Control For Stochastic Nonlinear Systems Research Articles

Sliding Mode Fuzzy Control of Stochastic Nonlinear Systems Under Cyber-Attacks.

In this article, the problem of integral sliding mode control (ISMC) for a class of nonlinear systems with stochastic characteristics under cyber-attack is investigated. The control system and the cyber-attack are modeled as an Itô-type stochastic differential equation. The stochastic nonlinear systems are approached by the Takagi-Sugeno fuzzy model. A dynamic ISMC scheme is applied and the states and control input are analyzed within a universal dynamic model. It is demonstrated that trajectory of the system can be confined to the integral sliding surface within finite time, and the stability of closed-loop system under cyber-attack will be guaranteed by using a set of linear matrix inequalities. Following a standard procedure of universal fuzzy ISMC, it is shown that all signals in the closed-loop system will be guaranteed bounded, and the states are asymptotic stochastic stable if some conditions are met. An inverted pendulum is applied to show the effectiveness of our control scheme.

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.

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.

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

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.

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.

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.

Command filter-based event-triggered fixed-time control for nonlinear systems with prescribed performance and actuator faults

This paper investigates command filter-based adaptive neural network (NN) minimal learning practical fixed-time control for stochastic nonlinear systems with prescribed performance and actuator faults. The considered system is in a high-order nonstrict-feedback stochastic structure with unknown dynamics and external disturbances. By combining NN with minimal learning parameter method, the need for prior knowledge of nonlinear functions is eliminated, and the number of weights’ updating laws for the NN is reduced to one, regardless of the system's order and number of neural nodes. This reduction significantly decreases the computational burden. Additionally, a unique property of the Gaussian basis function of NNs is applied to solve the algebraic loop problem of the nonstrict-feedback structure. A novel event-triggered control mechanism is proposed to save communication resources. In order to surmount the "explosion of complexity" and "singularity" problems, a novel fixed-time command filter is suggested, and then, a modified compensation mechanism is proposed to mitigate the errors that emerge from command filters. Furthermore, to improve the transient and steady-state performance of the tracking error, a prescribed performance function is taken into account. Via the Lyapunov stability theory, it will be shown that the developed adaptive backstepping control scheme, guarantees that the closed-loop system signals are bounded in probability in a fixed time, that the convergence time is independent of the initial value, and the tracking error remains within the decaying prescribed performance bounds all the time. Finally, the effectiveness and practicability of the theoretical results are verified by a practical simulation example.

New exploration on approximate controllability of fractional neutral‐type delay stochastic differential inclusions with non‐instantaneous impulse

This paper aims to derive a new set of sufficient conditions for the existence and approximate controllability of neutral‐type fractional stochastic integrodifferential inclusions with infinite delay and non‐instantaneous impulse in a separable Hilbert space using the Atangana–Baleanu Caputo fractional derivative. We investigate the existence of a mild solution for the Atangana–Baleanu Caputo fractional neutral‐type delay integrodifferential stochastic system while taking into account the non‐instantaneous impulses. For this purpose, the Atangana–Baleanu Caputo fractional neutral‐type impulsive delay stochastic system is transferred into an equivalent fixed point problem via an integral operator, and then, the Bohnenblust–Karlin fixed point approach is applied. Further, the approximate controllability results of the proposed nonlinear stochastic impulsive control system are established under the consideration that the corresponding linear system is approximately controllable. The set of sufficient conditions is established by using the concepts of stochastic analysis, fractional calculus, fixed point technique, semigroup theory of bounded linear operators, and the theory of multivalued maps. To illustrate the abstract results, we provide an example at the end of the paper.

Saturation-Tolerant Quantized Control for Nonlinear Stochastic Systems With Nonfragile Performance

Saturation-Tolerant Quantized Control for Nonlinear Stochastic Systems With Nonfragile Performance

Event-triggered Adaptive Tracking Control for Stochastic Nonlinear Systems With State Constraints

Event-triggered Adaptive Tracking Control for Stochastic Nonlinear Systems With State Constraints

Fuzzy-Based Optimal Control for Stochastic Nonlinear Systems With Constrained Inputs via Dynamic Event-Triggering

Fuzzy-Based Optimal Control for Stochastic Nonlinear Systems With Constrained Inputs via Dynamic Event-Triggering

Inverse optimally adaptive neural output‐feedback control of stochastic nonlinear systems

SummaryIn this article, for a class of stochastic nonlinear systems with non‐strict feedback, a neural adaptive inverse optimal output feedback control design scheme is presented. First, according to the existing inverse optimal criterion, an auxiliary system is established. On this basis, a novel observer is built to evaluate the unpredictable states. Second, in the control process, neural networks (NNs) are applied to estimate the unknown functions. Based on NNs and the backstepping technology, an adaptive neural inverse optimal output feedback controller is established. It is indicated that the proposed scheme could ensure the semi‐globally uniformly ultimately bounded of the closed‐loop system and also achieve the objective of inverse optimality. Eventually, an example is applied to testify the feasibility of this scheme.

Command filter and high gain observer based adaptive output feedback control for stochastic nonlinear systems with prescribed performance and input quantization

SummaryIn this paper, an adaptive output feedback dynamic surface control (DSC) strategy is proposed for strict‐feedback stochastic nonlinear systems with input quantization, prescribed performance and dynamic uncertainties. A new quantizer is used to process the input signal, which can avoid the chattering of the quantization signal and keep the upper bound of the quantization error constant. Radial basis functions are used to approximate unknown smooth functions, unmodeled dynamics are processed by dynamic signals, and unmeasurable states are estimated by high gain observer. Hyperbolic tangent functions are employed to handle prescribed performance. The second order command filter is used to replace the first order filter used in general DSC, and the compensation term is added in each step of DSC. By the Lyapunov stability analysis, all signals in the controlled system are semi‐globally uniformly ultimately bounded (SGUUB) in probability. Two examples further prove that the control scheme designed in this paper is reasonable and effective.

Practically Predefined-Time Adaptive Fuzzy Tracking Control for Nonlinear Stochastic Systems.

This article addresses the practically predefined-time adaptive fuzzy tracking control problem of strict-feedback nonlinear stochastic systems, where the system under consideration includes stochastic disturbances and uncertain parameters. First, in this study, practically predefined-time stochastic stabilization (PPSS) in the p th moment sense is introduced, and a Lyapunov-type criterion for PPSS is proposed to assure the stabilization of the system considered. With these ideas, based on the backstepping design method, a semiglobally practically predefined-time adaptive fuzzy tracking control algorithm is proposed with a fuzzy system used to approximate the unknown part of the system. Moreover, the settling time of the system response can be arbitrarily adjusted in a mean-value sense, and such freedom can be used to improve the stochastic finite-/fixed-time control results. Finally, a practical example and a numerical example of a comparison are provided to validate the effectiveness of the proposed control strategy.

Event-Trigger-Based Finite-Time Adaptive Fuzzy Control for Stochastic Nonlinear Systems With Unmeasured States

Event-Trigger-Based Finite-Time Adaptive Fuzzy Control for Stochastic Nonlinear Systems With Unmeasured States

A Novel Adaptive Controller for Nonlinear Stochastic Systems With Uncertain Virtual Control Gains and Input Nonlinearities

A Novel Adaptive Controller for Nonlinear Stochastic Systems With Uncertain Virtual Control Gains and Input Nonlinearities

Finite‐time prescribed performance adaptive fuzzy output feedback control for stochastic nonlinear systems with dead‐zone input

AbstractIn this paper, the issue of finite‐time prescribed performance control (PPC) is addressed for stochastic nonlinear systems with the effect of dead‐zone. Fuzzy logic systems are utilized for identifying unknown nonlinear characteristics. A model consisting of linear and disturbance‐like terms is constructed to approximate the nonlinearity of dead‐zone. Meanwhile, a state observer is employed to estimate unmeasured states. To improve the convergence rate, a finite‐time performance function is introduced, which transforms the tracking error of original system to error of converted system, thus prescribing the transient and steady‐state performance of the system. Eventually, based on backstepping technique, a finite‐time PPC strategy is proposed, which ensures the boundedness of all signals in closed‐loop system. Simultaneously, the tracking error converges to a prescribed region in finite‐time. Finally, two simulation examples are provided to verify the effectiveness of presented control strategy.

Adaptive neural optimised control for stochastic nonlinear systems with time-varying input delay via self-triggered mechanism

In this paper, an adaptive tracking control strategy based on neural networks (NNs) is proposed for the stochastic nonlinear strict-feedback system with a time-varying input delay and unmeasurable states. A state observer is constructed to solve the problem of unmeasurable state and the effect of the time-varying input delay is compensated by using an auxiliary signal. All the virtual controllers and the actual controller are designed as the optimised solution of the corresponding subsystems to ensure the entire obtained controllers are optimised. To ensure that the states of the system are constrained within some given compact sets, the barrier Lyapunov function (BLF) is used to design the controller and perform stability analysis. Meanwhile, this paper adds a self-triggered mechanism to reduce the communication burden of the data transfer. Thus, the proposed control strategy can achieve optimised control and all system states can be constrained within the given ranges. On the other hand, all closed-loop signals of system are bounded in probability. Finally, it is demonstrated that the proposed control strategy can achieve the expected system performance by a simulation experiment.