Observer-based state-feedback stabilization of high-order stochastic switched systems with output constraints

ABSTRACTThis paper investigates the problem of state-feedback stabilisation for a class of high-order nonlinear systems with an output constraint. A novel tangent-type barrier Lyapunov function is first developed to cope with the output constraint. Then, by introducing the sign function and incorporating the developed tangent-type barrier Lyapunov function, the celebrated adding a power integrator technique is revamped to systematically design a continuous state feedback stabilising controller that prevents violation of the output constraint during operation. The novelty of this paper is the development of an unified design procedure, which can tackle the stabilisation task of the systems with/without the output constraint simultaneously.

A state feedback stabilisation problem of switched non-linear systems with asymmetric output constraints (AOCs) is investigated in this study by combining a simple new common barrier Lyapunov function and then adding a power integrator technique. Smooth state feedback controllers are designed in a constructive and systematic way to make switched systems asymptotically stable and to prevent switched systems from violating AOCs. The proposed method, which is developed in a unified frame in some sense, works not only for switched systems with asymmetric or symmetric output constraints but also for those without output constraints. Illustrative examples are employed to verify the proposed method in this study.

Non-smooth fixed-time state feedback stabilization of uncertain switched systems with output constraints.

In this article, the problem of non-smooth finite-time (FT) adaptive state feedback stabilisation is investigated for asymmetric output-constrained cascade switched nonlinear systems (AOCCSNSs) with mixed powers, parametric uncertainties and zero dynamics. To better address the uncertain parameters and the asymmetric output constraints, a new type of common Lyapunov function (CLF) including a quadratic squared term of the estimated error and a tangent-type barrier Lyapunov function ( T t -BLF) is constructed. Then, with some mild assumptions, such as input-to-state stability (ISS) property of zero dynamics, upper boundedness of subsystems' nonlinear terms and some well-known small signal conditions, state feedback controllers (SFCs) constructed by adding a power integrator (AAPI) technique and the update law to estimate the unknown parameter are proposed to guarantee resultant closed-loop switched systems FT stable. The proposed method for switched systems is presented in a unified manner, capable of addressing FT stabilisation by effectively handling situations with or without output constraints. This is achieved through the construction of T t -BLF, which degenerates into a quadratic form when the output constraint disappears or approaches infinity. At last, the method is verified by a switched RLC circuit system (RLC-CS) and a numerical simulation.

Fast finite-time partial state feedback stabilization of high-order nonlinear systems with output constraint and dynamic uncertainties

In this article, the problem of adaptive nonsmooth state-feedback stabilization for uncertain output-constrained cascade switched systems with a general form, whose subsystems possess mixed powers (MPs) and zero dynamics (ZDs), is investigated. To solve the problem of adaptive control, on subsystems of switched systems, some mild assumptions, such as ZDs with input-to-state stability (ISS), nonlinear terms with a growth condition and some well-known small signal conditions, have been imposed. State-feedback control laws are designed and an adaptive law is constructed in a systematic way by revamping the so-called adding a power integrator (AAPI) technique, a special back-stepping-like method. In order to cope with output constraints (OCs), a common Lyapunov function, including a tangent-type barrier Lyapunov function term, is constructed. The method is proposed in a unified manner which can tackle adaptive stabilization of switched systems due to that it can deal with the cases of uncertain cascade switched systems with/without OCs, no need to change the structure of the controller. Simulation results are provided to illustrate the efficiency of the proposed method.

SummaryThis paper is concerned with the problem of state feedback stabilization for a class of high‐order nonlinear systems with an asymmetric output constraint. A novel asymmetric barrier Lyapunov function (BLF) is first proposed by deliberating the characteristics of the system nonlinearities. Then, the presented BLF, together with a skillful manipulation of sign functions, is utilized to delicately revamp the technique of adding a power integrator, thereby developing a systematic approach that guides us in constructing a continuous state feedback stabilizer and preventing the violation of a pre‐specified asymmetric output constraint during operation. The novelty of this paper is attributed to the development of a unified method that is able to simultaneously tackle the problem of stabilization for high‐order nonlinear systems with and without output constraints in a constructive fashion, without changing the controller structure. An illustrative example is presented to demonstrate the superiority of the proposed approach.

ABSTRACTIn this paper, the adaptive non‐smooth fixed‐time state feedback stabilization problem of output‐constrained switched systems are investigated. In order to well deal with the output constrains and uncertain parameters, a common barrier Lyapunov function which includes a tangent‐type term of the system state and a quadratic term of the uncertain parameter estimation error is constructed. Adaptive fixed‐time state feedback controllers and parameter update laws are designed by virtue of adding a power integrator technique with some mild assumption imposed on the subsystem's nonlinear terms. Simulation results of a numerical example and a two‐tank liquid‐level system presented in this paper explicitly demonstrate the effectiveness of the proposed approach in this paper. Subsystems powers considered in this article only need to be greater than zero, regardless of odd or even numbers, which make the structure of switched systems more general. The proposed method provides us to perform the design of the adaptive fixed‐time stabilizers for switched systems with/without output constraints simultaneously with the same controller structure, which means it has a unified nature.

Traditional Lyapunov stability theory cannot directly apply to constrained stochastic nonlinear systems when using barrier Lyapunov functions due to their inherent lack of radial unboundedness. This article presents a novel approach to establishing finite-time stability for such systems by employing Lyapunov functions. The proposed stability analysis relies on a time-varying gain function that remains uniformly bounded. This approach ensures that the system achieves finite-time stability with an arbitrarily prescribed upper bound on the settling time, thereby effectively avoiding the unbounded controller gain problem. The resulting stability is further extended to the finite-time state-feedback control for strict-feedback stochastic nonlinear systems with output constraints. Simulation studies validate the effectiveness of the proposed control scheme.

For output-constrained switched systems, uniformly local stabilization problem via state feedback is addressed. A unified tool, a common tangent-type barrier Lyapunov function (Tan-BLF), is developed to deal with the stabilization problem of switched systems and to cope with constraints imposed on system output with or without. Then, combining adding a power integrator technique (APIT) and the developed common barrier Lyapunov function, state-feedback stabilizing laws are designed systematically to make the resultant closed-loop switched systems asymptotically stable while preventing the violation of output constraints. The efficiency of the proposed method is illustrated by numerical results.

This study explores the issue of adaptive stabilization for a class of high-order uncertain nonlinear systems with asymmetric output constraint and zero dynamics. By combining skillful Barrier Lyapunov Function (BLF) with the technique of continuous feedback domination equipped with a group of integral functions including nested sign functions, a continuous state feedback stabilizer is established, which guarantees that the closed-loop system’s states converge to zero asymptotically while keeping the asymmetric output restriction inviolate. Superior to the existing methods, the developed strategy can not only simultaneously cope with the output asymmetric constraints and dynamic uncertainties, but also unifies the the construction and theory analysis for the limited and unlimited output. At last, a numerical simulation is offered to verify the efficiency of the developed method.

Finite-time state feedback stabilization of strict-feedback switched systems with asymmetric output-constraints

This paper investigates the adaptive state-feedback stabilisation for a class of output-constrained high-order nonlinear systems with integral input-to-state stability (iISS) inverse dynamics. The presence of weaker iISS inverse dynamics and parametric uncertainty makes the output-constrained systems in question essentially different from those in the related works. By integrating the tan-type barrier Lyapunov function, sign function and integral Lyapunov functions into the adding a power integrator technique, and choosing the appropriate designed functions and parameter update laws, a unified adaptive state-feedback controller, which can deal with both constrained and unconstrained systems, is constructed. It is proved that all the closed-loop signals are bounded, the symmetric output constraint is not violated, and system states converge to zero asymptotically. Finally, a simulation example is given to illustrate the effectiveness of this control scheme.