State Estimation Error Research Articles

A generalized Fourier transform by means of change of variables within multilinear approximation

The paper deals with approximations of periodic functions that play a significant role in harmonic analysis. The approach revisits the trigonometric polynomials, seen as combinations of functions, and proposes to extend the class of models of the combined functions to a wider class of functions. The key here is to use structured functions, that have low complexity, with suitable functional representation and adapted parametrizations for the approximation. Such representation enables to approximate multivariate functions with few eventually random samples. The new parametrization is determined automatically with a greedy procedure, and a low rank format is used for the approximation associated with each new parametrization. A supervised learning algorithm is used for the approximation of a function of multiple random variables in tree-based tensor format, here the particular Tensor Train format. Adaptive strategies using statistical error estimates are proposed for the selection of the underlying tensor bases and the ranks for the Tensor-Train format. The method is applied for the estimation of the wall pressure for a flow over a cylinder for a range of low to medium Reynolds numbers for which we observe two flow regimes: a laminar flow with periodic vortex shedding and a laminar boundary layer with a turbulent wake (sub-critic regime). The automatic re-parametrization enables here to take into account the specific periodic feature of the pressure.

Sliding-Mode Observer-Based Fault Reconstruction for T-S Fuzzy Descriptor Systems

This article discusses the problem of sliding-mode observer (SMO)-based fault reconstruction for T-S fuzzy descriptor systems by using the RBF neural network. First, a descriptor learning SMO, without the observability condition of fast subsystem, is developed such that the reconstruction of fault and states is achieved, simultaneously. Then, a sufficient linear matrix inequality (LMI) condition is presented to guarantee the admissibility of the sliding motion. Meanwhile, the LMI condition ensures the boundedness of the state and fault estimation errors. By utilizing robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> strategy, the impact of disturbance on the system can be reduced. Moreover, an RBF neural network-based sliding-mode control (SMC) strategy is adopted to estimate the nonlinearity, unknown positive constants, and ensure the reachability condition, simultaneously. Finally, an example is presented to verify the efficacy of our approach.

Impedance Control for Coordinated Robots by State and Output Feedback

The impedance control for coordinated robots interacting with the unknown environment is investigated in this article, subject to unknown system dynamics and the environment with which coordinated robots come into contact. For the whole system, impedance control is developed for coordinated robots. The notable feature is that the robot-environment interaction performance is improved without any information about the environment, so that the robotic system follows the commanded position trajectory in noncontact phase, while the desired destination is obtained according to the force exerted on the environment during contact phase. Moreover, based on assumption that some system signals are unmeasurable, output feedback control is designed for coordinated robot systems, where a state observer based on neural network technique is designed, that can force the state estimate error converge to a small neighborhood of zero. Simulation results are provided to demonstrate the effectiveness of the proposed control algorithm.

Fuzzy decentralized output feedback event-triggered control for interval type-2 fuzzy systems with saturated inputs

This paper studies the fuzzy decentralized output feedback event-triggered control problem for the interval type–2 Takagi-Sugeno (IT2 T-S) fuzzy interconnected system with actuator saturation. Firstly, a state decentralized observer is designed and an event-triggered mechanism is established by using the state estimation errors. Secondly, the saturated inputs are represented by a polyhedron model, and then a fuzzy decentralized output feedback even-triggered control approach is developed via the parallel distributed compensation (PDC) algorithm. The asymptotic stabilization sufficient conditions of the closed-loop system are derived by employing Lyapunov theory and linear matrix inequalities (LMIs) method. Finally, a numerical example is provided to verify the feasibility of the developed control scheme.

On the optimality of the Kitanidis filter for state estimation rejecting unknown inputs

As a natural extension of the Kalman filter to systems subject to arbitrary unknown inputs, the Kitanidis filter has been designed by one-step minimization of the trace of the state estimation error covariance matrix. In this technical communiqué, it is shown that the Kitanidis filter is also optimal for the whole gain sequence in the sense of matrix positive definiteness, which notably implies that the Kitanidis filter minimizes not only the trace criterion, but also the matrix spectral norm criterion.

Robust filtering algorithm against hybrid-attacks and randomly occurring nonlinearities: Application to a quadrotor UAV

This paper addresses the filtering problem for a class of discrete-time cyber-physical system (CPS) in simultaneous presence of physical attack, denial of service attacks (DoS), false data injection (FDI) attacks and randomly occurring nonlinearities (RONs). The malicious attacks can be simultaneously launched at the physical and cyber space to assault/disturb the system's state or block the measurement transmission channels. Firstly, the physical attack is considered as an injected unknown information, which can modify the system's state; then, a unified framework is proposed under which the phenomena of DoS attacks and FDI attacks are depicted by two independent Bernoulli distributed random variables, respectively. Furthermore, the available random probability information of the hybrid attacks and RONs are taken into account in the developed state estimation algorithm. Subsequently, by employing the stochastic analysis and matrix techniques, the exponential boundedness of the state estimation error is discussed from the theoretical aspects. As a typical CPS, a quadrotor unmanned aerial vehicle(UAV) system is provided to demonstrate the effectiveness and practicability of the proposed state estimation method.

Asynchronous observer design for switched T–S systems with unmeasurable premises and switching mismatches

This paper investigates the design of asynchronous switched observers for continuous-time nonlinear switched systems, where Takagi–Sugeno fuzzy models represents the nonlinear modes, with mismatching switching laws and bounded output disturbances (e.g. representing measurement bias, noise or fault). The proposed switched T–S observers allow state estimations when the systems’ premise variables are not necessarily measurable and when the observer’s active switched-mode does not necessarily match the one of the switched system. To derive the design conditions, a multiple Lyapunov function candidate is considered to cope with the asynchronous switching modes, together with a H∞ criterion to minimize the transfer between the output disturbance and the state estimation errors. Moreover, Lipschitz constraints are considered to cope with the unmeasurable premise variables. The proposed conditions are declined into four theorems as Linear Matrix Inequalities. Despite their increasing computational cost, these theorems bring successive conservatism improvements, allowing the users to select the appropriate conditions regarding to the complexity of their applications. Finally, an academic example and a practical one (dealing with a tunnel diode circuit) are given to compare the conservatism and to illustrate the effectiveness of the proposed asynchronous switched T–S observer design methodologies

A Bayesian smoothing for input‐state estimation of structural systems

AbstractInstantaneous output‐only inversion of a system with delayed appearance of input influences on the measured outputs via filtering methods suffer from intensive amplification of the observation noise in the estimated quantities due to the ill‐conditionedness. To remedy this issue, in this paper, a new unbiased recursive Bayesian smoothing method is developed for input‐state estimation of linear systems without direct feedthrough to reduce estimation uncertainty through an extended observation equation. By minimizing input and state estimation error variance, the optimal smoothing input and state gain matrices are derived. Moreover, a new efficient method is proposed for the recursive calculation of correlation of state estimation error with modeling and observation noise vectors.

Physics-guided deep neural network to characterize non-Newtonian fluid flow for optimal use of energy resources

Numerical simulations of non-Newtonian fluids are indispensable for optimization and monitoring of several industrial processes such as crude oil transportation, nuclear cooling, geothermal and fossil fuel production. The governing equations derived for non-Newtonian fluid models result in nonlinear differential equations. Thus, increasing the complexity even for simple geometries. The cumbersome numerical computation and rudimentary empirical solutions hinder faster analysis over a wide range of parameters. However, machine and deep learning methods have higher accuracy but rely heavily on the quality and amount of training data, and the solution may become inconclusive if data is sparse. In this research, a novel algorithm (Herschel Bulkley Network) is introduced to simulate the non-Newtonian fluid flow in a pipe using data redundant deep neural network (DNN) for fully developed, laminar, and incompressible flow conditions. The objective of this investigation is to develop a physics dominated DNN solely driven by minimizing residuals from the Navier-Stokes based governing equations, establishing benchmark research. Herschel-Bulkley model is used to approximate the complex rheological behavior of a non-Newtonian fluid. The proposed DNN algorithm is structured to incorporate initial/boundary conditions in cylindrical coordinates and approximate the solution without the aid of any simulated or training data. The simulated results and analysis demonstrate an excellent agreement between the proposed algorithm and non-Newtonian fluids flow attributes. The detailed parametric analysis exhibits the competency of the proposed algorithm to explain the rheological features. Monte-Carlo simulation is performed by propagating uncertainty to investigate the dominant parameters affecting simulated results. The uncertainty in fluid consistency index is responsible for higher variance in the calculated flow rate, while the least variation is observed due to fluid behavior index uncertainty. The performance of the algorithm is validated with experimental datasets. The statistical error estimation exhibits a mean absolute error of 11.5%, and root mean squared error of 0.87. A comprehensive analysis on training unsupervised DNN and adjusted hyperparameters is also highlighted to achieve expedite convergence.

The Salted Kalman Filter: Kalman filtering on hybrid dynamical systems

Many state estimation and control algorithms require knowledge of how probability distributions propagate through dynamical systems. However, despite hybrid dynamical systems becoming increasingly important in many fields, there has been little work on utilizing the knowledge of how probability distributions map through hybrid transitions. Here, we make use of a propagation law that employs the saltation matrix (a first-order update to the sensitivity equation) to create the Salted Kalman Filter (SKF), a natural extension of the Kalman Filter and Extended Kalman Filter to hybrid dynamical systems. Away from hybrid events, the SKF is a standard Kalman filter. When a hybrid event occurs, the saltation matrix plays an analogous role as that of the system dynamics, subsequently inducing a discrete modification to both the prediction and update steps. The SKF outperforms a naive variational update – the Jacobian of the reset map – by having a reduced mean squared error in state estimation, especially immediately after a hybrid transition event. Compared against a hybrid particle filter, the particle filter outperforms the SKF in mean squared error only when a large number of particles are used, likely due to a more accurate accounting of the split distribution near a hybrid transition.

Global adaptive output feedback stabilization for nonlinear time‐delay systems with unknown measurement sensitivity

AbstractIn this article, a global output feedback stabilization scheme is proposed for a class of time‐delay uncertain nonlinear systems with unknown measurement sensitivity. A new high gain observer is designed with which the sensitivity function can be tackled by only one dynamic gain and the coupled linear‐like controller is fairly simple. By introducing some transformations of the state estimation errors and observer states, and appropriately choosing Lyapunov–Krasovskii functionals, it is proved that the proposed controller can globally stabilize the system.

Sampled-data fuzzy observer design for nonlinear systems with a nonlinear output equation under measurement quantization

In this paper, a sampled-data fuzzy observer (SDFO) of oscillating nonlinear systems with a nonlinear output equation is proposed based on the Takagi–Sugeno (T–S) fuzzy-model-based approach. First, to handle the low transmission capacity of the network, measurements from the system of interest are assumed to be quantized. Next, we employ an exponentially time-varying gain matrix to the SDFO system for enhancing the decay rate performance of the state estimation error dynamics, and these are represented with the T–S fuzzy model. To show better performance on the state estimation, we focus on developing two points: a novel design methodology and a novel looped Lyapunov–Krasovskii functional (LKF). Furthermore, we propose a novel design condition of an SDFO for systems without measurement quantization, which is less conservative than conventional approaches. All of the proposed design conditions are formulated in terms of linear matrix inequalities (LMIs). Finally, appropriate simulation examples are given to validate the effectiveness of the proposed method, and these show better performance compared to the conventional studies.

Optimal Stealthy Innovation-Based Attacks With Historical Data in Cyber-Physical Systems

The problem of stealthy innovation-based attacks in cyber-physical systems is studied in this paper. Different from the existing results which only utilize the current data, a more general attack strategy is designed by combining the historical and the current innovations to deteriorate the estimation performance and keep stealthy to the detector simultaneously. Under the framework of the attacks, the remote state estimation error is analyzed, and the optimal attack policy is derived by solving a convex optimization problem to achieve the maximal estimation error. Moreover, it is proved that the optimal attack strategy is piecewise constant, such that the attack is designed with low calculation cost. Finally, simulation examples are provided to demonstrate the theoretical results.

Output Feedback Tracking Sliding Mode Control for Systems with State- and Input-Dependent Disturbances

In this paper, output feedback tracking sliding mode control was considered for uncertain multivariable linear systems. The uncertainties included external disturbance, the system state, and control input. A new property of the loop transfer recovery (LTR) observer was first established: the state estimation error of the LTR observer can be made arbitrarily small with respect to state- and input-dependent system uncertainties. Observer-based output feedback tracking sliding mode control using the LTR observer is presented. The proposed sliding mode control approach can maintain the boundedness of the system state and drive the system outputs arbitrarily close to the desired reference outputs; the degree of closeness was determined by a design parameter in the LTR observer. In the proposed approach, the most general and simple observer-based output feedback control formulation was used to achieve global tracking. Simulations with a two-degree-of-freedom (DOF) robotic manipulator application illustrated the claimed properties, and a peaking and chattering reduction technique was demonstrated to protect the actuator.

Observer design for semi-Markov jump systems with incremental quadratic constraints

This paper deals with the observer design problem for semi-Markov jump systems with incremental quadratic constraints. Based on the design objective that the state estimation error is stochastically stable, the sufficient conditions formulated by linear matrix inequalities are presented. To reduce the conservatism of sufficient conditions as well as the computational burden, the relaxation method with slack variable is employed. Finally, a simulation example verifies the effectiveness and superiority of the method studied in this paper.

Hybrid adaptive observer-based output feedback predictive control for the alternating activated sludge process

In this paper, an adaptive observer-based predictive controller is designed for the alternating activated sludge process which represents a nonlinear hybrid system. Precisely, our objective is to control the dissolved oxygen concentration during the aerobic phase. First, a hybrid adaptive observer is designed to estimate conjointly the unmeasured state (the ammonia concentration) and the unknown parameter (the coefficient of performance of heterotrophic biomass). Then the estimated signals are used in the output feedback predictive control law. The convergence of the state estimation, parameter reconstruction and tracking control errors are established through a Lyapunov stability analysis. Numerical simulations are dedicated to highlight the good performances of the developed output feedback control approach.

Observer Design for One-sided Lipschitz Uncertain Descriptor Systems with Time-varying Delay and Nonlinear Uncertainties

This paper investigates observer design for a class of one-sided Lipschitz descriptor systems with time-varying delay and uncertain parameters. In order to provide a general framework for large-scale systems, the paper considers uncertainties, nonlinearities, disturbance and time-varying delay at both output and state. By constructing Lyapunov–Krasovskii functional, and using the one-sided Lipschitz condition and the quadratic inner-boundedness inequality, we establish the sufficient condition which guarantees that the observer error dynamics is asymptotically stable, and the proposed observer ensures the $$L_2$$ gain bounded by a scalar $$\gamma .$$ Then, we change the condition into a strict matrix inequality condition. Furthermore, based on the obtained results, we establish the linear matrix inequality-based condition to ensure the asymptotically convergence of state estimation error and to accomplish robustness against $$L_2$$ norm bounded disturbances by utilizing change of variables. We propose the computing method of observer gain. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed method.

Synthetic state of charge estimation for lithium-ion batteries based on long short-term memory network modeling and adaptive H-Infinity filter

Accurate state of charge estimation is essential to improve operation safety and service life of lithium-ion batteries. This paper proposes a synthetic state of charge estimation method for lithium-ion batteries based on long short-term memory network modeling and adaptive H-infinity filter. Firstly, the long short-term memory network is exploited to roughly estimate state of charge with the input of voltage, current, operating temperature and state of health. Then, to mitigate the output fluctuation and improve the estimation robustness of long short-term memory network, the adaptive H-infinity filter is employed to flatten the estimation results and further improve the estimation accuracy. A main advantage of the proposed synthetic method lies in that precise battery modeling and burdensome model parameter identification tasks that are imperative in traditional observers or filters can be omitted, thus improving the application efficiency of the proposed algorithm. The proposed method is verified effective on two types of lithium-ion batteries under dynamic working scenarios including the varying temperature and aged conditions. The experimental results highlight that the estimation error of state of charge can be restricted within 2.1% in wide temperature range and different aging states, manifesting its high-precision estimation capacity and strong robustness.

Control-Aware Energy-Efficient Transmissions for Wireless Control Systems With Short Packets

In this article, we investigate control-aware energy-efficient transmission strategies for wireless control systems with short packets (WCSs), in which remote state estimation error, system stability, transmission energy consumption, and communication packets with finite-length coding are all taken into account. Specifically, we formulate the transmission strategy design problem as a multiobjective optimization problem, which minimizes the remote state estimation error and transmission energy consumption simultaneously under the constraints of system stability and short packet communications. To solve the multiobjective optimization problem, we first introduce a novel objective function that encapsulates two different objective functions into a single one by using weight parameters, and further prove that the solution of the new stochastic optimization problem is a nondominated solution of the original one. Moreover, to solve the new stochastic optimization, we propose a dynamic control-aware energy-efficient transmission (DCET) algorithm that pushes the objective cost close to the optimal with a tradeoff in virtual queue backlogs for constraints. In particular, to tackle the nonconvexity constraint due to short packet communications, we introduce an additional constraint, with which the optimization problem is convex. Finally, simulation results verified the superiority of our proposed transmission strategy as compared with schemes of TDMA and Aloha-RAM multi access.

Trajectory Optimisation for Cooperative Target Tracking with Passive Mobile Sensors

The paper considers the problem of tracking a moving target using a pair of cooperative bearing-only mobile sensors. Sensor trajectory optimisation plays the central role in this problem, with the objective to minimize the estimation error of the target state. Two approximate closed-form statistical reward functions, referred to as the Expected Rényi information divergence (RID) and the Determinant of the Fisher Information Matrix (FIM), are analysed and discussed in the paper. Being available analytically, the two reward functions are fast to compute and therefore potentially useful for longer horizon sensor trajectory planning. The paper demonstrates, both numerically and from the information geometric viewpoint, that the Determinant of the FIM is a superior reward function. The problem with the Expected RID is that the approximation involved in its derivation significantly reduces the correlation between the target state estimates at two sensors, and consequently results in poorer performance.