Uncertain Stochastic Systems Research Articles

Gaussian Filter for Nonlinear Stochastic Uncertain Systems With Correlated Noises

In this paper, a nonlinear Gaussian filter is designed for nonlinear stochastic uncertain system with correlated noises. Because the networked systems with random delays and packet losses can be transformed into those with correlated multiplicative noises in the state and measurement matrices, we consider the stochastic uncertain system with synchronously correlated multiplicative noises. The process and observation additive noises are one-step autocorrelated, respectively. Process and observation noises are two-step forward cross-correlated. Based on the abovementioned conditions, we proposed a nonlinear Gaussian recursive filter by using an alternative formulation and a new cubature Kalman filter is given on the basis of the third-degree spherical-radial rule. In order to compare with the algorithm proposed in this paper, a new version based on the extended Kalman filter is developed in Appendix B. In the simulation part, we give two simulation examples to show the effectiveness of the proposed algorithm.

Composite Robust <inline-formula> <tex-math notation="LaTeX">$H_\infty$</tex-math> </inline-formula> Control for Uncertain Stochastic Nonlinear Systems With State Delay via a Disturbance Observer

In this note, the robust stochastic stabilization and robust $H_\infty$ control problems are investigated for uncertain stochastic time-delay systems with nonlinearity and multiple disturbances. By estimating the disturbance, which can be described by an exogenous model, a composite hierarchical control scheme is proposed that integrates the output of the disturbance observer with the state feedback control law. Sufficient conditions for the existence of the disturbance observer and composite hierarchical controller are established in terms of linear matrix inequalities, which ensure the mean-square asymptotic stability of the resulting closed-loop system and the disturbance attenuation. It has been shown that the disturbance rejection performance can also be achieved. A numerical example is provided to show the potential of the proposed techniques and encouraging results have been obtained.

Robust H∞ filtering for polytopic uncertain stochastic systems under quantized sampled outputs

In this paper, the robust H∞ filtering of polytopic uncertain stochastic systems is designed under quantized sampled outputs. An novel parameters-dependent time-scheduled Lyapunov functional is constructed using segmentation technology and linear interpolation. Based on this new Lyapunov functional and convex combination method, sufficient stochastic exponential stability criteria of the filtering error dynamics are proposed and a prescribed H∞ performance level can be guaranteed by designing the stochastically stable filter. The better H∞ performance can be obtained with a larger interval dividing parameter. A numerical example is provided to illustrate the effectiveness of the proposed method.

Mean square consensus of uncertain discrete-time stochastic multi-agent systems with x-dependent noise

ABSTRACTIn this paper, the mean square consensus control problem is investigated for linear uncertain discrete-time multi-agent systems with x-dependent noise and time-varying delays. Under undirected connected topology, the robust consensus problem of multi-agent systems is converted into the robust stabilisation problem for the discrete-time stochastic systems. By utilising Lyapunov functional and the linear matrix inequality method, some new sufficient conditions are derived to guarantee the consensus of uncertain discrete-time stochastic multi-agent systems. Based on the state feedback controller protocol with time-varying delays, a new consensus criterion is established for the discrete-time stochastic multi-agent systems with parameter uncertainties. Finally, numerical examples are provided to illustrate the effectiveness of the proposed results.

Stability criteria on delay-dependent robust stability for uncertain neutral stochastic nonlinear systems with time-delay

This work mainly studies the robust stability analysis and design of a controller for uncertain neutral stochastic nonlinear systems with time-delay. Using a modified Lyapunov–Krasovskii functional and the free-weighting matrices technique, we establish some new delay-dependent criteria in terms of linear matrix inequality (LMI). The innovative point of this work is that we generalize the robust stability analysis of nonlinear stochastic time-delay systems to the uncertain neutral stochastic systems. Due to the added derivative term of time-delay, the proposed scheme can be applied more widely. Finally, numerical examples are provided to validate the derived results.

A sliding mode observer design for uncertain fractional Ito stochastic systems with state delay

ABSTRACTThis paper addresses the robust observer design problem for uncertain time-delay fractional Ito stochastic systems. A sliding surface is proposed and it is shown that state estimates converge towards it and remain there for the subsequent time. Additionally, by constructing a novel Lyapunov functional, a sufficient condition for the stability of the sliding motion of the estimated states is given in the form of Linear Matrix Inequalities (LMIs). It is demonstrated that the state estimates are stabilizable in probability provided that the LMI is feasible. Moreover, a finite-time sliding mode control law based on the estimated states is proposed. Simulation examples are given to show the validity and effectiveness of the results.

A Parameter-Dependent Sliding Mode Approach for Finite-Time Bounded Control of Uncertain Stochastic Systems With Randomly Varying Actuator Faults and Its Application to a Parallel Active Suspension System

This paper addresses the mean-square finite-time bounded control problem for uncertain stochastic systems via a sliding mode approach. The stochastic phenomena of randomly occurring uncertainties and randomly varying actuator faults modeled by two independent exponential distributions are addressed effectively. A key issue for the system under the consideration is how to ensure, for any prescribed finite (possibly short ) working time interval, the stochastic finite-time boundedness (SFTB) of the resultant closed-loop systems and the reachability of the specified sliding surface in mean-square sense. To this end, a parameter-dependent sliding mode control (SMC) law is designed to force ( with probability one ) the state trajectories into a domain around the specified sliding surface during the given finite-time interval. The upper bound of the sliding domain associated with the design parameters is obtained explicitly. The sufficient conditions are established, respectively, for guaranteeing the SFTB of the SMC systems over both reaching phase and sliding motion phase . Finally, the proposed finite-time SMC approach is illustrated via a parallel active suspension system.

Event‐triggered adaptive tracking control for a class of uncertain stochastic nonlinear systems with Markov jumping parameters

SummaryThis paper aims to investigate the problem of event‐triggered adaptive tracking control for a class of stochastic nonlinear systems with Markov jumping parameters. Since the stochastic system contains unknown parameters, the assumption of the stochastic input‐to‐state stability is a difficult task to check. To overcome the design difficulty, mode‐dependent adaptive controllers and the event‐triggered strategy are designed simultaneously with the help of backstepping technique. The stochastic input‐to‐state stability assumption is avoided by adding correction terms in controller to compensate the measurement errors. The proposed control schemes guarantee that all signals in the closed‐loop system remain bounded in probability and the tracking error signals eventually converge to the compact set in the sense of mean quartic value. Finally, simulation results show the effectiveness of the proposed approach.

The Adaptive Neural Control for a Class of High-Order Uncertain Stochastic Nonlinear Systems

This paper studies the problem of the adaptive neural control for a class of high-order uncertain stochastic nonlinear systems. By using some techniques such as the backstepping recursive technique, Young’s inequality, and approximation capability, a novel adaptive neural control scheme is constructed. The proposed control method can guarantee that the signals of the closed-loop system are bounded in probability, and only one parameter needs to be updated online. One example is given to show the effectiveness of the proposed control method.

Parametric Co-variance Assignment for a Class of Multivariable Stochastic Uncertain Systems: Output Feedback Stabilization Approach

Parametric Co-variance Assignment for a Class of Multivariable Stochastic Uncertain Systems: Output Feedback Stabilization Approach

Approximation-based decentralized output-feedback control for uncertain stochastic interconnected nonlinear time-delay systems with input delay and asymmetric input saturation

This paper proposes an adaptive observer-based neural controller for a class of uncertain large-scale stochastic nonlinear systems with actuator delay and time-delay nonlinear interactions, where drift and diffusion terms contain all state variables of their own subsystem. First, a state observer is established for estimating the unmeasured states, and a predictor-like term is utilized to transform the input delayed system into the delay-free system. Second, novel appropriate Lyapunov–Krasovskii functionals are used to compensate the time-delay terms, and neural networks are employed to approximate unknown nonlinear functions. At last, an output-feedback adaptive neural control scheme is constructed by using Lyapunov stability theory and backstepping technique. It is shown that the designed neural controller can ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error is driven to a small neighborhood of the origin. The simulation results are presented to further show the effectiveness of the proposed approach.

Optimal recursive estimation for networked stochastic uncertain systems with fading measurements and time-correlated channel noises

This paper is concerned with the optimal linear estimation problem for discrete-time stochastic system with time-correlated channel noises, correlated multiplicative noises and fading measurements. The time-correlated channel noises are described by a seemingly ARMA (autoregressive moving average) model. By an equivalent transformation, the original system is transformed into the same-dimension system with finite-step correlated virtual noises and multiple measurement delays. The statistical properties of correlation functions among noise, state and measurement are analyzed. Further, the optimal linear state estimators including filter, predictor and smoother are derived by using an innovation analysis approach. A simulation example shows the effectiveness of the proposed algorithms.

Probabilistic control of Markov jump systems by scenario optimization approach

This paper addresses the new problem of probabilistic robust stabilization for uncertain stochastic systems by using scenario optimization approach, where the uncertainties are not assumed to be norm-bounded. State feedback controllers are designed to guarantee that the closed-loop system is robust probabilistic stable. The problem of designing the controller gains is formulated and solved as linear matrix inequality (LMI) constraints. Simulation results are presented to illustrate the correctness and usefulness of the controllers designed.

Adaptive robust control for a class of uncertain stochastic systems with time‐varying delays

The problems of robust stochastic stabilization and adaptive robust control are studied for stochastic systems with parameter uncertainties and time‐varying state delays. In this study, an assumption is made that the parameter uncertainties are time‐varying norm‐bounded, the upper bounds of which are unknown positive constants, and that the time‐varying delays are non‐negative continuous and bounded functions. In particular, the derivatives of these time‐varying delays are not required to be less than 1. For such a class of stochastic systems, a delay‐independent adaptive robust state feedback controller is proposed. By employing the Lyapunov functional method, it has been demonstrated that the equilibrium x(t) = 0 of such systems is globally asymptotically stable in probability. Finally, a numerical example is given to demonstrate the effectiveness of the results. © 2018 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Adaptive fuzzy FTC design of nonlinear stochastic systems with actuator faults and unmodeled dynamics

SummaryThis paper investigates an adaptive fuzzy control method for accommodating actuator faults in a class of uncertain stochastic nonlinear systems with both immeasurable states and unmodeled dynamics. The considered faults are modeled as both loss of effectiveness and lock‐in‐place. To deal with the immeasurable states, a novel state observer containing the actuator faults is designed. Combining with the backstepping technique and stochastic small‐gain theorem, an adaptive fuzzy output feedback control method is developed. The presented design scheme can guarantee that the closed‐loop system is input‐to‐state practically stable in probability. Finally, a simulation example is shown to verify the effectiveness of the proposed control method.

Event-triggered fuzzy adaptive compensation control for uncertain stochastic nonlinear systems with given transient specification and actuator failures

In this paper, an event-triggered Fuzzy adaptive compensation controller is constructed for uncertain stochastic nonlinear systems with given transient specification and actuator failures. The main characteristics of the systems are that they take into account the effect of actuator failures and given transient specification, system communication resource limitation simultaneously. It is still an arduous task and challenge to design for uncertain stochastic nonlinear system specially. To stabilize the uncertain nonlinear stochastic systems, the fuzzy logic systems are used to approximate the unknown functions, an event-triggered control mechanism is established to save the system communication resource and a transformed system control mechanism is developed to satisfy the given transient specification all the time, in normal mode or faulty mode. Based on the Lyapunov approach, it is proved that all the signals of the closed-loop system are bounded, and the tracking error is limited to a given transient specification. The simulation results illustrates the effectiveness of the proposed control approach.

Exponential stability for Markovian neutral stochastic systems with general transition probabilities and time-varying delay

This paper discusses the problem of exponential stability for Markovian neutral stochastic systems with general transition probabilities and time-varying delay. Based on non-convolution type multiple Lyapunov functions and stochastic analysis method, we obtain the conditions which are independent to any decay rate of the exponential stability for uncertain transition probabilities neutral stochastic systems with time-varying delay. Finally, two examples are presented to illustrate the effectiveness and potential of the proposed results.

Adaptive multi‐dimensional Taylor network tracking control for SISO uncertain stochastic non‐linear systems

In this study, the problem of adaptive multi-dimensional Taylor network (MTN) control for single-input single-output (SISO) uncertain stochastic non-linear systems is investigated. How to minimise the influence of randomness and uncertain non-linearity for less complex computation, and how to improve the real-time performance of the controller are of great significance. To this end, a control approach based on MTN is proposed for tracking control of stochastic non-linear systems. MTNs are used to approximate the non-linearities, and the backstepping technique is employed to construct the MTN controller (MTNC). MTNC involves only addition and multiplication, featuring desirable simplicity and real-time performance. Stability of the system is guaranteed via Lyapunov approach, and it is proved that the proposed controller can guarantee that all signals of the closed-loop system remain bounded in probability, and the tracking error converges to an arbitrarily small neighbourhood around the origin. Finally, a numerical example is given to illustrate the effectiveness of the proposed design approach, and simulation results demonstrate that the method presented in this study has good real-time performance and control quality.

Voltage control for uncertain stochastic nonlinear system with application to energy Internet: Non-fragile robust H∞ approach

In this paper, a robust control method is used to intelligently regulate the DC bus voltage deviation for an islanded microgrid (MG) within the scenario of energy Internet (EI). In order to cope with the uncertain and nonlinear nature of the power exchange in EI, a new mathematical model is formulated to present the dynamics of the islanded MG, where the state equation is expressed by a class of nonlinear stochastic differential equations (SDEs) with parameter uncertainties appearing in system coefficients and the controllers. Specifically, the nonlinearities appear in both drift and diffusion parts of such SDEs. Our aim is to design a controller such that the effects of the modelling uncertainty and the external disturbance to the DC bus voltage of the off-grid MG are minimized. Mathematically, this can be regarded as problems of solving the non-fragile robust stochastic stabilization and non-fragile robust H∞ control, both of which can be solved via the linear matrix inequality (LMI) approach sufficiently. We emphasize such new control system with its solution can also be applied into fields of industry, economics, etc. Based on real world data, numerical results are illustrated, and simulations show that our target is achieved.

Robust exponential stability of uncertain stochastic systems with probabilistic time‐varying delays

SummaryThis paper is concerned with the problem of delay‐distribution–dependent robust exponential stability for uncertain stochastic systems with probabilistic time‐varying delays. Firstly, inspired by a class of networked systems with quantization and packet losses, we study the stabilization problem for a class of network‐based uncertain stochastic systems with probabilistic time‐varying delays. Secondly, an equivalent model of the resulting closed‐loop network‐based uncertain stochastic system is constructed. Different from the previous works, the proposed equivalent system model enables the controller design of the network‐based uncertain stochastic systems to enjoy the advantage of probability distribution characteristic of packet losses. Thirdly, by applying the Lyapunov‐Krasovskii functional approach and the stochastic stability theory, delay‐distribution–dependent robust exponential mean‐square stability criteria are derived, and the sufficient conditions for the design of the delay‐distribution–dependent controller are then proposed to guarantee the stability of the resulting system. Finally, a case study is given to show the effectiveness of the results derived. Moreover, the allowable upper bound of consecutive packet losses will be larger in the case that the probability distribution characteristic of packet losses is taken into consideration.