Identification Of Stochastic Systems Research Articles

Improvement of System Identification of Stochastic Systems via Koopman Generator and Locally Weighted Expectation

Improvement of System Identification of Stochastic Systems via Koopman Generator and Locally Weighted Expectation

A few-shot identification method for stochastic dynamical systems based on residual multipeaks adaptive sampling.

Neural networks are popular data-driven modeling tools that come with high data collection costs. This paper proposes a residual-based multipeaks adaptive sampling (RMAS) algorithm, which can reduce the demand for a large number of samples in the identification of stochastic dynamical systems. Compared to classical residual-based sampling algorithms, the RMAS algorithm achieves higher system identification accuracy without relying on any hyperparameters. Subsequently, combining the RMAS algorithm and neural network, a few-shot identification (FSI) method for stochastic dynamical systems is proposed, which is applied to the identification of a vegetation biomass change model and the Rayleigh-Van der Pol impact vibration model. We show that the RMAS algorithm modifies residual-based sampling algorithms and, in particular, reduces the system identification error by 76% with the same sample sizes. Moreover, the surrogate model accurately predicts the first escape probability density function and the P bifurcation behavior in the systems, with the error of less than 1.59×10-2. Finally, the robustness of the FSI method is validated.

Meta-state–space learning: An identification approach for stochastic dynamical systems

Available methods for identification of stochastic dynamical systems from input–output data generally impose restricting structural assumptions on either the noise structure in the data-generating system or the possible state probability distributions. In this paper, we introduce a novel identification method of such systems, which results in a dynamical model that is able to produce the time-varying output distribution accurately without taking restrictive assumptions on the data-generating process. The method is formulated by first deriving a novel and exact representation of a wide class of nonlinear stochastic systems in a so-called meta-state–space form, where the meta-state can be interpreted as a parameter vector of a state probability function space parameterization. As the resulting representation of the meta-state dynamics is deterministic, we can capture the stochastic system based on a deterministic model, which is highly attractive for identification. The meta-state–space representation often involves unknown and heavily nonlinear functions, hence, we propose an artificial neural network (ANN)-based identification method capable of efficiently learning nonlinear meta-state–space models. We demonstrate that the proposed identification method can obtain models with a log-likelihood close to the theoretical limit even for highly nonlinear, highly stochastic systems.

Data-driven discovery of stochastic dynamical systems with [formula omitted]-stable Lévy noise based on residual networks

Identifying evolution laws of complex systems from massive data has been a challenging issue in the cross field of stochastic dynamics and data science with greater and greater concern in recent years. So far, significant progress has been made in dealing with cases where differential equations are driven by Gaussian noise, yet work for non-Gaussian cases remains great room for growth. In this paper, a data-driven approach based on deep residual networks (ResNets) is proposed to extract governing laws of stochastic dynamical systems perturbed by non-Gaussian α-stable Lévy noise. Specifically, we firstly separate the non-Gaussian noise from drift term for subsequent extraction according to the fundamental theory of differential equations. For the noise part, the Lévy jump measure and noise intensity are estimated via some properties of α-stable distribution. Next the residual network is employed to identify drift. Numerical results of systems of 1 to 3 dimensions are given to demonstrate the feasibility of this method. It is necessary to emphasize here that the contribution of this method is mainly manifested in its effective resolution of the identification for complex non-Gaussian stochastic dynamical systems via cutting-edge machine learning techniques.

SVD-Based Parameter Identification of Discrete-Time Stochastic Systems with Unknown Exogenous Inputs

This paper addresses the problem of parameter identification for discrete-time stochastic systems with unknown exogenous inputs. These systems form an important class of dynamic stochastic system models used to describe objects and processes under a high level of a priori uncertainty, when it is not possible to make any assumptions about the evolution of the unknown input signal or its statistical properties. The main purpose of this paper is to construct a new SVD-based modification of the existing Gillijns and De Moor filtering algorithm for linear discrete-time stochastic systems with unknown exogenous inputs. Using the theoretical results obtained, we demonstrate how this modified algorithm can be applied to solve the problem of parameter identification. The results of our numerical experiments conducted in MATLAB confirm the effectiveness of the SVD-based parameter identification method that was developed, under conditions of unknown exogenous inputs, compared to maximum likelihood parameter identification when exogenous inputs are known.

Parameter identification of the linear discrete-time stochastic systems with unknown exogenous inputs

The paper addresses a parameter identification problem for linear discrete-time stochastic systems with unknown exogenous inputs. Such systems are considered when solving practical problems related to the measurements processing in the case when it is impossible to do any assumptions about the evolution of unknown input signal or its statistical characteristics that can change over time. We consider a class of discrete time linear stochastic systems with unknown exogenous inputs, where an additional source of a priori uncertainty of the system model is introduced, namely, the unknown parameter, on the elements of which the system model matrices can depend. This formulation of the parameter identification problem under the conditions of unknown inputs and the presence of random noises describes a high degree of uncertainty of a discrete time linear stochastic system. We propose a novel solution to this problem based on the construction of a new instrumental identification criterion. Minimization of this criterion allows for evaluating the unknown system model parameters simultaneously with the estimating of the state vector and unknown exogenous inputs of the system. Numerical experiments confirm the validity and efficiency of the proposed parameter identification method.

Pareto Optimal Strategy Under H∞ Constraint for the Mean-Field Stochastic Systems in Infinite Horizon.

This article focuses on the mean-field linear-quadratic Pareto (MF-LQP) optimal strategy design for stochastic systems in infinite horizon, which is with the H∞ constraint when the system is disturbed by external interferences. The stochastic bounded real lemma (SBRL) with any initial state in infinite horizon is first investigated based on the stabilizing solution of the generalized algebraic Riccati equation (GARE). Then, by discussing the convexity of the cost functional, the stochastic indefinite MF-LQP control problem is defined and solved based on the MF-LQ theory and Pareto theory. When the worst case disturbance is considered in the collaborative multiplayer system, we show that the Pareto optimal strategy design with H∞ constraint [or robust Pareto optimal strategy, (RPOS)] can be given via solving two coupled GAREs. When the worst case disturbance and the Pareto efficient strategy work, all Pareto solutions are obtained by a generalized Lyapunov equation. Finally, a practical example shows that the obtained results are effective.

Observer-based SMC design for stochastic systems with Levy noise

Abstract This work addresses the problem of sliding mode control (SMC) design for a continuous-time non-linear stochastic system with Levy-type noise. A state observer model is constructed to estimate the unavailable state information. Furthermore, Levy-type noise is considered to analyse small perturbations and to characterize the appearance of large samples that will occur in the system. Lyapunov stability and SMC theory are used to provide some sufficient conditions that ensure the stochastic stability of the error system and reachability of the predefined sliding surface. Finally, an example is given to demonstrate the feasibility of the proposed approach.

Active Fault Diagnosis for Stochastic Systems Within Bayesian Minimum Risk Decision Framework

In this paper, the active fault diagnosis (AFD) problem is investigated for a class of discrete-time stochastic systems. We consider multiple fault modes of the system, and the different types of misdiagnoses of these faults lead to different losses. A novel AFD framework is developed based on the Bayesian minimum risk decision framework. The misdiagnosis risk is derived to characterize the total losses caused by the misdiagnoses of all considered faults. The input is specifically designed to improve diagnosis performance by minimizing the risk of misdiagnosis. Since it is intractable to express the misdiagnosis risk in the closed form, we deduce an upper bound on it to establish a novel input design criterion based on the Bhattacharyya distance. The optimal input signal can be obtained for AFD via concave quadratic programming. For diagnosis performance enhancement and computation simplification purposes, we propose two new semi-online implementation manners of the input design for stochastic systems with and without multi-fault modes switching respectively. Given the optimal input signal and the proposed implementation manner, faults are diagnosed based on the minimum misdiagnosis risk decision principle. The effectiveness and superiority of the proposed AFD method are demonstrated by simulation results on a four-tank system.

Parametric identification of flat stochastic systems for effective connectivity characterization

Some of the mechanisms that generate neuronal signals are known at the cellular level and rest on a balance of excitatory and inhibitory interactions within and between populations of neurons. Neural mass models assume that a neuronal population can be approximated using very few state variables, generally limited to mean membrane currents, potentials, and firing rates. This article deals with nonlinear parametric identification problems in neurophysiologically based models simulating brain effective connectivity. We propose a novel approach which utilizes optimal control theory for partially flat stochastic differential systems. The optimization-based approach to effective connectivity characterization has been tested through simulation experiments and compared with the extended and unscented Kalman filters. A variety of case studies have been successfully used for connectivity parameter identification: constant functions, step functions, periodic functions and random functions.

Distributed sparse identification for stochastic dynamic systems under cooperative non-persistent excitation condition

This paper considers the distributed sparse identification problem over wireless sensor networks such that all sensors cooperatively estimate the unknown sparse parameter vector of stochastic dynamic systems by using the local information from neighbors. A distributed sparse least squares algorithm is proposed by minimizing a local information criterion formulated as a linear combination of accumulative local estimation error and L1-regularization term. The upper bound of the estimation error of the proposed algorithm is presented. Furthermore, by designing a suitable adaptive weighting coefficient based on the local observation data, the set convergence of zero elements with a finite number of observations is obtained under a cooperative non-persistent excitation condition. It is shown that the proposed distributed algorithm can work well in a cooperative way even though none of the individual sensors can fulfill the estimation task. Our theoretical results are obtained without relying on the independency assumptions of regression signals that have been commonly used in the existing literature. Thus, our results are expected to be applied to stochastic feedback systems. Finally, the numerical simulations are provided to demonstrate the effectiveness of our theoretical results.

Editorial: Advances in Stochastic System Modeling, Control, Optimization, and Their Applications

Stochastic systems can be widely adopted for describing practical complex systems, such as meteorology. Recently, there have been many advances in the design of stochastic systems, including system modeling, control, estimation, performance enhancement, and industrial applications. Motivated by these results, this Special Issue encourages researchers to publish their latest contributions in the study of stochastic systems. In summary, we first introduce the current technical challenges in stochastic systems. Then, a current prevalent problem is provided to demonstrate the challenges in these systems, while the developing trends for stochastic system research are summarised. In particular, data-driven non-Gaussian system analyses will be the one of the significant research focal points in future.

Attack‐parameter‐dependent state feedback controller design for stochastic systems with denial‐of‐service attacks

AbstractIn this article, we investigate the attack‐parameter‐dependent controller synthesis problem for a class of stochastic control system under aperiodic denial‐of‐service (DoS) attacks. Different from the classic DoS attack models, which are characterized by DoS frequency and DoS duration, a new type of time‐constrained DoS attack model that only restricts the upper and lower bounds of the sleeping and active periods of the DoS attacker is introduced. Considering the effect of such DoS attacks, a switching‐like stochastic system model is built. Then based on the attack‐parameter‐dependent time‐varying stochastic Lyapunov function method, a new mean square exponential stability criterion of the resulting stochastic system under the DoS attacks is formulated in the form of linear matrix inequalities. Also, the attack‐resilient controller is designed. Finally, taking an aircraft system as an example, the validity of the obtained theoretical results is verified.

Distributed system identification for linear stochastic systems with binary sensors

The problem of distributed identification of linear stochastic system with unknown coefficient θ∗ over time-varying networks is considered. For estimating θ∗, each agent in the network can only access the input and the binary-valued output of the local system. Compared with the existing works on distributed optimization and estimation, the binary-valued local output observation considered in the paper makes the problem challenging. By assuming that the agent in the network can communicate with its adjacent neighbors, a stochastic approximation-based distributed identification algorithm is proposed, and the consensus and convergence of the estimates are established. Finally, a numerical example is given showing that the simulation results are consistent with the theoretical analysis.

Identification and Stochastic Optimizing the UAV Motion Control in Turbulent Atmosphere

In a class of diffusion Markov processes, we formulate a problem of identification of nonlinear stochastic dynamic systems with random parameters, multiplicative and additive noises, control functions, and the state vector at a final time moment. For such systems, the identifiability conditions are being studied, and necessary conditions are formulated in terms of the general theory of extreme problems. The developed engineering methods for identification and optimizing nonlinear stochastic systems are presented as well as their application for unmanned aerial vehicles under wind disturbances caused by atmospheric turbulence, namely, for optimizing the autopilot parameters during a rotary maneuver of an unmanned aerial vehicle in translational motion, taking into account the identification of its angular velocities.

Online state and inputs identification for stochastic systems using recursive expectation-maximization algorithm

In this paper, an online joint state estimation and unknown inputs (UIs) identification approach for industrial processes represented by the state-space model is proposed. The UIs identification is achieved by applying the recursive expectation-maximization (REM) technique. In E-step, a recursively calculated Q-function is derived based on the maximum likelihood framework, and the Kalman filter (KF) is adopted to estimate the states. In M-step, analytical solutions for UIs are obtained via locally maximizing the recursive Q-function. A numerical example of a quadrupled water tank process and practice application to system modeling of a distillation tower are employed to illustrate the proposed REM-KF algorithm's effectiveness. It is also demonstrated that the REM-KF algorithm is more accurate than existing online solutions.

Adaptive fuzzy event-triggered control for nonstrict-feedback switched stochastic nonlinear systems with state constraints

Due to the frequent occurrence of random disturbances in practical physical systems, the control design of stochastic systems has a significant application background. This article presents an event-triggered adaptive fuzzy control scheme for nonstrict-feedback switched stochastic nonlinear systems with state constraints. The barrier Lyapunov functions are deployed to make all states maintain the prescribed regions. In addition, the event-triggered mechanism is incorporated into the backstepping framework to mitigate the data transmission. The fuzzy logic systems are exploited to cope with the system uncertainties, and then the adaptive fuzzy control strategy is recursively constructed. The devised event-triggered adaptive fuzzy controller can not only surmount the influence of state constraints but also decrease unnecessary resource consumption. In virtue of common Lyapunov function method, it is shown that all system signals are bounded under switching signals and the predefined constraints are not violated. Finally, the validity of the presented scheme is elucidated by simulation results.

A robust identification method for stochastic nonlinear parameter varying systems

<abstract><p>Successful identification procedures are undoubtedly important for accurate model description and the consequent implementation of control strategies. Linear Parameter Varying (LPV) models are nowadays standard for control design purposes and powerful identification techniques accordingly available. Anyhow, recent advances have brought to focus the class of Nonlinear Parameter Varying (NLPV) models, which keep some nonlinearities embedded to the formulation. Identification tools for this latter class are still not available. Therefore, this paper proposes a novel method for the robust identification of stochastic NLPV systems, considering that the nonlinear parameter part is <italic>a priori</italic> known and obeys a Lipschitz condition. The method is based on a modified extended Masreliez-Martin filter and yields the joint estimation of both NLPV systems states and model parameters. The method manages the stochasticity of the system by considering the presence of measurement outliers with non-Gaussian distributions. Results considering real data from a vehicle suspension system are presented in order to demonstrate the consistency of the proposed method.</p></abstract>

Identification of Fast Time-varying Communication Channels Using the Preestimation Technique

Abstract Accurate identification of stochastic systems with fast-varying parameters is a challenging task which cannot be accomplished using model-free estimation methods, such as weighted least squares, which assume only that system coefficients can be regarded as locally constant. The current state-of-the-art solutions are based on the assumption that system parameters can be locally approximated by a linear combination of appropriately chosen basis functions. The paper shows that tracking performance of the resulting local basis function estimation algorithms can be further improved by means of regularization. The method is illustrated by an important recent application - identification of fast time-varying acoustic channels used in underwater communication.

Sparse system identification for stochastic systems with general observation sequences

Focusing on identification, this paper develops techniques to reconstruct zero and nonzero elements of a sparse parameter vector θ of a stochastic dynamic system with general observation sequences, including stationary time series and feedback control, for which the current input may depend on the past inputs and outputs, system noises as well as exogenous dithers. First, a sparse parameter identification algorithm is introduced based on L2 norm with L1 regularization, where the adaptive weights are adopted in the optimization variables of L1 term. Second, estimates generated by the algorithm are shown to have both set and parameter convergence. That is, sets of the zero and nonzero elements in the parameter θ can be correctly identified with probability one using a finite number of observations, and further estimates of the nonzero elements converge to the true values almost surely. Third, it is shown that the results are applicable to a large number of applications, including variable selection, open-loop identification, and closed-loop control of stochastic systems. Finally, numerical examples are given to support the theoretical analysis.