Nonsmooth adaptive control design for uncertain stochastic nonlinear systems

This paper addresses the problem of state feedback control for a class of stochastic high-order feedforward nonlinear systems with multiple time-varying delays. A distinct property of the system to be investigated is that the control coefficients are not restricted to 1. By introducing the sign function and the adding one power integrator, a delay-independent state feedback controller is constructed. By Lyapunov-Krasovskii theorem and homogeneous domination approach, the global stochastic asymptotic stability of the closed-loop system under the above-mentioned controller is proved. Finally, a simulation example is given to illustrate the effectiveness of the results of this paper.

This paper discusses the problem of global finite-time stabilization in probability for a class of stochastic high-order nonlinear systems whose drift and diffusion terms satisfy lower-triangular growth conditions. By adopting adding one power integrator technique and constructing twice continuous differential Lyapunov functions, a continuous state-feedback controller is recursively designed. Based on stochastic finite-time stability theorem, it is proved that the solution of the closed-loop system is finite-time stable in probability. Several simulation examples are given to illustrate the effectiveness of the proposed design procedure.

For a class of more general stochastic high-order feedforward nonlinear systems, this paper deals with the problem of state feedback stabilization. By introducing an appropriate coordinate transformation, the original system is transformed into an equivalent one with tunable gain. After that, by reasonably extending the homogeneous domination approach and skillfully choosing the low gain scale, a state feedback controller is explicitly constructed to render the closed-loop system globally asymptotically stable in probability. Two numerical examples are provided to demonstrate the effectiveness of the proposed design method.

Global stabilization of stochastic high-order feedforward nonlinear systems with time-varying delay

The homogeneous domination approach is introduced to solve the state feedback stabilization problem for stochastic high-order nonlinear systems with time-varying delay. Under the weaker conditions on the drift and diffusion terms, by using the homogeneous domination approach and solving several troublesome obstacles in the design and analysis procedure, a state feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability.

The problem of robust tracking and model following is considered for a class of linear dynamical systems with multiple delayed state perturbations, time–varying uncertain parameters, and disturbance. A class of continuous memoryless state feedback controllers is proposed for robust tracking of dynamical signals. The proposed robust tracking controllers can guarantee that the tracking error decreases asymptotically to zero in the presence of multiple delayed state perturbations, time–varying uncertain parameters, and disturbance. A procedure for designing such a class of zero–error tracking state feedback controllers is also introduced. Finally, a numerical example is given to demonstrate the validity of the results.

Non-fragile robust stabilization and [formula omitted] control for uncertain stochastic nonlinear time-delay systems

Distributed containment output-feedback control for a general class of stochastic nonlinear multi-agent systems

Controlling stochastic multi-agent systems (MAS) is a promising branch of systems engineering owing to its ability to solve complex practical problems by taking inspiration from the social behavior of living organisms. Consensus on more than one state is a less considered problem in the framework of leader-following control of high-order uncertain nonlinear stochastic multi-agent systems with unknown dynamics. To this end, in this paper, a sliding surface integrates a tracking error polynomial with consensus error between states of the connected agents. Accordingly, a new distributed fuzzy sliding mode controller is designed for a class of stochastic multi-agent systems with partially unknown deterministic dynamics and unknown bounded stochastic dynamics. The proposed control protocol steers agents to reach agreement on states of the leader and concurrently approximates the unknown part of their deterministic dynamics by using fuzzy systems with adaptive parameters. In the sense of Lyapunov, it is proved that consensus error and all of the closed-loop signals of each agent are semi-globally uniformly ultimately bounded (SGUUB) in mean square. Under the designed controller, nonlinear closedloop experimental dynamics behave well in both tracking and reaching state consensus.

Adaptive fault tolerant tracking control for a class of stochastic nonlinear systems with output constraint and actuator faults

This paper mainly focuses on output feedback practical tracking controller design for stochastic nonlinear systems with polynomial function growth conditions. Mostly, there are some studies on output feedback tracking control problem for general nonlinear systems with parametric certainty in existing achievements. Moreover, we extend it to stochastic nonlinear systems with parametric uncertainty and system nonlinear terms are assumed to satisfy polynomial function growth conditions which are more relaxed than linear growth conditions or power growth conditions. Due to the presence of unknown parametric uncertainty, an output feedback practical tracking controller with dynamically updated gains is constructed explicitly so that all the states of the closed-loop systems are globally bounded and the tracking error belongs to arbitrarily small interval after some positive finite time. An example illustrates the efficiency of the theoretical results.

In this paper, a combined homogeneous domination and sign function design approach is presented to state feedback control for a class of stochastic high-order nonlinear systems with time-varying delay. The use of the combined approach relaxes the restriction on nonlinear functions and makes the closed-loop system globally asymptotically stable in probability.

In this paper, the dynamic surface control (DSC) algorithm is proposed for a class of stochastic nonlinear systems with nonminimum phase and the standard output-feedback form. The proposed algorithm is a stochastic vision by combining the traditional back-stepping together with the DSC technique, which can overcome the problem of ‘explosion of complexity’ in the back-stepping designing procedure for the stochastic nonlinear systems. Thus, it can reduce the computation complexity and is easy to be used in the actual implementation. It is shown that all the signals of the resulting closed-loop system are uniformly ultimately bounded.

Stability analysis for a class of stochastic delay nonlinear systems driven by G-Brownian motion

This article takes a fast finite-time control of stochastic nonlinear systems into account. The presence of unknown stochastic disturbance terms makes the traditional fast finite-time control approaches unavailable. To deal with this difficulty, by establishing an auxiliary function and using Jensen's inequality, in Lemma 6, a new criterion of fast finite-time stability is first established for the uncertain stochastic system. Based on the approximation ability of neural networks (NNs), an innovative fast finite-time strategy is put forward for stochastic nonlinear systems. Furthermore, by adopting the presented fast finite-time stability criterion, the stability of the stochastic systems is confirmed. Finally, two simulations are implemented to validate the feasibility of the presented NN control strategy.