Output Feedback Stabilization Research Articles

Dynamic output feedback stabilization for a class of nonsmooth stochastic nonlinear systems perturbed by multiple time-varying delays

Dynamic output feedback stabilization for a class of nonsmooth stochastic nonlinear systems perturbed by multiple time-varying delays

Robust fuzzy adaptive stabilization for uncertain nonlinear systems with quantized input and output constraints

In this paper, we study the problem of robust fuzzy adaptive output feedback stabilization for a class of nonlinear systems with quantized input and output constraints. The system under consideration has these characteristics: unknown state mismatch uncertainties and unknown disturbances, and unknown measurement noises. By employing the output filtering transformation, the fuzzy logic system (FLS) approximator, the backstepping, and the high gain observer technique, a non-fragile robust fuzzy adaptive observer and a hyperbolic tangent adaptive controller are presented to guarantee that the closed-loop system is ultimately uniformly bounded and the output is constricted in a prescribed performance curve. The effectiveness of the scheme is verified by numerical simulations.

Scaling technique for prescribed-time output feedback stabilization: Autonomous and non-autonomous paradigms and their comparative study

The present work is of both theoretical and tutorial value. Existing autonomous and non-autonomous paradigms are systematized for prescribed- and predefined-time controllers, and the scaling technique is revised for their analysis and synthesis. The fixed-time output feedback design is further developed in the paper under the paradigm with prescribed settling time upper bound. In the numerical study made for a closed-loop perturbed double integrator, pros and cons of the resulting algorithm are revealed and compared with those of prescribed/predefined-time output feedback. Thus, another contribution of the paper is in the exposition of the implementation feasibility for the different-type prescribed-time controllers.

The active disturbance rejection control approach to output feedback stabilization of an anti-stable wave equation with corrupted boundary observation

In this paper, we are concerned with the boundary output feedback stabilization for an anti-stable wave equation where the boundary observation is corrupted by a general disturbance. We cope with the disturbance by the approach of active disturbance rejection control. In contrast with the existing results, the assumptions on the derivative of the disturbance are removed. It is necessary to assume that the disturbance is Lipschitz continuous. A state observer together with a disturbance estimator is designed by using the corrupted output. Both the well-posedness and the stability of the closed-loop system are proved. The theoretical results are validated visually by some numerical simulations.

Robust state and output feedback stabilization for Lipschitz nonlinear systems in reciprocal state space: Design and real-time validation

In many engineering problems, modelling the state and output derivative variables in reciprocal state space form can be generated more easily than in standard state space one. The formulation of a robust [Formula: see text] control problem using feedback principle for continuous Lipschitz nonlinear systems with uncertainties in reciprocal state space is presented in this article. In contrast to the existing approaches, the considered model is affected by unknown disturbances, parameter uncertainties and derivative Lipschitz nonlinearities. The asymptotic stability based on the proper Lyapunov functions of the closed-loop system is guaranteed. The [Formula: see text] control design resolution problem is ensured through the linear matrix inequality technique, the lemmas and the use of new variables with S-procedure. The performance of the proposed approach is shown through the experimental results using real-time implementation with a digital signal processing device (DSpace DS 1104).

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

Output-feedback stabilization of n + m linear hyperbolic ODE-PDE-ODE systems

In this paper, we design an output-feedback controller to stabilize n + m hetero-directional transport partial differential equations (PDEs) coupled on both domain boundaries to ordinary differential equations (ODEs). This class of systems can represent, for instance, actuator and load dynamics at the boundaries of a hyperbolic system. The actuator is located at the connection point between the PDE and one of the ODEs, and we consider anti-collocated PDE measurements. We first design a state-observer by combining the backstepping methodology with time-delay system approaches. We then introduce a state feedback controller using analogous techniques before designing the wanted output-feedback control law.

Output-feedback stabilization of an underactuated network of interconnected hyperbolic PDE systems

Output-feedback stabilization of an underactuated network of interconnected hyperbolic PDE systems

Output-Feedback Stabilization of Stochastically-Sampled Networked Control Systems Under Packet Dropouts

Output-Feedback Stabilization of Stochastically-Sampled Networked Control Systems Under Packet Dropouts

Finite-time set stabilization of probabilistic Boolean control networks via output-feedback control

This paper investigates the finite-time output-feedback set stabilization problem for probabilistic Boolean control networks (PBCNs), a crucial aspect of set convergence. Firstly, an algorithm is presented to effectively identify the largest output-feedback control invariant subset in a given set. Next, a sufficient condition is put forward to bridge set stabilization and the question at hand via the minimum transient period. Additionally, sufficient and necessary criteria are proposed, addressing the solvability of finite-time output-feedback set stabilization, followed by two corresponding algorithms for effectively designing all feasible output-feedback stabilizers. Finally, a biological example is successfully explored to demonstrate our theoretical results.

New results on dynamic output state feedback stabilization of some class of time-varying nonlinear Caputo derivative systems

In modern control theory applications, input–output feedback often arises and plays a crucial role in stabilizing any target control systems. However, in many practical applications, the knowledge of full information on the state of systems may not be available in general due to measurements. In order to control such types of systems, this paper uses a universal concept of real order calculus to stabilize by the method of dynamic output feedback control. Is it possible to design a dynamic output feedback stabilization for time-varying real order control systems? This work develops a new dynamic output feedback control method and proposes linear homogeneous time-varying control law to stabilize incommensurate nonlinear time-varying real order systems under the action of Caputo derivative with an addendum of ultimate random initial-time. We utilize the ideas of the comparison method and establish order-dependent asymptotic results associated with uniform Lipschitz continuous functions that provide stabilization by means of the dynamic output state feedback control method. We provide three examples that include a practical system and show the importance of some theoretical results in the demonstration to stabilize the problems by means of proposed control method.

Output feedback and adaptive output feedback control design for input-affine nonlinear systems based on Riemannian metrics

This paper deals with output feedback and adaptive output feedback control design for input-affine nonlinear systems on the basis of Riemannian metrics. Firstly, an observer for the considered class of nonlinear systems is proposed. Then, it is shown that by combining the introduced observer with state-feedback controllers in a suitable way, output tracking can be achieved. Moreover, the obtained results are extended to be used for adaptive output feedback stabilization of uncertain nonlinear systems. The introduced adaptive controller is more general than the existing adaptive output feedback ones because it does not assume any constraint on the structure of the system and the parametric uncertainty. Simulation results are presented to verify the effectiveness of the proposed control methods.

Local Output Feedback Stabilization of a Nonlinear Kuramoto–Sivashinsky Equation

Local Output Feedback Stabilization of a Nonlinear Kuramoto–Sivashinsky Equation

Robust state estimation via twisting observer

In this paper, we propose the twisting observer for robustly estimating the states of a second-order uncertain system. It is well-known that the twisting algorithm achieves the second-order sliding mode condition using the sign information of both the plant states. When all the states are not available, the twisting algorithm cannot be extended to the estimation problem directly. Hence, our proposed observer approximates this unknown sign term for the non-measurable state in the twisting observer with a delayed output-based switching function. It is shown that under some suitable gain conditions, the observer can guarantee any arbitrary accuracy of estimation error for some appropriate delay parameter which can be varied online. The advantage of this observer is that one needs to control only the delay parameter to achieve the desired steady-state accuracy, unlike the additional nonlinear functions found in the existing observers. The application of this observer to output feedback stabilization is also discussed. The separation principle for the closed-loop system is shown by designing the gains of controller and observer independently. Finally, we illustrate the design and performance of the proposed state observation scheme through a numerical example.

Functional and dual observer based prescribed-time control of linear systems by periodic delayed feedback

In this paper the prescribed-time output feedback stabilization of linear systems is addressed using both a functional observer, which includes the reduced-order observer as a special case, and a dual observer. The approach is built upon smooth periodic delayed feedback which is a special case of linear periodic time-varying feedback. In contrast to existing periodic control approaches, the proposed feedback achieves prescribed-time convergence of the state to zero rather than asymptotic convergence. At the same time its synthesis requires solving algebraic equations rather than periodic differential equations. Compared with full-order observer based output feedback, the dimensions of the dynamic equations in the reduced-order observer and dual observer based output feedback are respectively n−p and n−m, where n,m and p are respectively the number of state variables, inputs and outputs, which indicates that the established controllers are less expensive than the full-order observer based controllers in implementations. A numerical example is given to verify the effectiveness of the proposed methods.

On a new method for the state and output feedback exponential stabilization of a cascaded wave PDE-ODE system with nonlinear boundary condition

Abstract This study presents a novel approach for the state and output feedback exponential control of cascaded unstable ODE-wave equations with nonlinear boundary condition. The new approach can be also used to investigate the state and output feedback stabilization of other cascaded ODE-partial differential equation (PDE) systems with nonlinear boundary condition. The interconnection between the ODE and wave PDE with the nonlinear boundary is bi-directional at two points. First, an exponential controller is planned and the well-posed and exponential stability of the closed-loop system is derived. Next, an exponential observer is designed, whereby the exponential stability of the overall error system is shown. Then, an observer-based output feedback control that causes the overall real system to be exponentially stable is built. The existence and exponential stability of the solution to the overall closed-loop system are further deduced. Finally, simulation results are given to verify the effectiveness, feasibility and validity of the proposed technique.

Output feedback stabilization for a wave–ODE cascaded system subject to uncertain disturbance

AbstractIn this paper, we consider output feedback stabilization for a wave–ODE cascaded system with uncertain disturbance flowing the control end. Firstly, a disturbance estimator is designed by the new active disturbance rejection control (ADRC) approach that we propose two auxiliary systems. Then, we design an observer for the coupled system based on the idea that copy of the original system plus injection of the output estimation error. Finally, by the backstepping method, we design an output feedback control and obtain the exponential stabilization of the closed‐loop system, which consists of the original coupled system, the observer, two new auxiliary systems, and the control. Due to the existence of the in‐domain anti‐damping in wave equation, the proposed two auxiliary systems are different from those in the previous literature. And their designs are inspired by the design idea of the observer. Some numerical simulations are given to illustrate the effectiveness of the control.

Global event-triggered output-feedback stabilization for switched nonlinear systems with time-delay and measurement sensitivity

In this paper, the problem of adaptive event-triggered output-feedback stabilization is addressed for a class of switched nonlinear systems with time-delay and output measurement sensitivity. With the assistance of the dynamic high gain technology and a novel event-triggered control mechanism, we overcome the design complexities arising from unknown polynomial growth rate with respect to the output, unknown large measurement sensitivity, unknown time-varying control coefficient and time-delay. Then, an effective constructive method is provided to design switched observers and a common event-triggered controller. Through introducing two key matrix inequalities and constructing a common Lyapunov-Krasovskii functional, sufficient conditions are given to get rid of Zeno behavior, and ensure that all the signals are bounded and the closed-loop system states converge to zero under arbitrary switchings. Two simulation studies are conducted for verifying the effectiveness of proposed scheme.

Output Feedback Stabilization of Doubly Fed Induction Generator Wind Turbines under Event-Triggered Implementations

The robust stabilization of doubly fed induction generators in wind turbines against external disturbances is considered in this study. It is assumed that the angular speeds of wind turbines can only be measured and sent to the controller in a discrete-time fashion over a network. To generate the sampling times, three different triggering schemes were developed: time-triggering, static event-triggering, and dynamic event-triggering mechanisms; moreover, performance comparisons were conducted between such approaches. The design methodology is based on emulation, such that the plant is first stabilized in continuous-time where a robust feedback law is constructed based on the linear quadratic Gaussian regulator (LQG) approach. Then, the impact of the network is taken into account, and an event-triggering mechanism is built so that closed-loop stability is maintained and the Zeno phenomenon is avoided by using temporal regularization. The necessary stability constraints are framed as a linear matrix inequality, and the whole system is modeled as a hybrid dynamical system. A numerical simulation is used to demonstrate the effectiveness of the control strategy. The results show that the event-triggering mechanisms achieve a significant reduction of around 50% in transmissions compared to periodic sampling. Moreover, numerical comparisons with existing approaches show that the proposed approach provides better performance in terms of the stability guarantee and number of transmissions.

Global output feedback control for uncertain strict-feedback nonlinear systems: A logic-based switching event-triggered approach

This paper addresses the global output-feedback stabilization for a class of uncertain nonlinear systems via a switching event-triggered approach. Typically, the system growth rates are allowed to be arbitrary unknown non-polynomial functions of system output. Note that such nonlinearities cannot be handled by generalizing the design rationales employed in polynomial rate cases. For this reason, an event-triggered mechanism together with a logic-based switching mechanism is proposed to determine not only when to sample but also when to switch the control parameter. With the help of the switching control parameter, an observer-based control scheme is developed to achieve global output-feedback stabilization. Particularly, the control parameter can be adaptively adjusted to a sufficiently large value, so the proposed control scheme has a stronger capability to deal with large uncertainties, inherent nonlinearities, and sampling errors of the system. For more efficient resource saving, an extended investigation is presented by constructing a dynamic event-triggered scheme. Finally, two simulation examples are given to illustrate the effectiveness of the switching event-triggered schemes.