Nonlinear Stochastic Systems Research Articles

Torus-Event-Based Fault Estimation for Stochastic Nonlinear Systems with Randomly Occurring Saturation and Missing Measurements

Torus-Event-Based Fault Estimation for Stochastic Nonlinear Systems with Randomly Occurring Saturation and Missing Measurements

Passivity-Based Stabilization for Switched Stochastic Nonlinear Systems

This paper addresses the passivity-based mean square exponential stabilization problem for switched stochastic nonlinear systems. A concept of generalized small-time normobservability is presented and an appropriate test condition is also provided. For pre-given passivity rate and average dwell time, a set of feedback controllers is designed by use of the passivity property. Then, combining with generalized small-time norm-observability, a sufficient condition to guarantee mean square exponential stabilization of a switched stochastic nonlinear system is given. As a special case, the switched stochastic linear system is also discussed. Finally, a numeral example shows the effectiveness of the proposed method.

Reliability control of nonlinear stochastic dynamical system based on discrete data

Stochastic optimal control based on reliability plays a crucial role in mitigating structural failure and ensuring safe operation. For general stochastic vibration systems, a data-driven method for reliability-based optimal control is proposed based on random state data. Firstly, the feedback control is split into conservative and dissipative components in coherence with physical intuition, and each component is expanded upon using pre-selected basic functions, resulting in a modified system with undetermined coefficients. Then, from discrete random samples, the expressions for the probability densities of the first-passage time and the stationary response can be identified, explicitly including system and excitation parameters, as well as initial and safety boundary conditions. Finally, a performance index, combining system reliability and control cost, is constructed and can be explicitly expressed in terms of the undetermined coefficients of the control forces. The optimal control problem for determining the optimal control forces is reformulated as an optimization problem for determining the coefficients that minimize the performance index. This unconstrained optimization problem can be easily solved. Three typical nonlinear stochastic systems, a controlled Duffing oscillator, a controlled nonlinear hysteretic system, and a controlled 2-DOF nonlinear dynamical system, are given to illustrate the validity and accuracy of the proposed data-driven method. Additionally, the control performance of the optimal control strategy in improving the system reliability is also discussed.

Adaptive RBF Neural Network Tracking Control of Stochastic Nonlinear Systems with Actuators and State Constraints

This paper investigates the adaptive neural network (NN) tracking control problem for stochastic nonlinear systems with multiple actuator constraints and full-state constraints. The issue of system full-state constraints is tackled by a generalized barrier Lyapunov function (GBLF), and the output constraints of the system are considered to be in the form of time-varying functions, which are more in line with the needs of real physical systems. The NN approximation technique is utilized to overcome the influence of the uncertainty term on controller design due to randomness. Based on the backstepping technique, a neural adaptive fixed-time tracking control strategy is designed. Under the designed control strategy, the tracking accuracy of the controlled system can reach the expectation in a fixed time. The multi-actuator constraints are converted into a generalized mathematical model to simplify the controller design process. Using the characteristics of the hyperbolic tangent function, a new function called practical virtual control signal is designed using the virtual control signal as the input. Due to the saturation constraint property of the hyperbolic tangent function, it is theoretically ensured that no state of the system exceeds the constraints through to the new form of the virtual controller. Using the adaptive controller constructed in this paper, the controlled system is semi-global fixed-time stabilized in probability (SGFSP). Finally, the effectiveness of the proposed control strategy is further verified by simulation examples.

Stability analysis of stochastic nonlinear switched systems with time‐delay and its application

AbstractThis paper studies the stability of stochastic nonlinear time‐delay systems with arbitrary switching and its application. A novel Krasovskii‐type stability theorem is introduced for stochastic nonlinear systems featuring arbitrary switching and time‐delay. Unlike previous results, this stability result removes the restriction that the infinitesimal generator of Lyapunov–Krasovskii functional (i.e., ) must be negative definite and allows to be indefinite. As an application, the tracking control is studied for a class of stochastic switched systems with inverse dynamics and time‐delay. The assumption condition imposed on the inverse dynamic subsystem is weaker compared with most of existing findings. Finally, we illustrate the feasibility and effectiveness of proposed control strategy by two simulation examples.

Adaptive output feedback control of stochastic systems with mismatched uncertainties input–output quantization

Inspired by the fact that remote control systems always demand to be quantified, and considering that there are always stochastic disturbances in the actual situation, this study discusses a sort of systems with unknown constants due to the existence of parameters that are untoward to measure. Therefore, in this research, a sort of stochastic nonlinear systems with input–output quantization mismatched uncertainties is studied by utilizing backstepping method. The difficulty is that the output signal becomes non-differential after being quantized. In addition, only the quantized output signal in the system can be regarded as known during the analysis. Therefore, the update of unknown parameters and the design of controller will grow arduous. In order to solve the above dilemma, a state observer and a projection operator are introduced. Moreover, in the design of the controller, the power form of Lyapunov function and differential method is employed to avoid the derivation of non-differentiable functions. Since the controller proposed in this study contains a small number of parameters that need to be designed, it is practical and can eliminate the problem of computational explosion. Simulation results demonstrate the effectiveness of the proposed scheme.

Event‐triggered adaptive tracking control for stochastic nonlinear systems under predetermined finite‐time performance

SummaryIn this paper, an event‐triggered adaptive tracking control strategy is proposed for strict‐feedback stochastic nonlinear systems with predetermined finite‐time performance. Firstly, a finite‐time performance function (FTPF) is introduced to describe the predetermined tracking performance. With the help of the error transformation technique, the original constrained tracking error is transformed into an equivalent unconstrained variable. Then, the unknown nonlinear functions are approximated by using the multi‐dimensional Taylor networks (MTNs) in the backstepping design process. Meanwhile, an event‐triggered mechanism with a relative threshold is introduced to reduce the communication burden between actuators and controllers. Furthermore, the proposed control strategy can ensure that all signals of the closed‐loop system are bounded in probability and the tracking error is within a predefined range in a finite time. In the end, the effectiveness of the proposed control strategy is verified by two simulation examples.

Predefined-time stabilization of stochastic nonlinear systems with application to UAVs

The paper presents a new Lyapunov-type predefined-time stabilization control algorithm for stochastic high-order nonlinear systems with asymmetric output constraints. In contrast to stochastic finite-time and fixed-time stabilization, the average value of the settling-time function for stochastic predefined-time stabilization control is independent of both the initial value and the control factors. To mitigate the significant uncertainties arising from the asymmetric output constraint, a tan-type barrier Lyapunov function is formulated. Furthermore, by harnessing the previously mentioned barrier Lyapunov function and integrating the power integrator technique, a controller design strategy is formulated based on the backstepping method. The rigorous analysis in this study proves that the designed controller ensures both the attainment of predefined-time convergence of the system states to the origin in probability and the satisfaction of the output constraint. Finally, an example of a roll angle subsystem for quadrotor UAVs and a numerical illustration are presented to corroborate the theoretical analysis.

Adaptive fuzzy control of stochastic nonlinear systems with predefined time via self-triggered mechanism

Adaptive fuzzy control of stochastic nonlinear systems with predefined time via self-triggered mechanism

Adaptive Fuzzy Tracking Control for Stochastic Nonlinear Systems with Full-State Constraints

Adaptive Fuzzy Tracking Control for Stochastic Nonlinear Systems with Full-State Constraints

Stability analysis for nonautonomous impulsive hybrid stochastic delay systems

In this paper, the problems on the existence and uniqueness, and the input-to-state stability for the global solution of nonlinear nonautonomous impulsive stochastic delay systems with Markovian switching are considered. The existence and uniqueness for the global solution of such systems is studied by using the Lyapunov function, the theory of stochastic analysis, and the function of the impulsive density. In order to overcome the difficulty stemming from the simultaneous presence of the indefinite derivative for the Lyapunov function, the bounded external disturbances, and a nonnegative and bounded time-varying delay, one impulsive generalized Halanay inequality of integral version is established. The input-to-state stability, the integral input-to-state stability, the stochastic input-to-state stability and the eλt(λ>0)-weighted input-to-state stability for the global solution of nonlinear nonautonomous impulsive stochastic delay systems with Markovian switching are investigated, respectively. One example is provided to illustrate the effectiveness of the theoretical results obtained.

Stabilization of nonlinear stochastic systems with input and output delays via event‐triggered predictive control

AbstractThe stabilization of nonlinear stochastic systems with input and output delays is investigated in this article. First, an observer that includes input delay information is designed to estimate the state information after eliminating the effect of input delay. Second, a predictive scheme with delay information is utilized to predict the system state affected by output delay, and an event‐triggered predictive controller is established to eliminate the effects of input and output delays simultaneously. Subsequently, the convergence of the prediction error is analyzed by utilizing a recursive method, and a sufficient condition to ensure the global exponential stability is given by constructing a new closed‐loop system. Finally, numerical simulations of two nonlinear stochastic systems with different delay sizes are utilized to verify the impact of the event‐triggered predictive control in addressing the stabilization of nonlinear stochastic systems with time delays.

Dynamic event-triggered adaptive tracking control for stochastic nonlinear systems with deferred time-varying constraints

This article investigates the problem of adaptive tracking control for stochastic nonlinear systems with deferred state constraints. The novel unified universal barrier function (UUBF) and deferred funnel error transformation are developed to handle various state constraints and adjust the tracking error more precisely, respectively. Multi-dimensional Taylor network (MTN) and dynamic event-triggered mechanism (DETM) are employed to design controller in the backstepping process, which can achieve full-state constraints and the tracking control after the preassigned time while conserving more communication resources. Finally, two simulation examples are presented to verify the effectiveness of the proposed control scheme.

Semi-global exponential stabilization of stochastic nonlinear systems with distributed delay under discrete-time state observations and application to circuit systems

This paper is aimed at studying the semi-global exponential stabilization problem for stochastic nonlinear systems with distributed delay under discrete-time state observations. An extended definition of horizontal translation of the segment function along the investigated systems is given, related to the stochastic disturbance and Brownian motion. Basically, the right and upper Dini’s derivative of the constructed functional is presented. Combining this with the global exponential stability of the stochastic nonlinear systems with distributed delay under continuous-time feedback control, the Lyapunov method and Halanay inequality, the maximum observation interval and some stabilization criteria to make the investigated systems under discrete-time state observations reach semi-global exponential stabilization are provided. The results indicate that the semi-global exponential stabilization is dependent upon stochastic disturbance, initial condition range, and maximum observation interval. Finally, an application to the circuit systems is discussed and the involved sufficient conditions for the circuit systems to keep semi-global stabilization are also proposed. Besides, the numerical simulation results confirm the effectiveness of the theoretical results.

Event-Triggered Adaptive Fuzzy Neural Network Output Feedback Control for Constrained Stochastic Nonlinear Systems.

This article investigates the problem of command-filtered event-triggered adaptive fuzzy neural network (FNN) output feedback control for stochastic nonlinear systems (SNSs) with time-varying asymmetric constraints and input saturation. By constructing quartic asymmetric time-varying barrier Lyapunov functions (TVBLFs), all the state variables are not to transgress the prescribed dynamic constraints. The command-filtered backstepping method and the error compensation mechanism are combined to eliminate the issue of "computational explosion" and compensate the filtering errors. An FNN observer is developed to estimate the unmeasured states. The event-triggered mechanism is introduced to improve the efficiency in resource utilization. It is shown that the tracking error can converge to a small neighborhood of the origin, and all signals in the closed-loop systems are bounded. Finally, a physical example is used to verify the feasibility of the theoretical results.

Boundedness and stability of nonlinear hybrid neutral stochastic delay differential equation with Lévy jumps under different structures

This paper investigates the boundedness and stability of a class of nonlinear hybrid neutral stochastic differential delay systems with Lévy jumps and different structures. The coefficients in this system satisfy the local Lipschitz condition and a suitable Khasminskii-type condition, and the state space of the system is separated into two subsets, the existence uniqueness, asymptotic boundedness, and exponential stability of the system are obtained by designing a new Lyapunov function and applying the M-matrix technique as well as dealing with the non-differentiable delay function. Different with the existing work, we not only consider the neutral term, but also the case of the delay function being bounded and non-differentiable. At last, numerical examples are performed to manifest the obtained results.

Exponential Stability of Stochastic Nonlinear Delay Systems Subject to Multiple Periodic Impulses

Exponential Stability of Stochastic Nonlinear Delay Systems Subject to Multiple Periodic Impulses

Finite-Time pth Moment Asymptotically Bounded for Stochastic Nonlinear Systems and Its Application in Neural Networks Synchronization

Finite-Time <i>p</i>th Moment Asymptotically Bounded for Stochastic Nonlinear Systems and Its Application in Neural Networks Synchronization

Stability Analysis of Switched Stochastic Nonlinear Systems With State-Dependent Delay

Stability Analysis of Switched Stochastic Nonlinear Systems With State-Dependent Delay

Predefined‐time adaptive fuzzy control for a class of stochastic nonlinear uncertain systems

SummaryThis article is mainly concentrated on the predefined‐time adaptive fuzzy control of stochastic nonlinear systems. To handle nonlinear functions that are uncertain, fuzzy logic systems (FLSs) are used to approximate them. Compared with the existing studies, a Lyapunov‐type criterion for practically predefined‐time stochastic stabilization (PPSS) is put forward to guarantee the stabilization of the system. The stabilization time is merely dependent on one design parameter, which means the parameter can be adjusted to set the stability time.