Lyapunov-based adaptive state estimation for a class of continuous-time nonlinear stochastic systems

In many circumstances involving heat and mass transfer issues, it is considered impractical to measure the input flux and the resulting state distribution in the domain. Therefore, the need to develop techniques to provide solutions for such problems and estimate the inverse mass flux becomes imperative. Adaptive state estimator (ASE) is increasingly becoming a popular inverse estimation technique which resolves inverse problems by incorporating the semi-Markovian concept into a Bayesian estimation technique, thereby developing an inverse input and state estimator consisting of a bank of parallel adaptively weighted Kalman filters. The ASE is particularly designed for a system that encompasses independent unknowns and /or random switching of input and measurement biases. The present study describes the scheme to estimate the groundwater input contaminant flux and its transient distribution in a conjectural two-dimensional aquifer by means of ASE, which in particular is because of its unique ability to efficiently handle the process noise giving an estimation of keeping the relative error range within 10% in 2-dimensional problems. Numerical simulation results show that the proposed estimator presents decent estimation performance for both smoothly and abruptly varying input flux scenarios. Results also show that ASE enjoys a better estimation performance than its competitor, Recursive Least Square Estimator (RLSE) due to its larger error tolerance in greater process noise regimes. ASE’s inherent deficiency of being slower than the RLSE, resulting from the complexity of algorithm, was also noticed. The chosen input scenarios are tested to calculate the effect of input area and both estimators show improved results with an increase in input flux area especially as sensors are moved closer to the assumed input location.

Accurate cubature and extended Kalman filtering methods for estimating continuous-time nonlinear stochastic systems with discrete measurements

International audience

The problem of approximation of unknown dynamics of a continuous-time observable nonlinear system is considered using a feedforward neural network, operating over delayed sampled outputs of the system. Error bounds are derived that explicitly depend upon the sampling time interval and network architecture. The main result of this note broadens the class of nonlinear dynamical systems for which adaptive output feedback control and state estimation problems are solvable.

This study proposes an active nonlinear control strategy for effective vibration mitigation in nonlinear dynamical systems characterized by uncertainty. The proposed scheme relies on the coupling of a Bayesian nonlinear observer, namely the Unscented Kalman Filter (UKF) with a two-stage control process. The UKF is implemented for adaptive joint state and parameter estimation, with the estimated states and parameters passed onto the controller. The controller comprises a first task of feedback linearization, allowing for subsequent integration of any linear control strategy, such as addition of damping, LQR control, or other, which then operates on the linearized state equations. The proposed framework is validated on a Duffing oscillator characterized by light damping and an uncertain nonlinear parameter under harmonic and stochastic disturbance. The demonstrated performance suggests that the proposed Bayesian approach offers a competitive approach for active vibration suppression in nonlinear uncertain systems.

This paper investigates adaptive event-triggered state estimation for T-S fuzzy systems with multiple cyber-attacks. In order to reduce network load, the adaptive event-trigger mechanism is used to adjust the threshold of event triggering condition adaptively on the premise of ensuring system performance. Considering the influence of cyber-attacks, a T-S fuzzy model for the state estimation is established with the adaptive event-trigger mechanism. On the basis of the model, the sufficient conditions to guarantee the system asymptotically stability are obtained by using Lyapunov stability theory. In addition, the gains of the estimator are acquired in the form of linear matrix inequalities (LMIs). Finally, a simulated example is given to testify the feasibility of the proposed method.

This paper presents a method for real time adaptive hybrid state estimation of the power system states using the SCADA as well as limited synchronous phasor measurements. The proposed method can track the power system dynamics by periodically updating the sensitivities to the unobservable buses during the intervals between successive outputs of state estimator with SCADA measurements. The performance of the proposed method is evaluated on a number of standard test systems for different sets of un-observability. Simulation result shows that the proposed method can track the electromechanical dynamics of the system during the large disturbances in the system, it also improves the accuracy of the estimates and enhances the numerical stability of the estimation.

One of the approaches to sampled-data controller design for nonlinear continuous-time systems consists of obtaining an appropriate model and then proceeding to design a controller for the model. Then, it is important to derive a good approximate sampled-data model because the exact sampled- data model for nonlinear systems is often unavailable to the controller designers. Recently, Yuz and Goodwin have proposed an accurate sampled-data model which includes extra zero dynamics, so-called the sampling zero dynamics, corresponding to the relative degree of the continuous-time nonlinear system. This paper shows that a more accurate sampled-data model is required for a controlled Van der Pol system with the relative degree two. The reason is that the closed-loop system becomes unstable when a controller design method based on cancellation of the zero dynamics is applied, and the phenomenon seems related to the instability of the sampling zero dynamics of the more accurate sampled-data model. Further, this paper derives a more accurate model than that of Yuz and Goodwin for continuous-time nonlinear systems with the relative degree two, and presents a condition which assures the stability of the sampling zero dynamics of the obtained model.

This paper studies fuzzy hyperbolic H/sub /spl infin// filter for signal estimation of nonlinear continuous-time systems with state time delay. The fuzzy hyperbolic model (FHM) can be used to establish models for certain unknown complex systems. Furthermore, the main advantage of using the FHM over the Takagi-Sugeno fuzzy model are that no premise structure identification is needed and no completeness design of premise variables space is needed. Also an FHM is a kind of valid global description and nonlinear model in nature. And it is easy to design a filter based on an FHM since FHM satisfies Lipschitz condition. First, FHM is proposed to represent the state-space model for nonlinear continuous-time systems. Next, we design a stable fuzzy H/sub /spl infin// filter based on the FHM, which assures asymptotic stability and a prescribed H/sub /spl infin// index for the filtering error system. A sufficient condition for the existence of such a filter is established through seeking the feasible solutions of a linear matrix inequality (LMI). Simulation example is provided to illustrate the design procedure of the proposed method.

Kalman filtering (KF) and hidden Markov model (HMM) signal processing techniques are coupled to demodulate signals transmitted through noisy fading channels. The demodulation scheme presented can be applied to both digital M-ary differential phase shift keyed (MDPSK) and analog frequency modulated (FM) signals. Adaptive state and parameter estimation algorithms are devised based on the assumption that the transmission channel introduces time-varying gain and phase changes, modelled by a stochastic linear system, and has additive Gaussian noise. Our technique is to use an HMM filter, for signal estimation, coupled with a KF, for channel parameter tracking. The approach taken can easily be generalised for other transmission schemes, such as continuous phase modulated (CPM) signals. >

Real Data Testing of Model Parameter Estimation Methods for Macroscopic Traffic Flow Model

Path planning over spatiotemporal models can be applied to a variety of applications such as UAVs searching for spreading wildfire in mountains or network of balloons in time-varying atmosphere deployed for inexpensive internet service. A notable aspect in such applications is the dynamically changing environment. However, path planning algorithms often assume static environments and only consider the vehicle’s dynamics exploring the environment. We present a spatiotemporal model that uses a cross-correlation operator to consider spatiotemporal dependence. Also, we present an adaptive state estimator for path planning. Since the state estimation depends on the vehicle’s path, the path planning needs to consider the trade-off between exploration and exploitation. We use a high-level decision-maker to choose an explorative path or an exploitative path. The overall proposed framework consists of an adaptive state estimator, a short-term path planner, and a high-level decision-maker. We tested the framework with a spatiotemporal model simulation where the state of each grid transits from normal, latent, and fire state. For the mission objective of visiting the grids with fire, the proposed framework outperformed the random walk (baseline) and the single-minded exploitation (or exploration) path.

In this paper, we model the generalized power system state estimation problem as a hybrid estimation problem in which the network configuration and voltage phasor states are treated as discrete and continuous states, respectively. We propose the Multiple model Adaptive Power system State Estimator (MAPSE), which implements a multiple model adaptive estimator with a bank of Unscented Kalman Filters (UKFs) to provide a running estimate of the voltage phasor states and a probability distribution for the candidate network configurations. The MAPSE updates the network configuration probability distribution by applying a Bayesian recursion to the measurement residuals from each of the UKFs at each timestep. Simulation on a modified version of the 33 node distribution network demonstrates successful network configuration detection and accurate voltage phasor state estimation.

This paper describes a deterministic approach to adaptive state and parameter estimation using a multiple model structure. In the set-up adopted, the plant of interest is described by a finite dimensional model with parametric uncertainty. To each choice of a finite number of parameter values there corresponds a finite set of multiple design models and a corresponding set of observers. Assuming the latter have been chosen, a Dynamic Weighting Signal Generator (DWSG) performs on-line adaptation of the weights given to the individual observer estimates based on the energy of the output error signals. In the present paper we develop a distance-like pseudo norm between the true plant and the identified model in a deterministic setting, based on the energy of the output error signals. Furthermore we show, under a distinguishability condition, that the model identified is the one that is closest to the true plant in the defined deterministic norm. We also prove that the convergence of the parameter estimate is exponentially fast. Performance and convergence of the CT-MMAE procedure are illustrated with Monte-Carlo simulation runs using the model of an inverted pendulum.

This work describes the development of a vehicle state estimator, designed to be employed onboard in real-time, based on the data acquisitions already available within the vehicle CAN bus infrastructure. The proposed estimation algorithm, taking into account the suspension elasto-kinematics, the longitudinal, lateral and combined dynamics of the tyres as well as the aligning interaction torques at the ground, represents at the current stage a significantly complete tool, since it also provides an estimation of road slope and banking angles, generalising the adoption of the presented vehicle model even on highly inclined roads. A further advantage of the presented estimator consists of its capability to identify in real-time and with a good level of accuracy the tyre/road interaction physical characteristics in terms of grip and cornering stiffness.