Control For Stochastic Nonlinear Systems Research Articles

Command Filter-Based Adaptive Fuzzy Fixed-Time Tracking Control for Stochastic Nonlinear Systems with Input Saturation and Dead Zone

Command Filter-Based Adaptive Fuzzy Fixed-Time Tracking Control for Stochastic Nonlinear Systems with Input Saturation and Dead Zone

Fast finite‐time stabilization of stochastic nonlinear systems with output constraints and an application to single‐link robot

AbstractThis article studies the fast finite‐time stabilization problem for stochastic nonlinear systems with asymmetric output constraints. To address the issue of slow convergence encountered in previous finite‐time control designs of stochastic nonlinear constrained systems, this paper extends the fast finite‐time stabilization mechanism to such systems. First, a novel asymmetric barrier Lyapunov function is employed to tackle the output constraint. Then, by adding a power integrator technique and the barrier Lyapunov function, a state‐feedback controller for stochastic nonlinear systems is explicitly designed using the backstepping method. The designed controller achieves fast finite‐time stability in probability of the stochastic nonlinear system while ensuring no violation of the output constraints. Finally, two examples are presented to demonstrate the effectiveness of the controller scheme.

Existence of a mild solution and approximate controllability for fractional random integro-differential inclusions with non-instantaneous impulses

This paper investigates the existence and approximate controllability (ACA) of fractional neutral-type stochastic differential inclusions (NTSDIs) characterized by non-instantaneous impulses within a separable Hilbert space (HS) framework. Employing the Atangana–Baleanu–Caputo (ABC) derivative, we transform the system into an equivalent fixed-point (FP) problem through an integral operator. Subsequently, the Bohnenblust–Karlin FP theorem is leveraged to establish existence results. By assuming ACA of the corresponding linear system, we derive sufficient conditions for the ACA of the nonlinear stochastic impulsive control system. Our analysis relies on concepts from stochastic analysis, fractional calculus, FP theory, semigroup theory, and the theory of multivalued maps (MVMs). The theoretical findings are illustrated through a concrete example.

Adaptive Fuzzy Finite‐Time Command Filtered Control for Stochastic Nonlinear Systems With Unmodeled Dynamics and Dead‐Zone Constraints

ABSTRACTIn this article, the issue of adaptive fuzzy finite‐time command filtered control is discussed for nonlinear stochastic systems subject to unknown dead‐zone constraints and unmodeled dynamics. The packaged unknown nonlinearities are approximated by introducing fuzzy logic systems. An improved technique is introduced to cope with unknown functions with the structure of nonstrict‐feedback in the operation of controller design. Under the criterion of finite‐time stability, a novel fast convergent control scheme is developed. Additionally, the effect of filter errors bought by the command filters is diminished via applying corresponding error compensating signals and a measurable dynamic signal is adopted to handle unmodeled dynamics. The improved designed controller not only guarantees all the closed‐loop signals remain finite‐time bounded, but also makes the system output follows the given desirable trajectory under the bounded error. The usefulness of the designed strategy can be verified through the numerical and practical examples.

Predefined time fuzzy adaptive control for stochastic nonlinear systems with limited time interval output constraints

This article investigates the problem of fuzzy adaptive predefined time tracking control for stochastic nonlinear systems with limited time interval output constraints. Firstly, the considered output constraints occur within a finite time interval after the system starts running. By constructing shift functions and barrier Lyapunov functions (BLFs), the constrained system is converted into an unconstrained system, which solves the problem of function discontinuity resulting from output constraints within limited time intervals. Then, with the help of adaptive backstepping technique and predefined time control method, which reduces the parameters to be designed and removes the limitation of relatively large initial control input in existing approaches. The designed control technique ensures the boundedness of all variables of the stochastic system, the tracking error converges within a predetermined time, and the outputs do not exceed their constraint boundaries in a finite time interval. And this algorithm is applicable to both infinite time constraints and unconstrained outputs cases. Finally, the validity of this approach is demonstrated through simulation examples.

Output feedback control of stochastic nonlinear systems with external disturbances and inverse dynamics

SummaryThis work presents an approach to control a type of stochastic cascade nonlinear systems, which involve external disturbances and nonlinear terms. The external disturbances under the consideration are not measurable and regarded as extended states. The proposed method addresses the problem of unmeasured states and external disturbances by introducing an extended state observer (ESO). Based on the above work, a new stochastic nonlinear system including ESO is established. To ensure the stability and boundedness of the system, an adaptive output feedback controller is designed by using stochastic integrated input‐to‐state stability and backstepping design technique. This controller guarantees that all the states remain almost surely bounded and globally asymptotically stable in probability. Simulation experiments are conducted to validate the effectiveness of the proposed control scheme.

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

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.

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

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

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.

Finite‐Time Adaptive Fuzzy Control for Stochastic Nonlinear Systems with Input Quantization and Actuator Faults

Finite‐Time Adaptive Fuzzy Control for Stochastic Nonlinear Systems with Input Quantization and Actuator Faults

Adaptive Neural Network Finite-Time Event Triggered Intelligent Control for Stochastic Nonlinear Systems with Time-Varying Constraints

Adaptive Neural Network Finite-Time Event Triggered Intelligent Control for Stochastic Nonlinear Systems with Time-Varying Constraints