended distributed model predictive load frequency control of multi-area interconnected power systems

How to design a set of optimal distributed load frequency controllers for a multi-area interconnected power system is an important but still challenging issue in the field of modern electric power systems. This paper presents an adaptive population extremal optimization-based extended distributed model predictive load frequency control method called PEO-EDMPC for a multi-area interconnected power system. The key idea behind the proposed method is formulating the dynamic load frequency control issue of each area power system as an extended distributed discrete-time state-space model based on an extended state vector, obtaining a distributed dynamic extended predictive model, and rolling optimization of real-time control output signal by adopting an adaptive population extremal optimization algorithm, where the fitness is evaluated by the weighted sum of square predicted errors and square future control values. The superiority of the proposed PEO-EDMPC method to a traditional distributed model predictive control method, a population extremal optimization-based distributed proportional-integral control algorithm and a traditional distributed integral control method is demonstrated by the simulation studies on two-area and three-area interconnected power systems in cases of normal, perturbed system parameters and dynamical load disturbances.

Determining the observer parameters for back EMF estimation for selected types of electrical motors

AbstractIn the paper a procedure for determining the observer parameters for selected types of electrical motors is discussed. The procedure is based on the identity observer developed by Luenberger. The paper presents determining the parameters using calculation examples for the DC motor and also for the permanent magnet synchronous motor (PMSM), which utilize the extended state vector to estimate the back electromotive force (BEMF). Presented observer for PMSM does not need to use the information about load torque. The main task of this study is to show how to utilize these general theory to a specified type of motors. Such procedure avoids the use of time-consuming methods of the parameters selection, which are based on random algorithms or the computational intelligence.

Gyroscopic power take-off wave energy point absorber in irregular sea states

The Gyroscopic power take-off (GyroPTO) wave energy point absorber has the operational principle somewhat similar to the so-called gyroscopic hand wrist exerciser. Inside the float of the GyroPTO, there is a mechanical system made up of a spinning flywheel with its spin axis in rolling contact to a ring. At certain conditions, the ring starts to rotate at a frequency equal to the peak angular frequency of the wave excitation. In this synchronized state, the flywheel is running at almost constant speed, so the generated power from the generator becomes constant as well. In this paper, the performance of GyroPTO in irregular sea waves is investigated. To improve the stability (synchronization) margin of the device, a magnetic coupling mechanism has been added between the spin axis and the flywheel, which also makes the semi-active control of the device possible. Theoretical modeling of the GyroPTO is carried out using analytical rigid body dynamics, and a 4-DOF nonlinear model is established. Further, linear wave theory has been applied to calculate the hydrodynamic moments acting on the float. Rational approximation is performed on the frequency response function of the radiation damping moments, leading to an extended state vector formulation of the coupled structure- wave system. Simulation results show that magnetic coupling successfully improves the stability of the flywheel in irregular sea states. With given significant wave height and peak frequency, it is shown that the synchronization of the device is more easily obtained in narrow-banded wave than in broad-banded wave. As a result, larger values of generator gain can be chosen in narrow-banded waves, leading to larger power output. Making use of both the generator and the magnetic coupling, semi-active control algorithm might further improve the performance of the GyroPTO in real sea.

Force identification using correlated noise models

The problem of input identification using Bayesian estimation methods is considered. The forcing function is a time varying quantity hence it requires solution strategies that can account for the time variation, which is in contrast to methods for time invariant parameter identification. In the existing literature, in the absence of any prior information the forcing function is assumed to have a white noise model and the parameters associated with the model are taken such that the noise is uncorrelated to those associated with the response quantities. In the present work, the derivative of the force is assumed to be a white noise process and the noise parameters of this prior model and the system response quantities are taken to be correlated. The motivation to adopt this model is driven by the fact that the structure acts as a sensor in recording the load acting on it, which is available in the form of the measured structural responses. Furthermore, the estimation of the forcing function is governed by the updating of the predicted state at each time instant with respect to the measured system responses. Hence, a correlation between the force and response noise quantities may result in convergence in the estimation. The extended state vector approach, wherein the unknown force is introduced as an additional state to the system response quantities is adopted. The identification algorithm involves application of the Kalman filter and the sequential filters for the linear and nonlinear systems, respectively. The performance of the proposed algorithm will be illustrated on lower order linear and nonlinear dynamical systems.

Online structural damage identification technique using constrained dual extended Kalman filter

Periodic health assessment of large civil engineering structures is an effective way to ensure safe performance all through their service lives. Dynamic response-based structural health assessment can only be performed under normal/ambient operating conditions. Existing Kalman filter-based parameter identification algorithms that consider parameters as the only states require the measurements to be sufficiently clean in order to achieve precise estimation. On the other hand, appending parameters in an extended state vector in order to jointly estimate states and parameters is reported to have convergence issues. In this article, a constrained version of the dual extended Kalman filtering (cDEKF) technique is employed in which two concurrent extended Kalman filters simultaneously filter the measurement response (as states) and estimate the elements of state transition matrix (as parameters). Constraints are placed on stiffness and damping parameters during the estimation of the gain matrix to ensure they remain within realistic bounds. The proposed method is compared against the existing Kalman filter-based parameter identification techniques on a three-degrees-of-freedom mass-spring-damper system adopting both unconstrained and constrained estimation approaches. cDEKF is then employed on a numerical six-story shear frame and a 3D space truss to validate its robustness and efficacy in identifying structural damage. The results suggest that cDEKF algorithm is an efficient online damage identification scheme that makes use of ambient vibration response.

Mean-square state and parameter estimation for stochastic linear systems with Gaussian and Poisson noises

This paper proposes new mean-square filter and parameter estimator design for linear stochastic systems with unknown parameters over linear observations, where unknown parameters are considered as combinations of Gaussian and Poisson white noises. The problem is treated by reducing the original problem to a filtering problem for an extended state vector that includes parameters as additional states, modelled as combinations of independent Gaussian and Poisson processes. The solution to this filtering problem is based on the mean-square filtering equations for incompletely polynomial states confused with Gaussian and Poisson noises over linear observations. The resulting mean-square filter serves as an identifier for the unknown parameters. Finally, a simulation example shows effectiveness of the proposed mean-square filter and parameter estimator.

Simultaneous state and output disturbance estimations for a class of switched linear systems with unknown inputs

ABSTRACTThe paper considers the issues of state estimation and output disturbance reconstruction for a class of switched linear systems with unknown inputs. A singular switched system is derived from the original switched system by taking the output disturbance as a part of a new extended state vector. For the constructed singular switched system, a robust sliding-mode switched observer which can not only estimate the states of original switched system but also reconstruct output disturbances is proposed, where the switching of the observer is synchronous with that of the switched system. A sufficient condition is provided to guarantee the existence of the switched observer by the feasibility of an optimisation problem with linear matrix inequality constraint, and the corresponding switching signal with average dwell time is designed such that the convergence of the estimation error system is proven to be exponential. Based on the state estimation of singular switched system, the methods of state estimation and output disturbance reconstruction of original switched system are proposed. Finally, the simulation results confirm the predicted performance of the proposed methods.