State-feedback stabilization of stochastic feedforward nonlinear time-delay systems

This paper discusses the problem of adaptive stabilization for stochastic feedforward nonlinear systems with time-delay. A universal-type adaptive update law is introduced into the observer and controller to deal with unknown growth rates. With the help of the appropriate Lyapunov-Krasovskii functional and stochastic Barbalat's lemma, it can be proved that the universal-type adaptive output feedback controller can regulate all the states of the closed-loop system almost surely. A simulation example is given to illustrate the effectiveness of the proposed method.

This article aims to investigate the global stabilization for a class of stochastic continuous time-delay nonlinear systems involved with unknown control coefficients and stochastic-input-to-state-stable-like conditions. Without involving the traditional adaptive compensation approach, a dominate gain is adopted to deal with uncertain nonlinearities, which not only include unmeasurable state but also involve input and state delays. On account of homogeneous domination manner and stochastic stability theory, a delay-independent controller is developed to guarantee that the closed-loop system is globally asymptotically stable in probability. Finally, a simulation example is supplied to show the virtue of the devised strategy.

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

This paper investigates the problem of output feedback stabilization for a class of stochastic feedforward nonlinear systems with time-varying input delay. The drift and diffusion terms satisfy the linear growth condition and are dependent on unmeasurable states and the delayed input. First, we use a change of coordinates to introduce a scaling gain into the system. Then, based on the high-gain observer technique, a delay-free output feedback controller with the scaling gain is developed. Based on the Lyapunov–Krasovskii method and the idea of feedback domination, it is shown that the closed-loop system can be rendered globally asymptotically stable in probability via appropriately choosing the scaling gain. Finally, two examples are presented to illustrate the effectiveness of the proposed scheme.

This paper focuses on the problem of approximation-based adaptive fuzzy tracking control for a class of stochastic nonlinear time-delay systems with a nonstrict-feedback structure. A variable separation approach is introduced to overcome the design difficulty from the nonstrict-feedback structure. Mamdani-type fuzzy logic systems are utilized to model the unknown nonlinear functions in the process of controller design, and an adaptive fuzzy tracking controller is systematically designed by using a backstepping technique. It is shown that the proposed controller guarantees that all signals in the closed-loop system are fourth-moment semiglobally uniformly ultimately bounded, and the tracking error eventually converges to a small neighborhood of the origin in the sense of mean quartic value. Simulation results are provided to demonstrate the effectiveness of our results. Further developments will consider how to generalize the proposed strategy to nonstrict-feedback nonlinear systems with input nonlinearities.

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 is concerned with the output feedback \(\mathcal {H}_\infty \) control problem for a class of stochastic nonlinear systems with time-varying state delays; the system dynamics is governed by the stochastic time-delay It\(\hat{o}\)-type differential equation with state and disturbance contaminated by white noises. The design of the output feedback \(\mathcal {H}_\infty \) control is based on the stochastic dissipative theory. By establishing the stochastic dissipation of the closed-loop system, the delay-dependent and delay-independent approaches are proposed for designing the output feedback \(\mathcal {H}_\infty \) controller. It is shown that the output feedback \(\mathcal {H}_\infty \) control problem for the stochastic nonlinear time-delay systems can be solved by two delay-involved Hamilton–Jacobi inequalities. A numerical example is provided to illustrate the effectiveness of the proposed methods.

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.

ABSTRACTThis paper considers the problem of global finite-time stabilisation by output feedback for a class of feedforward (upper triangular) nonlinear systems with input saturation. Based on the finite-time stability theorem, and by skillfully using the homogeneous domination approach and the nested saturation technique, a saturated output feedback controller is successfully constructed, which renders the origin of the closed-loop system globally finite-time stable. In simulation studies, a numerical example is illustrated to show the effectiveness of the control scheme. Moreover, the design strategy is successfully applied to solve the saturated finite-time control problem for vertical wheel on rotating table.

We study the problem of output feedback stabilization for stochastic nonlinear systems. We consider a class of stochastic nonlinear systems in observer canonical form with stable zero-dynamics. We introduce a sequence of state transformations that transform the system into a lower triangular structure that is amenable for integrator backstepping design. Then we design the output feedback controller and prove that the closed-loop system is bounded in probability. Under an infinite-horizon risk-neutral cost criterion, the controller designed can guarantee an arbitrarily small long term average cost. Furthermore, when the disturbance vector field vanishes at the origin, the closed-loop system is asymptotically stable in the large, and the risk-neutral cost is guaranteed to be zero. With special care, the controller preserves the equilibrium of the nonlinear system.

This note is devoted to study the stabilization problem of stochastic nonlinear delay systems with exogenous disturbances and the event-triggered feedback control. By introducing the notation of input-to-state practical stability and an event-triggered strategy, we establish the input-to-state practically exponential mean-square stability of the suggested system. Moreover, we investigate the stabilization result by designing the feedback gain matrix and the event-triggered feedback controller, which is expressed in terms of linear matrix inequalities. Also, the lower bounds of interexecution times by the proposed event-triggered control method are obtained. Finally, an example is given to show the effectiveness of the proposed method. Compared with a large number of results for discrete-time stochastic systems, only a few results have appeared on the event-triggered control for continuous-time stochastic systems. In particular, there have been no published papers on the event-triggered control for continuous-time stochastic delay systems. This note is a first try to fill the gap on the topic.

This paper considers a more general stochastic nonlinear time-delay system driven by unknown covariance noise and investigates its adaptive state-feedback control problem. As a remarkable feature, the growth assumptions imposed on delay-dependent nonlinear terms are removed. Then, with the help of Lyapunov-Krasovskii functionals and adaptive backstepping technique, an adaptive state-feedback controller is constructed by overcoming the negative effects brought by unknown time delay and covariance noise. Based on the designed controller, the closed-loop system can be guaranteed to be globally asymptotically stable (GAS) in probability. Finally, a simulation example demonstrates the effectiveness of the proposed scheme.

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.

In this brief, the global output-feedback stabilization is addressed for a class of uncertain feedforward nonlinear systems. By integrating a dynamic event-triggered mechanism, a novel observer-based control scheme is established, where a time-varying gain is introduced to cope with large uncertainties and sampling errors in the system. Under this control scheme, the global convergence is ensured for the resulting closed-loop system states. Different from the related results, the system states are intermittently monitored by imposing suspension time after each sampling, so that the inter-event intervals have a uniform positive lower bound, and the Zeno behavior is automatically ruled out. Additionally, an internal dynamic variable is incorporated into the triggering mechanism to further extend the inter-event intervals. Finally, the obtained results are extended to a class of feedforward nonlinear systems with unknown time-varying growth rates. A simulation example is given by applying the proposed scheme to a nonlinear liquid level control (LLC) resonant circuit system.

SummaryThis article is concerned with the global stabilization problem of a family of feedforward nonlinear time‐delay systems whose linearized system consists of multiple distinct oscillators. To fully utilize the delayed information and maintain the state decoupling property in the controller design, the considered nonlinear feedforward system is first transformed into a new system which contains time delays in both its input and states based on a novel model transformation containing time delays, and then the stabilizing saturated controller for the transformed system is designed based on the recursive design method. Meanwhile, explicit stability conditions are also provided. When the linearized system is a cascade of multiple oscillators and multiple integrators, a modified saturated feedback control utilizing not only the current state but also the delayed state is also established for the corresponding global stabilization problem. Two examples, including a practical one, are given to show the effectiveness and superiority of the proposed approaches.