Output Feedback Stabilization Research Articles

Novel Results on Output-Feedback LQR Design

This paper provides novel developments in output-feedback stabilization for linear time-invariant systems within the linear quadratic regulator (LQR) framework. First, we derive the necessary and sufficient conditions for output-feedback stabilizability in connection with the LQR framework. Then, we propose a novel iterative Newton's method for output-feedback LQR design and a computationally efficient modified approach that requires solving only a Lyapunov equation at each iteration step. We show that the proposed modified approach guarantees convergence from a stabilizing state-feedback to a stabilizing output-feedback solution and succeeds in solving high dimensional problems where other, state-of-the-art methods, fail. Finally, numerical examples illustrate the effectiveness of the proposed methods.

Global Output-Feedback Stabilization for Uncertain Feedforward Nonlinear Systems via Dynamic Event-Triggered Control

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.

Output feedback stabilization for a class of nonlinear systems with hysteresis input and sensor uncertainties

Output feedback stabilization for a class of nonlinear systems with hysteresis input and sensor uncertainties

Boundary output feedback stabilization of state delayed reaction–diffusion PDEs

This paper addresses the problem of output feedback stabilization of a class of 1-D reaction–diffusion PDEs in the presence of a state delay in the reaction term. The control input applies through a Robin boundary condition. The system output is selected as either a Dirichlet or Neumann boundary trace. The developed control design procedure does not aim to compensate, but rather to dominate the state delayed term. This is achieved by introducing an observer that only estimates a finite number of modes of the PDE while applying a suitable pole shifting-based procedure on a truncated model that captures the unstable part of the plant. We show that the reported output feedback control strategy always achieves, for an arbitrarily given value of the state delay, the exponential stabilization of the plant in H1-norm. A notable feature of the domination-based approach is that the tuning of the controller and observer gains, as well as the subsequent stability conditions, appears to be independent of the value of the state delay.

A numerical method for ℋ2$$ {\mathscr{H}}_2 $$ control of linear delay systems

SummaryThis paper is concerned with the output feedback stabilization of linear delay systems with exogenous disturbances. Based on the norm, an optimization problem is formulated for the suppression of exogenous disturbances in the linear delay systems. The effectiveness of the presented approach is demonstrated via several numerical examples.

Boundary state and output feedback stabilisation of a coupled time fractional hyperbolic equation

In this paper, the boundary stabilisation of a coupled time fractional hyperbolic equation system is investigated by both state and output feedback. A target system is first introduced, which, by the semigroup method and the Lyapunov one, is proved to admit a unique solution and is Mittag–Leffler stable. A boundary state feedback controller and state observer are designed via the backstepping technique, with explicit formulae for the gain functions. An observer-based output feedback stabilising controller is then proposed for the controlled system. Some rigorous theoretical proofs are given to demonstrate that the resulting closed-loop system under the state and output feedback controllers has a unique solution and is Mittag–Leffler stable. Some numerical simulations are performed to validate the effectiveness of the proposed control approach.

Stabilization for a class of strict-feedback nonlinear systems via the PWM control law

This paper studies the PWM control problem of a class of nonlinear systems. During a modulation period, the PWM control signal maintains a pulse waveform with tunable width and fixed magnitude. The PWM control only possesses finite states, and has relatively limited control capability. This causes the degradation of system performance, and even the instability when implementing into a nonlinear system. We will introduce a novel method to design both the state feedback stabilizer and the output feedback stabilizer for strict-feedback nonlinear systems via the PWM control. The system performance is analyzed in a novel framework and the stability criteria is derived to ensure the system convergence. At last, two examples are considered to illustrate the effectiveness of our proposed method.

Boundary Output Feedback for Fixed-time Stabilization of Distributed Parameter Systems With Time and Space Dependent Reactivity

Boundary Output Feedback for Fixed-time Stabilization of Distributed Parameter Systems With Time and Space Dependent Reactivity

LMI conditions for contraction, integral action, and output feedback stabilization for a class of nonlinear systems

This article focuses on the class of linear systems coupled with a nonlinearity satisfying a sector bound or a monotonic condition. First, we present a set of sufficient conditions based on Linear Matrix Inequalities (LMIs) to establish if such a system defines a contraction. Then, we propose a contractive state-feedback control law designed via the use of LMIs which may include nonlinear terms. Furthermore, the design is extended to the case in which an integral action is included in order to achieve constant output regulation. Following a similar approach, the design of contractive observers for the aforementioned class of systems is also considered. Finally, based on previous conditions, we establish a new nonlinear separation principle in which the feedback and the observer gains may be designed independently. Throughout the paper, we illustrate our results by means of practical examples.

Practical Finite-Time Sampled-Data Output Feedback Stabilization for a Class of Upper-Triangular Nonlinear Systems With Input Delay

Practical Finite-Time Sampled-Data Output Feedback Stabilization for a Class of Upper-Triangular Nonlinear Systems With Input Delay

Output Feedback Stabilization of Non-uniformly Observable Systems

Output Feedback Stabilization of Non-uniformly Observable Systems

Adaptive event-triggered output-feedback stabilisation with double-side communication reduced for nonlinear systems with non-parametric uncertainties

This paper aims at adaptive event-triggered output-feedback stabilisation in the presence of intractable non-parametric uncertainties. Typically, double-side (i.e. sensor-to-controller and controller-to-actuator) event-triggered communication is pursued for efficient resource utilisation, unlike in related works only reducing single-side communication. This renders more constrained information transmitted via network, challenging the co-design of the compensation and event-triggering mechanisms. By incorporating a switching-varying mechanism, a distinctive adaptive event-triggered output-feedback scheme is established based on a switching filter reconstructing the unmeasurable states. Crucially, a convergence-preserving event-triggering mechanism is proposed with the adaptiveness for uncertainty compensation, by suitably exploiting the switching-varying gain. As such, a desired event-triggered output-feedback control is designed with linearity (with respect to the system output and the filter states) rendered for the controller signal. Just owing to the linearity, the controller signal is subtly kept from entering the event-triggering mechanism, so as to match the double-side event-triggered architecture. Furthermore, it is achieved that the system and filter states converge to zero while a positive minimum inter-execution time is ensured.

Global Output Feedback Stabilization for Stochastic Nonlinear Systems with Multiple Uncertainties

Global Output Feedback Stabilization for Stochastic Nonlinear Systems with Multiple Uncertainties

On Sontag’s formula for the sampled-data observer-based stabilization of nonlinear time-delay systems

In this paper, a new methodology for the design of sampled-data dynamic output feedback (DOF) stabilizers for control-affine nonlinear time-delay systems is proposed. In particular, the methodology here developed is based on the Artstein’s theory of control Lyapunov functions and related Sontag’s formula, here extended, for the first time in the literature, to the case of DOF controllers. Firstly, the new notion of Steepest Descent Error Dynamics (SDED) is introduced and used to suitably re-formulate the well-known Sontag’s universal formula for the case of DOF controllers. Then, it is shown that, under suitably fast sampling, a proposed sampled-data DOF controller based on the new provided version of Sontag’s universal formula ensures the semiglobal practical stability of the related sampled-data closed-loop system. Time-varying sampling intervals, as well as the intersampling system behavior, are taken into account. In the theory here developed, the case of delay-free systems is addressed as a special case. Applications are presented for the validation of the proposed theoretical results.

Autonomous Output Feedback Stabilization With Prescribed Settling-Time Bound

Novel output feedback stabilization is developed for a chain of integrators to impose on the closed-loop system an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> given settling-time bound regardless of the initial state. The intended design is deduced from fixed-time stabilization using a proportional time–space scaling. The resulting nonsmooth feedback relies on time-independent gains thereby admitting its straightforward implementation as opposed to the original design (Song et al., 2017) with time-varying gains, escaping to infinity as time goes to the prescribed-time instant. The proposed observer-based output feedback design with constant gains and with prescribed convergence rate constitutes the main contribution of this article.

Finite‐time sampled‐data output feedback stabilization for a class of feed‐forward non‐holonomic systems

AbstractThis article considers a finite‐time sampled‐data output feedback stabilization problem for a class of feed‐forward non‐holonomic systems. Due to that the states of the focused system are unavailable, a reduced‐order observer is designed to estimate the unavailable states with the sampled output detection of the non‐holonomic system, and two finite‐time sampled‐data stabilizers are respectively constructed by combining the backstepping and adding a power integral techniques. Based on the stepped and switching control strategies, the corresponding closed‐loop system can be globally finite‐time stable by the constructed stabilizers with allowable design constants and sampling period, and this can be proved by choosing an appropriate Lyapunov function candidate. In the end, two simulation examples, which include a numerical and a practical examples, are provided to verify the effectiveness of the proposed finite‐time stabilization method.

Anti-disturbance control for a nonlinear flexible beam with velocity disturbance at the boundary

This paper deals with the output feedback stabilization for a nonlinear flexible beam system with a general disturbance at the boundary. An extended state observer is designed to reject the uncertain disturbance estimated by a relatively independent estimator in the feedback loop via the active disturbance rejection control approach. The existence and uniqueness of the solution to the closed-loop beam system are investigated by means of the Galerkin approximation. The asymptotic stability of the closed-loop beam system is shown by utilizing the energy perturbation method. To demonstrate the control performance, numerical simulations are provided by the finite element method.

Predictor-Based Global Sampled-Data Output Feedback Stabilization for Nonlinear Uncertain Systems Subject to Delayed Output

In this article, we address the problem of global sampled-data output feedback stabilization for a class of nonlinear uncertain systems with delayed output using the continuous-discrete method. Thanks to the prediction technique and feedback domination method, a novel coupled design method of predictor-based continuous-discrete observer and linear controller is proposed when only delayed sampled-data output is accessible. The proposed predictor-based observer can effectively estimate the unknown state by compensating the influences of sampling and output delay. The main advantage of the proposed control method is that the full state information and accurate model nonlinearities do not need to be known any more. The global exponential stability of the overall hybrid control system can be ensured when there hold some sufficient conditions with respect to the maximum allowable sampling period and output delay.

Event-Triggered Output-Feedback Stabilization With Prescribed Convergence Rate

This article addresses event-triggered output-feedback stabilization with a prescribed convergence rate for uncertain nonlinear systems. Typically, the systems allow completely unknown nonlinearities, from which no any information is available for feedback. Nevertheless, an enhanced stabilization objective is pursued in this article to guarantee not only convergence, but particularly prescribed convergence rate. To this end, a distinct event-triggered output-feedback scheme is developed by integrating a powerful compensation technique with the event-triggering mechanism. Specifically, a set of delicate gains, motivated by the funnel control method, are introduced not only to handle the completely unknown nonlinearities and the execution error, but also to guarantee a prescribed rate. Particularly, a new event-triggering mechanism is given, where the threshold and suspension time are online adjusted with respect to the gains. As such, the threshold and suspension time could become adequately small as the gains increase, ensuring timely execution for the effectiveness of the compensation technique. It turns out that the designed event-triggered output-feedback controller guarantees the system states to globally converge to zero with the prescribed convergence rate.

Output Feedback Stabilization for an ODE Coupled with a Wave Equation with Variable Coefficients

Output Feedback Stabilization for an ODE Coupled with a Wave Equation with Variable Coefficients