Uncertain Stochastic Systems Research Articles

Fusion estimation for stochastic uncertain systems with time-correlated rician fading channels

In this article, a fusion estimation scheme is proposed for stochastic uncertain systems with time-correlated fading channels (TFCs). A batch of random variables obeying Gaussian distributions is employed to describe the parameter uncertainties. The sensor communicates with the local filter through a TFC where the evolution of the channel coefficient is characterized by a certain dynamic process with one-step correlated noises. For further analyzing the effects of TFCs, a class of additional variables is first introduced by augmenting the dynamics of channel coefficients and the concerned system. Then, a new group of modified local filters is developed and the unbiasedness of local filters is examined by means of inductive method. Furthermore, the filter gains which minimize the local filtering error covariances are designed for the modified local filters in the simultaneous presence of stochastic uncertainties and TFCs. Subsequently, the cross-covariances among local estimates are computed iteratively and, based on the obtained cross-covariances as well as the unbiased local estimates and their corresponding filtering error covariances, a fusion estimate is obtained by using weighted least square fusion method. Finally, the effectiveness of the proposed fusion estimation scheme is verified by two examples.

Design of Distributed Fusion Predictor and Filter without Feedback for Nonlinear System with Correlated Noises and Random Parameter Matrices

Abstract This work presents distributed predictor and filter without feedback for nonlinear stochastic uncertain system with correlated noises. Firstly, for the problem that the process noise and measurement noise are correlated, the two-step prediction theorem based on projection theorem is used to replace the one-step prediction theorem, and the two-step prediction value of a single sensor is obtained. Secondly, the two-step prediction value of each sensor state is used as the measurement information to modify the distributed fusion predictor to obtain the distributed fusion prediction value. Then, according to the projection theorem, the prediction value of distributed fusion is used as measurement information to modify the filtering value of distributed fusion. Finally, the Cubature Kalman filter (CKF) algorithm is used to implement the algorithm proposed in this paper. By comparison with existing methods, the algorithm proposed in this paper solves the problem that existing methods cannot handle state estimation and prediction problems for nonlinear multi-sensor stochastic uncertain systems with correlated noises.

Research on Hover Control of AUV Uncertain Stochastic Nonlinear System Based on Constructive Backstepping Control Strategy

The paper is concerned with station keeping control problem via backstepping for an autonomous underwater vehicle (AUV) systems with nonlinear continuous function. This paper is the first time to using backstepping control method for stochastic nonlinear systems. Under nonlinear growth conditions, when the AUV motion affected the driving force, resistance of ocean and the force generated by current the difficulty arising from the underwater robot system output feedback makes the station keeping problems challenging and forward-looking. There exist two problems to research the fast response time and good station keeping, respectively. There a new control method is proposed for the first time to construct a backstepping stabilizing controller. In this paper, a concept of randomness to study the station keeping control problem of output feedback of stochastic nonlinear systems, remove the original harsher growth conditions, make it meet the more general function growth conditions. In order to deal with the station error of system converges to arbitrarily small domains. Under all the states of the system meet boundedness, a coordinate transformation is proposed. A useful technical theorem is proposed in the stability analysis to show that combined with the backstepping method to cleverly construct a set of Lyapunov functions, and obtain the output controller to ensure that the system is asymptotically probabilistic in the global scope. Finally, through the ocean library in the Simulation X simulation software and the Hardware-in-the-loop simulation, the controller design results are imported into the AUV actuator model to verify the effectiveness of the controller design.

Globally Optimal Centralized and Sequential Fusion Filters for Uncertain Systems With Time-Correlated Measurement Noises

This paper is concerned with the fusion filtering problem for stochastic uncertain multi-sensor systems with time-correlated measurement noises, where the stochastic uncertainties are described by white multiplicative noises, and the additive measurement noises are first-order Gauss-Markov Processes. By introducing the recursive measurement noise estimators, the centralized fusion filter (CFF) based on the idea of batch process and sequential fusion filter (SFF) based on the idea of sequential process are designed in the linear minimum variance (LMV) sense by an innovation analysis approach, respectively. The proposed SFF can achieve the same estimation accuracy as the CFF. It is also globally optimal. The equivalence on estimation accuracy of the SFF and CFF is strictly proved by mathematical induction method. The stability and steady-state properties of the proposed fusion filters are analyzed. Two examples show the effectiveness of the proposed fusion algorithms.

An Order Insensitive Optimal Generalized Sequential Fusion Estimation for Stochastic Uncertain Multi-Sensor Systems with Correlated Noise

An Order Insensitive Optimal Generalized Sequential Fusion Estimation for Stochastic Uncertain Multi-Sensor Systems with Correlated Noise

Adaptive Asymptotic Regulation for Uncertain Nonlinear Stochastic Systems with Time-Varying Delays

In this paper, for a class of uncertain stochastic nonlinear systems with input time-varying delays, an adaptive neural dynamic surface control (DSC) method is proposed. To approximate the unknown continuous functions online, the neural network approximation technique was applied, and based on the DSC scheme, the desired controller was constructed. A compensation system is presented to compensate for the effect of the input delay. The Lyapunov–Krasovskii functionals (LKFs) were employed to compensate for the effect of the state delay. Compared with the existing works, based on using the DSC scheme with the nonlinear filter and stochastic Barbalat’s lemma, the asymptotic regulation performance of this closed-loop system can be guaranteed under the developed controller. To certify the availability for the designed control method, some simulation results are presented.

Optimal linear filtering for networked control systems under time correlated fading channel and noise

In this paper, the optimal filtering problem for discrete-time networked control systems affected by fading channels is investigated where both the fading channel and channel noise are time-correlated. Each fading channel is modeled as a scalar uncertain stochastic discrete-time system, and the channel noise is described by a discrete-time linear system perturbed by white noise. By using multiple recursive terms and the correlations of the signals in the systems, an optimal linear filter is proposed such that it is implemented in a recursive manner. The optimal filter designed has time independent computation structure, hence is easier to be implemented in practice. A vehicle tracking example is provided to illustrate the effectiveness and performance of the theoretic results obtained.

Finite-time Stochastic Stability and Stabilization for Uncertain Discrete-time Stochastic Systems with Time-varying Delay

This paper deals with the problems of finite-time stochastic stability and stabilization for discrete-time stochastic systems with parametric uncertainties and time-varying delay. Using the Lyapunov-Krasovskii functional method, some sufficient conditions of finite-time stochastic stability for a class of discrete-time stochastic uncertain systems are established in term of matrix inequalities. Then, a new criterion is proposed to ensure the closed-loop system is finite-time stochastically stable. The controller gain is designed. Finally, two numerical examples are given to illustrate the effectiveness of the proposed results.

Adaptive fuzzy control of uncertain stochastic nonlinear systems with full state constraints

This article studies the problem of fuzzy adaptive control design for a class of stochastic nonstrict feedback nonlinear systems with unknown virtual control coefficients and full state constraints. Firstly, fuzzy logic systems (FLSs) are utilized to approximate the unknown nonlinear dynamics of the system under consideration. Secondly, an asymptotic tracking control scheme is presented by introducing a bounded estimation method and some smooth functions. Meanwhile, by constructing barrier Lyapunov functions (BLFs), it is proved that all variables of the controlled system are bounded; the tracking error asymptotically converges to zero, and all states of the stochastic system do not exceed its boundaries. Finally, an illustrative simulation instance is applied to verify the superior performance of the presented adaptive algorithm.

A novel fuzzy control with filter-based event-triggered mechanism for nonlinear uncertain stochastic systems suffered input hysteresis

In this paper, an adaptive fuzzy tracking control with filter-based event-triggered mechanism for stochastic nonlinear uncertain system suffered input hysteresis is presented. Considering stochastic disturbances and input hysteresis, Fuzzy Logic Systems (FLSs) are adopted to handle such issues. A time-varying vector contained weight vector and approximation error is established. Then, a class of smooth function is introduced to develop the adaptive control laws. It is aiming to avoid the chattering issue. Further, to achieve the desired tracking performance, this paper considers the discontinuous control input caused by the event-triggered control strategy. And the filter-based event-triggered strategy is presented. With the aid of Lyapunov function and Backstepping technique, the fuzzy event-triggered tracking control method is established for the considered system. It is testified that all signals are bounded under the action of the proposed method. Finally, the theoretical results are verified by the presented simulation examples.

Non-fragile [formula omitted] finite-time sliding mode control for stochastic Markovian jump systems with time delay

This article mainly discusses the realization of H∞ finite-time control for a class of uncertain stochastic time-delay systems with unmeasured states through sliding mode control (SMC). The purpose of this paper is to design a suitable SMC controller to suppress the influence of factors such as model switching and time delay on the system performance, so that the system state can be stabilized within a limited time interval. First, the state of the system is reconstructed through the H∞ state observer, and the SMC law based on the state observer is designed so that the state trajectory reaches the specified sliding surface (s.s.s) in a given finite time. Next, by introducing the concept of time-partitioning strategy, the finite-time boundedness (FTBs) of the reaching phase and the sliding motion phase are realized respectively. Then, according to the linear matrix inequality(LMI), the asymptotic stochastic stability of the system and sufficient conditions for sliding mode dynamics with a given interference attenuation level are derived. Finally, the numerical example and single-link robot arm model (S-lram) show the effectiveness of the method.

Adaptive output feedback control for a class of uncertain stochastic nonlinear systems

This article concentrates on the output feedback controller design for a class of stochastic nonlinear systems with unknown homogeneous growth rates. First, a full-order observer is proposed coupling with a dynamic gain so as to obtain system state estimates. Then, an adaptive output feedback controller is put forward by the homogeneity theory and adding a power integrator technique. Combined with the stochastic Barbalat’s lemma, the signals of the closed-loop system are demonstrated to be bounded and all the system states are proved to converge to the origin in probability. Besides, the results are also expanded to the controller design of upper-triangular stochastic nonlinear system. Two simulation results indicate usefulness of the designed control algorithm.

Joint parameter and state estimation for stochastic uncertain system with multivariate skew t noises

Due to the pulse interference, measurement outliers and artificial modeling errors, the multivariate skew t noise widely exists in the real environment. However, to date, little attention has been paid to the state estimation for systems in which the process noise and the measurement noise are both modeled as the heavy-tailed and skew non-Gaussian noise. In this paper, the multivariate skew t distribution is utilized to model the heavy-tailed and skew non-Gaussian noise. Then a probabilistic graphical form of the multivariate skew t distribution is given and proved. Based on the probabilistic graphical form, a hierarchical Gaussian state space model for stochastic uncertain systems is proposed, which transforms the estimation problem for systems with the heavy-tailed and skew non-Gaussian noises into the one with a hierarchical Gaussian state space model. Next, given the designed Gaussian state space model, the robust Bayesian filter and smoother based on the variational Bayesian inference are proposed to approximately estimate the system state and the unknown noise parameters. Furthermore, the complexity analysis together with the controllability and observability for stochastic uncertain systems with multivariate skew t noises is given. Finally, the simulation results of the target tracking scenario verify the validity of the proposed algorithms.

Optimal control for uncertain stochastic dynamic systems with jump and application to an advertising model

Randomness is an objective indeterminacy, while uncertainty is a subjective indeterminacy. As an effective methodology, chance theory is applicable for disposing of indeterminacy composing of both uncertainty and randomness. Based on chance theory, the optimal control for uncertain stochastic dynamic systems described by both a stochastic differential equation driven by the standard Wiener process and an uncertain differential equation driven by the Liu process and V−n jumps process is considered. Then the principle of optimality is presented by drawing on the dynamic programming method. Particularly, the equation of optimality is established to solve the proposed problem. Furthermore, the optimal control problems with linear and quadratic objective functions are discussed by using the obtained equation. As an application, an advertising problem is analyzed, the corresponding optimal pricing policies and advertising strategies are provided.

Adaptive Event-Triggered Fuzzy Tracking Control of Uncertain Stochastic Nonlinear Systems With Unmeasurable States

This article is concerned with the problem of adaptive event-triggered tracking control for a class of uncertain stochastic nonlinear systems in strict-feedback form. First, with the help of fuzzy logic systems to approximate the unknown nonlinear functions, a robust fuzzy state observer is constructed to estimate all the unmeasurable states. Next, an adaptive output feedback controller, which can adjust the variables online is designed by using the backstepping scheme. Concomitantly, in order to reduce the computation of communication process, a new event triggering condition involving the decreasing function of tracking errors is introduced. Moreover, the desired closed-loop stability of the resulting systems can be achieved by exploiting Lyapunov function analysis. Finally, simulation results verify the effectiveness of the proposed method.

Global FLS-based Consensus of Stochastic Uncertain Nonlinear Multi-agent Systems

Using graph theory, matrix theory, adaptive control, fuzzy logic systems and other tools, this paper studies the leader-follower global consensus of two kinds of stochastic uncertain nonlinear multi-agent systems (MAS). Firstly, the fuzzy logic systems replaces the feedback compensator as the feedforward compensator to describe the uncertain nonlinear dynamics. Secondly, based on the network topology, all followers are divided into two categories: One is the followers who can obtain the leader signal, and the other is the follower who cannot obtain the leader signal. Thirdly, based on the adaptive control method, distributed control protocols are designed for the two types of followers. Fourthly, based on matrix theory and stochastic Lyapunov stability theory, the stability of the closed-loop systems is analyzed. Finally, three simulation examples are given to verify the effectiveness of the proposed control algorithms.

Active disturbance rejection control for lower triangular uncertain stochastic nonlinear systems driven by coloured noises

In this paper, the active disturbance rejection control approach is addressed for a class of lower triangular uncertain stochastic nonlinear systems driven by coloured noises. An extended state observer is first constructed to estimate the stochastic total disturbance including the total effects of internal uncertainties and external disturbances affecting system performance, and then an active disturbance rejection controller based on estimation and compensation is designed to obtain desired closed-loop performance. It is shown with a rigorous analysis that the closed-loop state tracks a reference trajectory generated from the target system in practically mean square and almost sure sense. Some numerical simulations are performed to validate the practicality of the proposed control strategy.

Adaptive Neural Control Using Tangent Time-Varying BLFs for a Class of Uncertain Stochastic Nonlinear Systems With Full State Constraints.

In this paper, an adaptive neural network (NN) control scheme is developed for a class of stochastic nonlinear systems with time-varying full state constraints. In the controller design, RBF NNs are employed to approximate the unknown terms, and the backtracking technique is introduced to overcome the restriction of matching conditions. At the same time, tangent type time-varying barrier Lyapunov functions (tan-TVBLFs) are constructed to ensure the full state constraints are never violated, where tan-TVBLFs are beneficial to integrate constraint analysis into a common method. Furthermore, the Lyapunov stability theory is used to prove that all closed-loop signals are semiglobal uniformly ultimately bounded in probability and error signals remain in the compact set do not violate the time-varying constraints. A simulation example will be used to exhibit the effectiveness of the proposed control scheme.

Robust Recursive Filtering for Stochastic Systems With Time-Correlated Fading Channels

This article is concerned with the robust recursive filtering (RF) problem for a class of stochastic uncertain systems subject to time-correlated fading channels. The measurement received by the sensor is transmitted to the remote filter through the time-correlated fading channel where the channel coefficient evolves according to a certain dynamics and hence exhibits a time-correlated nature. The parameter uncertainties of the system are described by norm-bounded unknown matrices. By introducing a class of auxiliary variables, an augmented system is constructed to reflect the dynamics of the fading coefficient and state simultaneously. Then, a recursive filter is designed which is capable of online computation. Furthermore, an upper bound is guaranteed for the filtering error covariance (FEC) for the possible parameter uncertainties as well as the time-correlated fading channels. With the help of the completing-the-squares technique, filter gains are parameterized by minimizing the obtained upper bound. Finally, two examples are employed to verify the effectiveness of the proposed robust RF method.

Adaptive output feedback regulation for a class of uncertain feedforward stochastic nonlinear systems

This paper addresses the global output feedback regulation problem for a class of uncertain feedforward stochastic nonlinear systems. Unlike the previous works, the drift’s growth rate depends not only on an unknown constant but also on an output polynomial function and an input function. Moreover, the diffusion’s growth rate depends on an unknown constant or an output polynomial function and an input function. By using the general stochastic convergence theorem, an output controller is constructed to guarantee the boundedness and stochastic convergence of the resulting closed-loop system.