Uncertain Stochastic Nonlinear Systems Research Articles

Adaptive stabilization of stochastic systems with polynomial nonlinear conditions, unknown parameters, and dead‐zone actuator

AbstractMany practical dynamic models always suffer from complex nonlinearities, parameter uncertainties and random noises. Such kind of models are always characterized by uncertain stochastic nonlinear systems. Besides, many factors will lead to dead‐zone actuator, which further adds more challenges to control engineering. This paper studies stabilization issue of stochastic systems with polynomial nonlinear conditions, unknown parameters and dead‐zone actuator. An adaptive control approach is proposed by exploring homogeneous domination control and using dynamic‐gain‐based adaptive design strategy. It shows that all the signals are bounded almost surely and the system states converge to the origin almost surely. The presented method is successfully applied to the mass spring mechanical system.

Command filtered adaptive fuzzy tracking control for uncertain stochastic nonlinear systems with event-triggered input

Command filtered adaptive fuzzy tracking control for uncertain stochastic nonlinear systems with event-triggered input

Switching Event-Triggered Adaptive Resilient Dynamic Surface Control for Stochastic Nonlinear CPSs With Unknown Deception Attacks.

This work concentrates on the adaptive resilient dynamic surface controller design problem for uncertain nonlinear lower triangular stochastic cyber-physical systems (CPSs) subject to unknown deception attacks based on a switching threshold event-triggered mechanism. The adverse effect of deception attacks on the stochastic CPSs is that the exact system state variables become unavailable. Furthermore, it should be emphasized that the coexistence of unknown nonlinearities, stochastic perturbations, and unknown sensor and actuator attacks makes it a very difficult and challenging event to implement the control design. To get the desired controller, radial basis function (RBF) neural networks (NNs) are introduced so that the design obstacle caused from the unknown nonlinearities can be easily solved. On this basis, in order to save resources and effectively transmit, the event-triggered control scheme based on a switching threshold strategy is further considered. In the backstepping design process, the dynamic surface control (DSC) technique is presented to deal with the issue of "explosion of complexity." By skillfully designing a new coordinate transformation and the attack compensators, the problem of unknown deception attacks is successfully handled. Under our proposed control scheme, all the closed-loop signals are bounded in probability and the stabilization errors converge to an adjustable neighborhood of the origin in probability. Finally, the simulation results on the double chemical reactor show the validity of the proposed design scheme.

New stochastic convergence theorems: Overcoming the limitations of LaSalle theorems

LaSalle theorems, sometimes called as invariance-like theorems, have witnessed abundant applications as powerful tools of analysing system convergence. However, these theorems have twofold limitations: On the one hand, the uniformity of convergence with respect to initial state values cannot be offered, which indicates that the possibility of excessively slow convergence could not be ruled out for a given bounded set of initial state values. On the other hand, unbounded time-variations are not allowed in the systems, and meanwhile, the boundedness of all the states are required even if one merely concerns the convergence of partial states, precluding many scenarios with the unboundedness (e.g., induced by stochastic noise) for some states defined on the whole time horizon. Towards the limitations of LaSalle theorems, this paper seeks to further develop convergence theorems in the stochastic framework. First, a Lyapunov-like function based theorem on the convergence owning the uniformity with respect to initial state values is presented for Itô-type stochastic systems, with the infinitesimal of Lyapunov-like functions exploited more delicately than those in stochastic LaSalle theorems. Based on this, a framework of adaptive stabilization with the uniformity of convergence is established for uncertain stochastic nonlinear systems. In particular, the performance specifications involved are impossible to achieve by applying LaSalle theorems as in the related results. Second, an enlarged convergence theorem is established with Lyapunov-like conditions moderately relaxed, which allows the unboundedness for partial states defined on the whole time horizon and has potential applications in the presence of unbounded time-variations. What is notable, the enlarged convergence theorem is nontrivial to verify, which compels us to propose an extended Barbălat lemma with the conventional requirement of uniform continuity relaxed in the stochastic framework.

State and output feedback’s finite-time guaranteed cost [formula omitted] control for uncertain nonlinear stochastic systems with time-varying delays

The problems of guaranteed cost control and H∞ control are studied in this paper for nonlinear uncertain Itô’s stochastic systems with time-varying delays in finite-time. It is assumed that the nonlinear function in the systems satisfies the quasi-one-sided Lipschitz nonlinear constraint condition, which is weaker and less conservative than the one-sided Lipschitz condition. Some novel sufficient conditions for the existence of guaranteed cost control strategies are derived by using the Gronwall’s inequality, Dynkin’s formula, and Lyapunov–Krasovskii functional. The state and output feedback’s controllers based on event-triggered control guarantee that the closed-loop system is finite-time stochastically bounded and the given quadratic cost function has an upper bound. Finally, the effectiveness of the suggested method is illustrated by numerical simulation.

Reduced-order K-filters-based event-triggered adaptive command filtered tracking control for stochastic constrained nonlinear systems

To ensure better performance and simultaneously save resources, an event-triggered adaptive command filtered dynamic surface control (ACFDSC) method for uncertain stochastic nonstrict-feedback nonlinear systems with dynamic output constraints and prescribed performance is designed in this article. Firstly, with the help of reduced-order K-filters, linearly parameterized neural networks and specific coordinate transformation technique, the unmeasurable states, nonlinearities, two types of unmodeled dynamics and output constraints are dealt with respectively. Then, an event-triggered ACFDSC strategy is proposed to ensure that the tracking error reaches a specific bound within a finite time. By introducing the compensated signal into the complete Lyapunov function, and with the assistance of the compact set defined in the stability analysis, all signals are strictly demonstrated to be semi-globally uniformly ultimately bounded. The simulation results verify the effectiveness of the proposed method.

Event-triggered adaptive fuzzy asymptotic control design for uncertain stochastic nonlinear systems

The adaptive fuzzy asymptotic tracking control (AFATC) method is presented for uncertain stochastic nonlinear systems by virtue of event-triggered mechanism. The fuzzy logic systems are borrowed to address system uncertainties. By applying the backstepping technique, the AFATC strategy is recursively constructed. Different from the existing approximation-based methods, the developed controller can achieve asymptotic convergence feature. Moreover, the event-triggered mechanism is integrated into the controller design process to reduce data transmission and unnecessary resource waste. By applying the Lyapunov analysis and several helpful lemmas, the stability and convergence of the considered systems are ensured. Finally, the availability of the theory analysis is verified by a chemical reactor system.

Research on Uncertain Stochastic Nonlinear System Based on Piecewise Loosely Constrained Nonlinear Characteristics and Backstepping Design Through Memristor Mode

Research on Uncertain Stochastic Nonlinear System Based on Piecewise Loosely Constrained Nonlinear Characteristics and Backstepping Design Through Memristor Mode

Dynamic event-triggered adaptive control for uncertain stochastic nonlinear systems

In this paper, the dynamic event-triggered adaptive tracking control problem is investigated via backstepping technology for uncertain stochastic nonlinear systems. First, the stochastic nonlinear system with unknown parameter is considered. By introducing an additional dynamic variable, a dynamic event-triggered adaptive controller is designed such that the closed-loop signals are uniformly ultimately bounded in the sense of the fourth moment. Then, a more general partially unknown stochastic nonlinear system is further considered, and the designed adaptive neural network control scheme ensures that the closed-loop signals are fourth moment semi-globally uniformly ultimately bounded (SGUUB). The proposed dynamic event-triggering mechanism (DETM) guarantees that the lengths of time intervals between each two consecutive events are lower-bounded by a positive constant. It is necessary to point out that the DETM is better at saving resources than the static event-triggering mechanism (SETM). Finally, two simulations are conducted to show the validity of the control strategies for these two systems, respectively.

IBLF-Based Adaptive Neural Control of State-Constrained Uncertain Stochastic Nonlinear Systems.

In this article, the adaptive neural backstepping control approaches are designed for uncertain stochastic nonlinear systems with full-state constraints. According to the symmetry of constraint boundary, two cases of controlled systems subject to symmetric and asymmetric constraints are studied, respectively. Then, corresponding adaptive neural controllers are developed by virtue of backstepping design procedure and the learning ability of radial basis function neural network (RBFNN). It is worth mentioning that the integral Barrier Lyapunov function (IBLF), as an effective tool, is first applied to solve the above constraint problems. As a result, the state constraints are avoided from being transformed into error constraints via the proposed schemes. In addition, based on Lyapunov stability analysis, it is demonstrated that the errors can converge to a small neighborhood of zero, the full states do not exceed the given constraint bounds, and all signals in the closed-loop systems are semiglobally uniformly ultimately bounded (SGUUB) in probability. Finally, the numerical simulation results are provided to exhibit the effectiveness of the proposed control approaches.

Fully probabilistic control for uncertain nonlinear stochastic systems

AbstractThis paper develops a novel probabilistic framework for stochastic nonlinear and uncertain control problems. The proposed framework exploits the Kullback–Leibler divergence to measure the divergence between the distribution of the closed‐loop behavior of a dynamical system and a predefined ideal distribution. To facilitate the derivation of the analytic solution of the randomized controllers for nonlinear systems, transformation methods are applied such that the dynamics of the controlled system becomes affine in the state and control input. Additionally, knowledge of uncertainty is taken into consideration in the derivation of the randomized controller. The derived analytic solution of the randomized controller is shown to be obtained from a generalized state‐dependent Riccati solution that takes into consideration the state‐ and control‐dependent functional uncertainty of the controlled system. The proposed framework is demonstrated on an inverted pendulum on a cart problem, and the results are obtained.

Command filter based adaptive DSC of uncertain stochastic nonlinear systems with input delay and state constraints

In this paper, a command filter based dynamic surface control (DSC) is developed for stochastic nonlinear systems with input delay, stochastic unmodeled dynamics and full state constraints. An error compensation system is designed to constrain the filtering error caused by the first-order filter in the traditional dynamic surface design. On this basis, the stability proof of DSC for stochastic nonlinear systems based on command filter is proposed. The definition of state constraints in probability is presented, and the problem of stochastic full state constraints is solved by constructing a group of coordinate transformations with nonlinear mappings. The Pade approximation is adopted to deal with input delay. The stochastic unmodeled dynamics is considered, which is processed by utilizing the property of stochastic input-to-state stability (SISS) and changing supply function. All the signals of the system are proved to be semi-globally uniformly ultimately bounded (SGUUB) in probability, and the full state constraints are not violated. The two simulation examples also verify the effectiveness of the proposed adaptive DSC scheme.

Adaptive fault‐tolerant decentralized tracking control of switched stochastic uncertain nonlinear systems with time‐varying delay

SummaryIn this article, an adaptive neural fault‐tolerant decentralized tracking control problem is investigated for switched stochastic large‐scale uncertain nonlinear systems, in which time‐varying delay and unknown control coefficient are under consideration. By incorporating the quadratic Lyapunov function and Lyapunov Krasovskii function into the backstepping approach, an adaptive neural fault‐tolerant decentralized control strategy is proposed, which ensures that signals in the closed‐loop system are stable in probability and the tracking error converges to a small neighborhood of the origin under arbitrary switching. At last, to verify the presented strategy is feasible, a simulation example is given.

A Nonlinear Stochastic Matrix Model for the Analysis of the Association between International Trade Growth and Environmental Change

This study uses a nonlinear stochastic matrix for an in-depth analysis of the association between international trade growth and environmental change. First, for a class of uncertain stochastic nonlinear time-lag systems, this study investigates its time-lag-related robust stochastic stabilization problem. A memory-free state feedback controller for the system is then obtained to ensure the effectiveness of the system performance. This makes the system more general and the corresponding theoretical results less conservative. Finally, numerical examples are given to further verify the validity and feasibility of the results. The “tariff measure” based on the magnitude of adverse changes in trade policy is not an accurate measure of trade policy uncertainty; the stochastic volatility method measures trade policy uncertainty by including tariff fluctuations that have been communicated in advance in the trade policy uncertainty indicator and fail to identify the different commodities that occur during the current trade friction. The trade policy uncertainty index constructed through textual analysis of newspapers can better reflect the trade policy uncertainty during this trade friction between China and the United States, and the rich time-varying nature can also reflect the alternating changes of tension and détente in economic and trade relations over some time. The analysis of the mechanism reveals that exporters have fewer emission reduction facilities than nonexporters but significantly lower energy consumption intensity for coal and water than nonexporters, reasoning that the mechanism by which exporters are more environmentally friendly than nonexporters lies in their cleaner energy use mix. Following the conclusions of this study, relevant policy recommendations are put forward, specifically the use of more efficient energy sources in the production process and more investment in energy efficiency and emission reduction to combat pollution.

A Bound Estimation Approach for Adaptive Fuzzy Asymptotic Tracking of Uncertain Stochastic Nonlinear Systems.

The adaptive fuzzy tracking control problems for a class of uncertain stochastic nonlinear systems are investigated in this article using the backstepping control approach. Different from the existing research, the crucial but highly restrictive hypothesis on the prior knowledge of unknown virtual control coefficients (UVCCs) is removed from this article. An asymptotic tracking control scheme is proposed by applying smooth functions and a bounded estimation method. By delicately constructing a specific composite Lyapunov function for the controlled system and several useful inequalities, the stability and asymptotic tracking performance with unknown nonlinear function and unknown UVCCs can be guaranteed almost surely. Finally, the method is illustrated with simulation examples.

Fast finite‐time adaptive fuzzy control for quantized stochastic uncertain nonlinear systems

SummaryThe issue of fast finite‐time adaptive control is studied for quantized stochastic nonlinear systems. Unlike the existing works about fast finite‐time control, the input signals are quantized, and the stochastic disturbances and nonlinear functions are unknown. According to universal approximation capacity of fuzzy logic system, combined with backstepping technique, a novel fast finite‐time adaptive fuzzy control strategy of quantized stochastic nonlinear system is proposed. The nonlinear decomposition method is introduced to set up the relationship among the control signals and the quantization signals, which overcomes the technical difficulties result from the piecewise quantization input. The proposed tactics can assure the tracking error situate in a neighborhood of the origin point and the closed‐loop system signals keep bounded. Finally, an algorithm simulation is conducted to test the validity of the method.

Pareto Suboptimal Strategy for Uncertain Mean-Field Nonlinear Stochastic Systems

In this paper, a static output feedback (SOF) Pareto suboptimal strategy for an uncertain mean-field nonlinear stochastic system is discussed. It is assumed that the nonlinear function in the stochastic system for each player is unknown and constrained by a norm-bounded function. As a preliminary result, the single-player case problem is solved in terms of the guaranteed cost control technique. As a result, it is shown that the necessary conditions satisfying the suboptimality of the upper bound of the cost are established by stochastic coupled-matrix equations (SCMEs). Next, the aforementioned results are applied to a mean-field stochastic system with a large population. Notably, a new necessary condition is described by the solvability condition related to large-scale SCMEs. To avoid the treatment of high-order computation for solving SCMEs, a new reduced-order numerical technique based on the fixed point iteration method is introduced. Consequently, the centralized strategy set is computed, although a large population is considered. Finally, to demonstrate the effectiveness of the proposed scheme, an academic example is solved.

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.

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.

PID control of uncertain nonlinear stochastic systems with state observer

PID control of uncertain nonlinear stochastic systems with state observer