Observability Matrices Research Articles

Estimating Control Points for B-Spline Surfaces Using Fully Populated Synthetic Variance–Covariance Matrices for TLS Point Clouds

A flexible approach for geometric modelling of point clouds obtained from Terrestrial Laser Scanning (TLS) is by means of B-splines. These functions have gained some popularity in the engineering geodesy as they provide a suitable basis for a spatially continuous and parametric deformation analysis. In the predominant studies on geometric modelling of point clouds by B-splines, uncorrelated and equally weighted measurements are assumed. Trying to overcome this, the elementary errors theory is applied for establishing fully populated covariance matrices of TLS observations that consider correlations in the observed point clouds. In this article, a systematic approach for establishing realistic synthetic variance–covariance matrices (SVCMs) is presented and afterward used to model TLS point clouds by B-splines. Additionally, three criteria are selected to analyze the impact of different SVCMs on the functional and stochastic components of the estimation results. Plausible levels for variances and covariances are obtained using a test specimen of several dm—dimension. It is used to identify the most dominant elementary errors under laboratory conditions. Starting values for the variance level are obtained from a TLS calibration. The impact of SVCMs with different structures and different numeric values are comparatively investigated. Main findings of the paper are that for the analyzed object size and distances, the structure of the covariance matrix does not significantly affect the location of the estimated surface control points, but their precision in terms of the corresponding standard deviations. Regarding the latter, properly setting the main diagonal terms of the SVCM is of superordinate importance compared to setting the off-diagonal ones. The investigation of some individual errors revealed that the influence of their standard deviation on the precision of the estimated parameters is primarily dependent on the scanning distance. When the distance stays the same, one-sided influences on the precision of the estimated control points can be observed with an increase in the standard deviations.

Design of event‐triggered interval functional observers for systems with input and output disturbances

Design of event‐triggered functional observers for linear systems subject to input and output disturbances is presented in this paper. A new dynamic event‐triggered mechanism is first proposed and then a novel event‐triggered interval functional observer is designed. The designed observer provides upper and lower bounds of the unknown linear function of the state vectors. By constructing a Lyapunov function, conditions ensuring the existence of the event‐triggered functional observer are established. The smallest bound of the estimated error and an effective algorithm for determining observer matrices are also presented. Finally, the obtained results in this paper are used to estimate linear functions of the state vector of a battery and motor circuit model of electric vehicles.

Semiglobal Observer-Based Positive Scaled Edge-Consensus of Networked Discrete-Time Systems Under Actuator Saturation

In this article, by using the linear graph theory, modified algebraic Riccati equation (MARE)-based method and duality principle, two interaction protocols are proposed to achieve the scaled edge-consensus of networked discrete-time systems with unmeasurable edge-sates. Meanwhile, drawing support from MARE-based low-gain feedback technique and positive system theory, sufficient conditions are derived to ensure the bounded control inputs and positive edge-states. Moreover, feedback matrices and observer matrices are, respectively, constructed by utilizing the solutions of MARE and modified algebraic dual Riccati equation (MADRE). Remarkably, the theoretical results only use the edge number and vertex number of network rather than the global information of network. Finally, five examples are shown to demonstrate the feasibility of the interaction protocols.

Design of distributed functional interval observers for large-scale networks impulsive systems

In this paper, we consider the problem of designing distributed functional interval observers (IOs) for a class of large-scale networks impulsive systems with bounded uncertainties. We first design IOs for linear functions of the state vector of each system of the considered system. We then provide conditions for the existence of such IOs and an effective algorithm for computing unknown observer matrices. Finally, two examples and simulation results are given to illustrate the effectiveness of the proposed design method.

Robust observer‐based‐controller design for uncertain fractional‐order time‐varying‐delay systems

AbstractThis article focuses on the robust observer‐based controller (‐ROBC) for Uncertain Fractional‐Order Systems with Time‐Varying‐Delay (DU‐FOS‐TVD). First, the existence conditions of ‐ROBC are given. Then, based on the diffusive representation of the fractional‐order derivative and the indirect Lyapunov approach, a new sufficient condition is obtained and presented as a convex optimization problem with a Linear Matrix Inequality (LMI) constraint, which guarantees the robust stability of the estimation errors and the stabilization of the DU‐FOS‐TVD simultaneously. All observer matrices gains and control laws can be computed by solving the given LMI. A Numerical example is given to illustrate the validity of the proposed method.

Wind turbine robust disturbance accommodating control using non‐smooth H∞ optimization

SummaryDisturbance accommodating control (DAC) has been developed in the last decades for wind turbines to control the rotor/generator speed and to reduce structural loads. The method allows accommodating unknown disturbance effects by using the combination of disturbance observers and disturbance rejection controllers. The actual main problem of DAC is to define suitable disturbance observer and controller gain matrices to achieve the desired overall performance including turbine speed regulation in combination with structural load mitigation. The disturbance rejection controller is often designed and tuned separately for individual applications and operating conditions. The closed‐loop system stability and uncertainties due to the use of the linearized reduced‐order model in controller synthesis procedure are not fully considered. This paper introduces a method to design DAC by optimizing the observer and controller parameters simultaneously to guarantee system performance respecting to structural loads mitigation, power regulation, and robustness. To eliminate the rotor speed control steady‐state error due to model uncertainties, partial integral action is included. Simulation results using NREL reference wind turbine models show that the proposed method successfully regulates the rotor speed without error despite the presence of the model uncertainties. Structural loads are also reduced using proposed method compared to DAC designed by Kronecker product method. The proposed approach is able to define a stable and robust DAC controller by solving a non‐smooth H∞ optimization problem with structure and stability constraints.

Decentralized Cooperative Online Estimation With Random Observation Matrices, Communication Graphs and Time Delays

We analyze convergence of decentralized cooperative online estimation algorithms by a network of multiple nodes via information exchanging in an uncertain environment. Each node has a linear observation of an unknown parameter with randomly time-varying observation matrices. The underlying communication network is modeled by a sequence of random digraphs and is subjected to nonuniform random time-varying delays in channels. Each node runs an online estimation algorithm consisting of a consensus term taking a weighted sum of its own estimate and neighbours' delayed estimates, and an innovation term processing its own new measurement at each time step. By stochastic time-varying system, martingale convergence theories and the binomial expansion of random matrix products, we transform the convergence analysis of the algorithm into that of the mathematical expectation of random matrix products. Firstly, for the delay-free case, we show that the algorithm gains can be designed properly such that all nodes' estimates converge to the true parameter in mean square and almost surely if the observation matrices and communication graphs satisfy the stochastic spatio-temporal persistence of excitation condition. Secondly, for the case with time delays, we introduce delay matrices to model the random time-varying communication delays between nodes. It is shown that under the stochastic spatio-temporal persistence of excitation condition, for any given bounded delays, proper algorithm gains can be designed to guarantee mean square convergence for the case with conditionally balanced digraphs.

Closed-loop time-varying continuous-time recursive subspace-based prediction via principle angles rotation

This paper presents a closed-loop time-varying continuous-time recursive subspace-based prediction method utilizing principle angles rotation. A simple linear mapping can be provided by generalized Poisson moment functionals, which can deal with the time-derivatives problems of input–output Hankel matrices. The parity space employed in fault detection field is adopted instead of using the observable subspace. The system matrices are estimated consistently by the instrumental variable method and principal component analysis, which solves the identification problems of biased results for the system operating in closed-loop with a feedback controller. The system matrices are predicted by the principle angles rotation of the signal subspaces spanned from the extended observability matrices. The effectiveness of the proposed method is illustrated by the numerical simulations and real applications.

Recurrent dictionary learning for state-space models with an application in stock forecasting

In this work, we introduce a new modeling and inferential tool for dynamical processing of time series. The approach is called recurrent dictionary learning (RDL). The proposed model reads as a linear Gaussian Markovian state-space model involving two linear operators, the state evolution and the observation matrices, that we assumed to be unknown. These two unknown operators (that can be seen interpreted as dictionaries) and the sequence of hidden states are jointly learnt via an expectation–maximization algorithm. The RDL model gathers several advantages, namely online processing, probabilistic inference, and a high model expressiveness which is usually typical of neural networks. RDL is particularly well suited for stock forecasting. Its performance is illustrated on two problems: next day forecasting (regression problem) and next day trading (classification problem), given past stock market observations. Experimental results show that our proposed method excels over state-of-the-art stock analysis models such as CNN-TA, MFNN, and LSTM.

Second order discrete time-varying and time-invariant linear continuous systems and Kalman type conditions

<p style='text-indent:20px;'>The paper deals with the controllability and observability of second order discrete linear time varying and linear time-invariant continuous systems in matrix form. To this case, we generalize the classical conditions for linear systems of the first order, without reducing them to systems of the first order. Within the framework of Kalman-type criteria, we investigate these concepts for second-order linear systems with discrete / continuous time; we define the initial values and input functions uniquely if and only if the observability and controllability matrices have full rank, respectively. Also a conceptual partner of controllability, that is, reachability of second order discrete time-varying systems is formulated and a necessary and sufficient condition for complete reachability is derived. Also the transfer function of the second order continuous-time linear state-space system is constructed. We have given numerical examples to illustrate the feasibility and effectiveness of the theoretical results obtained.</p>

EFFECT OF LOW TEMPERATURE ON CARDIOINTERVALS DURING PHYSICAL TRAINING IN MEN

Introduction: Effects of low temperature and excessive physical load on the cardiovascular system are among the issues of human physiology that require better understanding for successful exploration of the Arctic. Aim: To study cardiac rhythm before and after winter marathon (50 km) in men. Methods: Altogether, 15 healthy men took part in this study. Cardiorhytm parameters were measured using "Elox-01S" device before and after a 50 km marathon in winter at -12 0C. Matrices of paired observations before and after the exposure were constructed. The number of k-pares belonging to the to the same population were identified. Wilcoxon test for paired samples was applied for before-after comparisons. Results: Significant differences were revealed in six main parameters of the heart rate at p ≤ 0.05 before and after the marathon. Pairwise comparisons matrices of samples showed an increase in the proportion of chaos, since decreased the number of cardiointervals samples pairwise comparisons for which P ≥ 0.05 (k1 = 15 before and k2 = 11 after the marathon), which seems to be typical for the winter period. Other studies have reported that in women the differences were significant for three parameters only, while in men, all 6 parameters are changed after the winter marathon. The role of chaos increases for the studied parameters after long physical exercise. Conclusion: Our results suggest that heavy physical load in winter may result in increasing of the role of sympathetic neuro-vegetative system and decreasing of the role of the parasympathetic system.

Multi-objective Unified qLPV Observer: Application to a Semi-active Suspension System

Abstract This work concerns the design of a multi-objective unified qLPV observer for the state estimation problem in LPV systems with a parameter-dependent control input matrix. The standard forms of the system and the observer are first presented, where the observer matrices are functions of the estimated states (qLPV problem). The effects of bounded unknown input disturbances are decoupled from the estimation error thanks to the parameterization of the observer matrices. To treat the disturbance caused by inexact scheduling parameters, we introduce an upper bound on the parameter estimation error, which is considered uncertainty. Then, the effects of the control input and the random measurement noise on the estimation error are minimized using the H∞ and generalized H2 conditions, respectively, as a multi-objective optimization problem. In the solution of the LMI sets, the projection lemma is applied to reduce the high conservativeness that would otherwise lead to suboptimal results. Then this observer is applied to a semi-active automotive suspension system written in LPV form, using simulations with real data measured from our experiment test platform, and compared with the linear time-invariant H∞ and H2 observers.

Observer-Based Distributed Sensor Fault-Tolerant Model Predictive Control for Intermittent Faults

Abstract For distributed control systems with intermittent sensor faults, a distributed fault and state combined observer is designed, and an observer switching mode strategy is proposed to improve the observer convergence performance, then a distributed fault-tolerant model predictive is designed based on the observer. In the proposed observer, the distributed system observer matrices, and state and fault estimation are computed in a totally distributed way with some transition matrices, which can consider the coupled states. The switching mode observer can be more targeted. The two modes: state only estimation, both state and fault estimation are switched due to the absence or presence of the sensor faults. The approach is shown effective through a simulated example.

A state observer for the computational network model of neural populations.

A state observer plays a vital role in the design of state feedback neuromodulation schemes used to prevent and treat neurological or psychiatric disorders. This paper aims to design a state observer to reconstruct all unmeasured states of the computational network model of neural populations that replicates patterns seen on the electroencephalogram by using the model inputs and outputs, as the theoretical basis for designing state feedback neuromodulation clinical schemes. The feasibility problem of linear matrix inequality conditions, which is the most important one for observer design of the computational network model of neural populations, is solved by using the input-output stability theory and the Lurie system theory. The observer matrices of the designed observer are formed by the optimal solution of the linear matrix inequality conditions. An illustrative example shows that the observer can simultaneously reproduce internal state variables of normal and lesion populations of the computational network model of neural populations under the background of focal origin brain dysfunction, and the designed observer has certain robustness toward input uncertainty and measurement noise. To the best of our knowledge, no observers have previously been designed for the computational network model of neural populations. The design of state feedback neuromodulation schemes based on the computational network model of neural populations is a new direction in the field of computational neuroscience.

Choosing an Adequate Convex Structure for Controller and Observer Gains in Takagi-Sugeno Control Systems

Abstract This work presents a methodology to choose the convex structure for nonlinear gains in approaches based on Takagi-Sugeno models. The proposal faces the problem of numerical complexity in LMI-based approaches within this area; it gives a finer convex structure for controller and observer matrices depending on two criteria: less number of LMI constraints or more decision variables while keeping the same number of LMIs in traditional approaches. The advantages of the proposal are illustrated via numerical examples.

Robust filtering and propagation of uncertainty in hidden Markov models

We consider the filtering of continuous-time finite-state hidden Markov models, where the rate and observation matrices depend on unknown time-dependent parameters, for which no prior or stochastic model is available. We quantify and analyze how the induced uncertainty may be propagated through time as we collect new observations, and used to simultaneously provide robust estimates of the hidden signal and to learn the unknown parameters, via techniques based on pathwise filtering and new results on the optimal control of rough differential equations.

Approximate guaranteed estimates for matrices in linear regression problems with a small parameter

The problem of finding linear unbiased estimates of the linear operator of unknown matrices — components of the observations vector, is investigated. It is assumed that the observation vector additively depends on a random vector with zero expected value, and the unknown correlation matrix belongs to a known bounded set. For the introduced class of linear estimates, necessary and sufficient conditions for the existence of solutions of operator equations that determine the unknown parameters of the vector estimate, are proved. The form of the guaranteed mean square error of the estimate is introduced on the sets of constraints of the problem parameters. The influence on the linear unbiased estimate of small perturbations of known rectangular matrices, which are the composites of the observations vector components, is also investigated. The analytical form is given through the parameters of the perturbed set of singularities for the introduced special operators that depend on a small parameter, which determine the corresponding operator equations, as well as their approximate solutions, in the first approximation of the small parameter method. A test example of solving the problem of finding a linear unbiased estimate under the condition of perturbation of both linearly independent and linearly dependent known observation matrices is presented.

Transfer Learning and Identification Method of Cross-View Target Trajectory Utilizing HMM

The behavior identification of the target trajectory is one of the important issues in space behavior analysis. Since the target trajectory model obtained from a fixed view cannot be adapted to the change of the observation perspective, it needs to be retrained when being faced with a new view, which leads to a great amount of increment in application cost. This study proposes a hidden Markov model (HMM) based on the cross-view transfer learning and the recognition method that firstly constructs a linear mapping relationship between the observation matrices of the source and target view utilizing the domain trajectory of the HMMs and obtains the observation matrix parameters of the target domain through the mapping system. Secondly, the transfer probability of the source domain is further optimized to obtain the target domain of the HMM and to identify the behavior of the target domain trajectory utilizing a small number of samples from the view of the target domain. The experimental results denote that the proposed method could effectively realize the identification of the trajectory behavior utilizing a small sample size in the target domain and would greatly reduce the application cost of the identification of the cross-view target trajectory.

Observer-Based Event-Triggered Predictive Control for Networked Control Systems under DoS Attacks.

This paper studies the problem of DoS attack defense based on static observer-based event-triggered predictive control in networked control systems (NCSs). First, under the conditions of limited network bandwidth resources and the incomplete observability of the state of the system, we introduce the event-triggered function to provide a discrete event-triggered transmission scheme for the observer. Then, we analyze denial-of-service (DoS) attacks that occur on the network transmission channel. Using the above-mentioned event-triggered scheme, a novel class of predictive control algorithms is designed on the control node to proactively save network bandwidth and compensate for DoS attacks, which ensures the stability of NCSs. Meanwhile, a closed-loop system with an observer-based event-triggered predictive control scheme for analysis is created. Through linear matrix inequality (LMI) and the Lyapunov function method, the design of the controller, observer and event-triggered matrices is established, and the stability of the scheme is analyzed. The results show that the proposed solution can effectively compensate DoS attacks and save network bandwidth resources by combining event-triggered mechanisms. Finally, a smart grid simulation example is employed to verify the feasibility and effectiveness of the scheme’s defense against DoS attacks.

$$H_{\infty }$$ Optimization-Based Stabilization for Nonlinear Disturbed Time Delay Systems

This paper contemplates designing a $$H_{\infty }$$ dynamic output-feedback decentralized control for nonlinear interconnected disturbed time delay systems. Pursuant to Lyapunov–Krasovskii functional techniques and linear matrix inequality methods, asymptotic stability conditions for the robust stability and stabilization of the studied system are conducted in an optimization problem subject to linear matrix inequalities. The resolution of such a problem enables computing jointly the robust observation and control gain matrices, maximizing the bounds of nonlinear interconnections tolerated by the system without being unstable, improving the performance of the proposed control strategy by minimizing a $$H_{\infty }$$ criterion and ensuring the stability of the closed-loop system despite exogenous disturbances applied to the subsystems. Simulation results are provided by a prominent application example of a 3-interconnected machine power system with time delay to demonstrate the efficacy of the designed delay-independent control approach.