Stochastic High-order Nonlinear Systems Research Articles

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.

Fixed-time stabilization of output-constrained stochastic high-order nonlinear systems

Fixed-time stabilization of output-constrained stochastic high-order nonlinear systems

Prescribed-time stabilization and inverse optimal control of stochastic high-order nonlinear systems

Prescribed-time stabilization and inverse optimal control of stochastic high-order nonlinear systems

Prescribed-time adaptive stabilization of high-order stochastic nonlinear systems with unmodeled dynamics and time-varying powers

<p>In this paper, the control problem of prescribed-time adaptive neural stabilization for a class of non-strict feedback stochastic high-order nonlinear systems with dynamic uncertainty and unknown time-varying powers is discussed. The parameter separation technique, dynamic surface control technique, and dynamic signals were used to eradicate the influences of unknown time-varying powers together with state and input unmodeled dynamics, and to mitigate the computational intricacy of the backstepping. In a non-strict feedback framework, the radial basis function neural networks (RBFNNs) and Young's inequality were deployed to reconstruct the continuous unknown nonlinear functions. Finally, by establishing a new criterion of stochastic prescribed-time stability and introducing a proper bounded control gain function, an adaptive neural prescribed-time state-feedback controller was designed, ensuring that all signals of the closed-loop system were semi-global practical prescribed-time stable in probability. A numerical example and a practical example successfully validated the productivity and superiority of the control scheme.</p>

Finite-Time Output Feedback Stabilization for High-Order Stochastic Nonlinear Systems With Unknown Output Function

Finite-Time Output Feedback Stabilization for High-Order Stochastic Nonlinear Systems With Unknown Output Function

Prescribed-Time Control for Stochastic High-Order Nonlinear Systems With Parameter Uncertainty

This brief focuses on the problem of prescribed-time mean-square control for uncertain stochastic high-order (p-normal) nonlinear systems. Compared to existing results, a more general model is considered. First, a prescribed-time mean-square stable controller is constructed with the assistance of the power integrator technique, the time-varying prescribed-time function and a non-scaling framework. Then, based on the stability theorem of stochastic systems and the useful proposition of the selected Lyapunov function, the prescribed-time mean-square stability of all signals is analyzed. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed control strategy.

State feedback stabilization problem of stochastic high-order and low-order nonlinear systems with time-delay

<abstract><p>This manuscript considers the state feedback stabilization problem for a class of stochastic high-order and low-order nonlinear systems with time-delay. Compared with the previous results, a distinctive feature to be studied is that the considered systems involve high-order, low-order, intricate stochastic diffusion terms and time-delay simultaneously. First, the homogeneous domination approach and suitable coordinate transformations are introduced to obtain the updating laws. Then, a state feedback controller is devised to make the closed-loop systems globally asymptotically stable in probability. Finally, a simulation example is shown to prove the proposed approach powerfully.</p></abstract>

Output feedback finite-time stabilization of a class of large-scale high-order nonlinear stochastic feedforward systems

This paper considers the output feedback finite-time stabilization in probability for a class of large-scale high-order stochastic nonlinear feedforward systems. The output feedback finite-time stabilized controller in probability is firstly designed for the nominal systems by the adding one power integrator. Then with the homogeneous domination method, by introducing an appropriate coordination, an equivalent system of the original system with tunable gain is obtained. After that, by constructing a observer and determining the tunable gains, the output feedback stabilized controller in probability of the original systems is finally given and analysed.

A Unified Fuzzy Control Approach for Stochastic High-Order Nonlinear Systems With or Without State Constraints

A unified approach to fixed-time tracking control of stochastic high-order nonlinear systems (HONSs) with or without full-state constraints is studied in this article. By introducing two important universal-constrained functions and using coordinate transformation technology, the stochastic HONS with full-state constraints is transformed into an equivalent one without state constraints. Compared with the existing control schemes, the proposed scheme not only eliminates the feasibility conditions, but also accurately analyzes the scope of tracking error. Moreover, the limitation that the constraint functions need to be bounded is also removed; thus, the proposed scheme is a unified approach that can be applied to stochastic HONSs with or without state constraints. With the help of fixed-time stability theory and adaptive fuzzy control technology, a novel fixed-time fuzzy controller is designed. In addition, an adaptive event-triggering mechanism that the threshold parameters can be adjusted adaptively according to the tracking performance is introduced to reduce the communication burden. Simulation results verify the scheme developed.

Fast Finite-Time Stability and Its Application in Adaptive Control of High-Order Stochastic Nonlinear Systems

In this article, a new design method for an adaptive fast finite-time controller (FTC) is proposed for the finite-time stability (FTS) issue of a class of high-order stochastic nonlinear systems (HOSNSs) with unknown parameters. Using a power integrator technology and Lyapunov function approach, an adaptive state feedback controller is derived to ensure fast FTS of HOSNSs. The developed adaptive fast FTC is equipped with less settling time to obtain better steady-state accuracy compared with the traditional FTC. The effectiveness of the proposed adaptive control scheme is demonstrated by a numerical example.

Distributed adaptive control for high-order stochastic nonlinear systems with unknown control gains and uncertainties

The leader-following tracking consensus problem of a class of high-order stochastic nonlinear multi-agent systems with unknown control gains and unknown system parameters is solved in this paper. For a class of high-order stochastic nonlinear multi-agent systems in parametric strict-feedback, the distributed control scheme is designed by using backstepping technology. The adaptive control method is used to deal with the unknown control gains and unknown system parameters. Besides, to save communication resources, the event-trigged control is applied. The control algorithms ensure that all states in the closed-loop system and tracking errors are globally bounded stable in probability. Two simulation examples verify the effectiveness of the designed algorithms.

Event-triggered adaptive fuzzy tracking control for high-order stochastic nonlinear systems

This paper is concerned with event-triggered adaptive fuzzy tracking control for high-order stochastic nonlinear systems. The approach of fuzzy logic systems (FLSs) approximation is extended to high-order stochastic nonlinear systems to deal with the unknown nonlinear uncertainties. A novel high-order adaptive fuzzy tracking controller is firstly presented via a backstepping approach and event-triggering mechanism which can mitigate the unnecessary waste of computation and communication resources. Based on the above techniques, frequently-used growth assumptions imposed on unknown system nonlinearities are removed and the influence for the high order is handled. The proposed high-order adaptive fuzzy tracking control method not only deals with the influence of high order, but also ensures that the tracking error converges to a small neighborhood of the origin in probability. Finally, the effectiveness of the proposed control method is illustrated by a numerical example.

Adaptive output feedback controller design for high-order stochastic nonlinear systems with uncertain output function

This paper concentrates on the adaptive output feedback controller design for a class of high-order stochastic nonlinear systems(SNSs) with uncertain output function. Firstly for the nominal system, a homogeneous observer and output feedback controller is put forward through adding a power integrator method. Secondly, a dynamic gain technique is adopted into the observer and controller to guarantee the convergence of original system states and boundedness of the dynamic gain in probability. Besides, the proposed controller design scheme can be also broadened to upper-triangular SNSs. Finally, two numerical examples are provided to indicate the effectiveness of the proposed method.

Prescribed-time control of stochastic high-order nonlinear systems.

In this paper, the prescribed-time stabilization is studied for stochastic high-order nonlinear systems. Different from the previous research results on stochastic high-order nonlinear systems where only asymptotic stabilization or finite-time stabilization is considered, this paper proposes a new design to achieve stabilization in the prescribed-time. Specifically, the designed controller can ensure that the closed-loop system has an almost surely unique strong solution and the equilibrium of the closed-loop system is prescribed-time mean-square stable. The design method is verified by an example.

Finite-time stabilization of output-constrained stochastic high-order nonlinear systems with high-order and low-order nonlinearities

This paper investigates finite-time stabilization of output-constrained stochastic high-order nonlinear systems with stochastic inverse dynamics and high-order and low-order nonlinearities. By characterizing the unmeasured stochastic inverse dynamics with finite-time stochastic input-to-state stability and introducing nonlinear transformations, a new design and analysis method is constructed. It is rigorously proved that all the closed-loop signals are bounded almost surely, the asymmetric output constraint isn’t violated almost surely, and the trivial solution of the closed-loop system is finite-time stable in probability.

Decentralized stabilization of large-scale stochastic nonlinear systems with time-varying powers

In this paper, we study the decentralized stabilization problem for large-scale high-order stochastic nonlinear systems with time-varying powers. By using the backstepping design technique, a new decentralized state-feedback controller is constructed to ensure the closed-loop system is globally asymptotically stable (GAS) in probability. Then we further redesign a new optimal controller to solve the decentralized inverse optimal stabilization (IOS) problem. Specifically, our redesigned stabilizing backstepping controller is not only globally asymptotically stable for the closed-loop system but also optimal for the meaningful cost function. Finally, a simulation example is given to illustrate the effectiveness of the designed controllers.

Adaptive state-feedback stabilization of state-constrained stochastic high-order nonlinear systems

Adaptive state-feedback stabilization of state-constrained stochastic high-order nonlinear systems

Event-Triggered/Self-Triggered Leader-Following Control of Stochastic Nonlinear Multiagent Systems Using High-Gain Method.

In this article, the event-triggered and self-triggered leader-following output-feedback control problems are investigated for a class of high-order stochastic nonlinear multiagent systems (MASs) under an undirected graph. First, using the high-gain method, the observer is designed to estimate the unmeasured state variables of the given nonlinear system. Then, by introducing an internal dynamic variable, a distributed Zeno-free dynamic event-triggered controller is constructed. Compared with the static event-triggering results, the interevent time of the proposed dynamic event-triggering mechanism is shown to be prolonged and, thus, the advantages of the event-triggered control approaches can be enhanced. Further, to avoid continuously monitoring the states, a Zeno-free self-triggering mechanism is given. It is shown that the expectations of the output tracking errors converge to an arbitrarily small set if the diffusion terms are different for all agents, and that the expectations of all state tracking errors converge to an arbitrarily small set if the diffusion terms are the same for all agents. Finally, simulation studies are given to illustrate the effectiveness of the proposed methods.

Finite-Time Adaptive Fuzzy Prescribed Performance Control for High-Order Stochastic Nonlinear Systems

In this article, the high-order nonlinear system is commonly studied in an underactuated weakly coupled mechanical system, the control design is difficult from the tractional control design for nonlinear systems. Thus, we study the finite-time fuzzy adaptive error constraint control problem for stochastic high-order nonlinear nonstrict feedback systems. Fuzzy logic systems are utilized to identify the unknown nonlinear dynamics, a new error transfer variable is used to achieve the prescribed performance. Based on adding a power integrator technique and adaptive backstepping recursive control, a novel adaptive fuzzy finite-time prescribed performance control scheme is developed. By utilizing stochastically finite-time stable theory, the proposed control method can guarantee that the high-order system is semi-global finite-time stable in probability. Finally, both numerical and practical simulations are provided to verify the feasibility and effectiveness of the developed control method.

Output Tracking Control via Neural Networks for High-Order Stochastic Nonlinear Systems with Dynamic Uncertainties

This paper is concerned with the problem of output tracking control for a class of high-order stochastic nonlinear systems with dynamic uncertainties. The systems under investigation have dynamic uncertainties, unknown high-order terms, and uncertain nonlinear functions simultaneously. The packaged unknown nonlinearities are manipulated successful by using radial basis function neural networks. Two dynamic signals are introduced to dominate the dynamic uncertainties and adjust the tracking accuracy, respectively. The proposed continuous controller guarantees that all states of the closed-loop system are bounded in probability, and the tracking error converges to a preassigned range. Finally, a simulation example is provided to demonstrate the effectiveness of the control scheme.