Output Feedback Stabilization Research Articles

A new adaptive output-feedback controller against unknown control directions and intrinsic growth

ABSTRACT This paper addresses global output-feedback stabilisation in the context of unknown control directions and intrinsic unmeasurable-states-dependent growth, and focuses on rectifying the substantial deficiencies in the related works and developing a new adaptive output-feedback controller essentially reducing conservativeness. First, a varying parameter which takes value 1 or , instead of in an unbounded countable set, is specialised to capture the unknown control direction and accordingly a supervisory mechanism is delicately constructed to decide when to switch the parameter from 1 to or from to 1. A dynamic high gain, rather than a switching one, is appointed to compensate the serious system uncertainties. Then, the wanted controller is constructed, for which the design functions and design parameters are recursively generated by backstepping method (instead of analytically defined owing to the unknown control coefficients). Based on the designations and supervisory mechanism, it turns out that no Zeno phenomenon occurs, and global boundedness and convergence (to zero) hold, both for the resulting closed-loop system. An example is given to show the effectiveness and the advantage of the proposed scheme.

Robust H∞$H_\infty$ dynamic output feedback control of the DC–AC converter with a neutral leg

This paper investigates the problem of robust H ∞ $H_\infty$ dynamic output feedback control of 3-phase 4-wire converter with neutral bridge arm in the application of smart grid and distributed generation. Based on Lyapunov functions, a novel sufficient Linear Matrix Inequality condition analysis was performed on the dynamic output feedback stabilisation controllers. Meanwhile, some auxiliary slack variables with special structure and well-established performance conditions are employed to reduce design conservatism. This topology along with the H ∞ $H_\infty$ controller can solve the DC link balancing problem and maintain the deviation between the neutral point and the midpoint of DC supply very small. The achievable performance is analysed quantitatively and the controller design method was conducted and verified both in MATLAB simulation and the real-time simulation platform built by StarSim and MT, respectively.

Local output feedback stabilization of reaction–diffusion PDEs with saturated measurement

AbstractThis paper addresses the topic of output feedback stabilization of general one-dimensional reaction–diffusion partial differential equations (PDEs) in the presence of a saturation in the measurement. The boundary control and the second boundary condition take the form of Dirichlet/Neumann/Robin boundary conditions. The measurement is selected as a boundary Dirichlet trace. The boundary measurement, as available for feedback control, is assumed to be subject to a saturation. In this context, we achieve the local exponential stabilization of the reaction–diffusion PDE while estimating a subset of the domain of attraction of the origin.

Sampled‐data output feedback stabilization for a class of upper‐triangular nonlinear systems with input delay

AbstractThis article focuses on the sampled‐data output feedback stabilization for a class of upper‐triangular nonlinear systems with input delay and ‐normal structure, a reduced‐order observer with the detected sampled output measurement is constructed to evaluate the unavailable states of the considered system, and the backstepping method with adding a power integral technique are adopted to construct the sampled‐data output feedback stabilizer. By selecting a suitable Lyapunov–Krasovskii functional, we can demonstrate that the adverse effects caused by the uncertain input delay can be effectively constrained, and the resulting closed‐loop system with appropriate design constants and allowable sampling period can reach globally stable. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed control method.

Fixed‐time output feedback stabilization of a class of high‐order planar nonlinear systems

AbstractIn this article, the fixed‐time output feedback stabilization of a class of high‐order planar nonlinear systems is addressed. A fixed‐time output feedback controller is originally designed by using the bi‐limit homogeneous method and integrating with an auxiliary filter to estimate the unmeasured state. The local fixed‐time stability of the resulting closed‐loop system is theoretically proved. Moreover, the proposed controller is structurally simple and has the strong robustness against uncertainties, which makes it affordable for practical applications. Finally, numerical simulations are presented to verify the effectiveness and advantages of the proposed controller.

Nearest neighbor control for practical stabilization of passive nonlinear systems

This paper studies static output feedback stabilization of continuous-time (incrementally) passive nonlinear systems where the control actions can only be chosen from a discrete (and possibly finite) set of points. For this purpose, we are working under the assumption that the system under consideration is large-time norm observable and the convex hull of the realizable control actions contains the target constant input (which corresponds to the equilibrium point) in its interior. We propose a nearest-neighbor based static feedback mapping from the output space to the finite set of control actions, that is able to practically stabilize the closed-loop systems. Consequently, we show that for such systems with m-dimensional input space, it is sufficient to have m+1 discrete input points (other than zero for general passive systems or the target constant input for constant-incrementally passive systems). Furthermore, we present a constructive algorithm to design such m+1 nonzero input points that satisfy the conditions for practical stability using our proposed nearest-neighbor control.

Compensator-Based Output Feedback Stabilizers for a Class of Planar Systems With Unknown Structures and Measurements

This article considers the problem of output feedback stabilization for a class of nonlinear planar systems with unknown structures and measurements, which prevent the construction of conventional state observers. By taking advantage of the stability-increasing capability of a lead compensator, we propose a dynamic output feedback controller to globally stabilize the uncertain planar systems. For the special case of linear planar systems with unknown coefficients, a finite-time output feedback stabilizer based on a nonlinear compensator is constructed for a faster convergence rate.

Output Feedback Stabilization of Unstable Heat Equations with Time Delay in Boundary Observation

In this paper, an unstable heat equation where the observation signal suffers from a given time delay has been considered. In order to remove the unstable boundary condition, the original system has been converted into the stabilizing system by backstepping transformation under which the form of the stabilizing controller can be obtained. For the sake of overcoming instability produced by the time delay, firstly, we construct the Luenberger observer and design the predictor. Then, the estimated output feedback controllers have been obtained based on the observer and predictor systems. It is shown that the closed-loop system is stable exponentially. At last, numerical simulations have been given to illustrate the effectiveness of the stabilizing output feedback controllers.

A Model-Free Output Feedback Control Approach for the Stabilization of Underactuated TORA System with Input Saturation

The horizontal translational oscillator with a rotational actuator (TORA) is a typical underactuated mechanical system, whose control problem is still open and theoretically challenging. At present, the existing control methods are structurally complicated and require an exact knowledge of the system parameters. Moreover, few works have considered the output feedback stabilization of the TORA system subject to practical constraints of input saturation and angular velocity unmeasurement. To address these problems, this paper proposes a novel model-free amplitude-limited control approach to stabilize the TORA system at the origin using only angle feedback. Firstly, the passivity of the horizontal TORA system is analyzed, based on which a novel Lyapunov function augmented with an auxiliary signal is constructed by taking the input saturation into account. Then, an amplitude-limited control law is derived in a straightforward manner. In order to make the control law independent of velocity feedback, the auxiliary signal is designed in terms of the ball rotational angle and an output of a dynamic system. The asymptotic stability of the entire control system is rigorously guaranteed by utilizing Lyapunov theory and LaSalle’s invariance principle. Finally, simulation results with comparisons to existing methods demonstrate the effectiveness and superiority of the proposed control approach.

LMI-based consensus of linear multi-agent systems by reduced-order dynamic output feedback

This work proposes new conditions for consensus of homogeneous multi-agent systems subjected to exogenous disturbances in directed communication graphs by dynamic output feedback protocols. The agents under investigation are described as linear dynamics, and the communication network is such that each agent receives as information only the output of neighbor agents. The synchronization problem is rewritten as an output feedback stabilization without requiring the Laplacian matrix to be diagonalizable. As the main appeal, we propose new necessary and sufficient conditions for the design of dynamic output feedback controllers of arbitrary order – including static output feedback as a particular case – and sufficient Linear Matrix Inequalities (LMIs) for H∞ consensus. Numerical experiments illustrate the effectiveness of the proposed approach.

Global adaptive stabilization via asynchronous event-triggered output-feedback

This paper aims to establish a novel adaptive event-triggered scheme of global output-feedback stabilization for nonlinear systems with unmeasurable state dependent growth under the architecture with network communication among sensor, observer-based controller and actuator. To suppress the inherent system nonlinearities (reflected by the polynomial-of-output growth rate), a dynamic gain is integrated into event-triggered scheme. While reducing execution as much as possible to maintain efficiency, it is critical to ensure timely information transmission and control updating for the effectiveness of adaptive mechanism. To this end, double-side asynchronous adaptive event-triggering mechanisms, instead of a one-side or (double-side) synchronous one, are delicately designed by fully exploiting the dynamic gain, upon which adaptive event-triggered output-feedback control is established to ensure the system states to converge to zero. Particularly, the time of evaluation suspension and the threshold parameter for the events on system output and observer states are not fixed but rather online adjusted with the alteration of dynamic gain, to make sure to counteract the influence of sampling/actuation error. Unlike the related results, the adaptive event-triggering mechanisms render the inter-execution times determined purely according to system behavior and without explicit upper-bound limit, which retain the desired potential in execution reducing.

Output Feedback Stabilization for a Wave-ODE Cascade System with the Time-Varying Input and Output Delay

Output Feedback Stabilization for a Wave-ODE Cascade System with the Time-Varying Input and Output Delay

Output feedback stabilization of Euler–Bernoulli beam equation with general corrupted boundary observation

This paper aims to study the stabilization problem for a Euler–Bernoulli beam equation with boundary observation subject to a general external disturbance. A new infinite dimensional estimator is designed to estimate the disturbance in the corrupted boundary angular velocity signal in real time. Furthermore, a boundary output feedback control is constructed to stabilize the related system. By using the Riesz basis approach, it is proven that, in case the initial conditions satisfy certain smoothness, the closed-loop system is exponentially stable and all internal signals are bounded. Finally, a numerical example is given to show the validity of our theoretical results.

Robust dynamic output feedback stabilization for uncertain singular Markovian jump systems with time‐varying delays

AbstractThe article investigates robust dynamic output feedback (DOF) stabilization for uncertain time‐varying delays singular Markovian jump systems (SMJSs). First, by using improved Lyapunov–Krasovskii functional, sufficient conditions of robust admissibility (namely regularity, non‐impulsiveness, and asymptotic stability) for unforced nominal time‐varying delays SMJSs are given. Second, by constructing a DOF controller such that the resulting closed‐loop system satisfies robust admissibility, the robust DOF stabilization problem is solved in terms of linear matrix inequalities via orthogonal complement technique. Finally, the availability and practicality of the prime results are certified by two numerical examples and a practical example of the oil catalytic cracking process.

Output Feedback Stabilization for a 1-D Conservative Wave Equation with General Corrupted Boundary Observation

In this paper, we consider the output feedback stabilization of a 1-D conservative wave equation, where the boundary velocity observation is subjected to a general disturbance. We first consider using only the output of the system to online estimate the disturbance by active disturbance rejection control (ADRC). The observer is designed in terms of the disturbance estimator. Then we present an observer-based output feedback law to achieve stabilization. The estimated disturbance is proved to be convergent to the unknown disturbance and the velocity signal can be asymptotically recovered when time tends to infinity. At the same time, the asymptotic stability of the closed-loop system can be verified. Finally, some simulations are given to illustrate the theoretical conclusions.

An LMI Approach for Stability Analysis and Output-Feedback Stabilization of Discrete-Time Lur’e Systems Using Zames-Falb Multipliers

This letter investigates the problem of stability analysis and output-feedback stabilization of discrete-time Lur'e systems where the nonlinearity is odd and slope bounded. Using the linear matrix inequality (LMI) conditions from the literature to handle the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm and positive realness constraints, an iterative algorithm based on LMIs is constructed to assess stability through the existence of a Zames-Falb multiplier of any given order based on independent positive definite matrices for the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm and positive realness. More important, the method can also deal with output-feedback stabilization. Numerical examples illustrate the performance of the proposed approach when compared with other methods.

Local output feedback stabilization of reaction-diffusion PDEs with saturated measurement

Local output feedback stabilization of reaction-diffusion PDEs with saturated measurement

Output Feedback Stabilization for a Class of Uncertain High-Order Nonlinear Systems

We investigate output feedback stabilization for a class of high-order nonlinear systems whose output function and nonlinear terms are unknown. First, a smooth state feedback control law is designed by adding a power integrator technique. Next, we design a high-order observer to estimate the unmeasurable state, and allocate gains of the observer one by one in an iterative way. Finally, a dynamic output compensator is achieved such that the closed-loop system converges to the equilibrium point quick. Two examples are provided to demonstrate the effectiveness of the proposed method.

A new robust output feedback control for a class of uncertain nonlinear systems

This paper presents studies on a robust adaptive output feedback stabilisation for a class of nonlinear systems, which is subjected to parametric uncertainties and disturbances. The disturbances are considered to be general, i.e. both the matched and unmatched ones are present. A novel robust adaptive control is developed for this problem. A technique is employed to avoid the difficulty in handling the nonlinear gain functions associated with the disturbances. For this, a new Lemma is obtained to handle the nonlinear functions that simplify the controller derivation steps. The unknown parameters and disturbances are tackled by deriving the tuning functions using a backstepping design. Finally, simulation is carried out to validate and show the effectiveness of the proposed robust controller.

Finite-Time Output Feedback Stabilization for a Class of Output-Constrained Planar Switched Systems

This note investigates a unified finite-time output feedback control strategy for a class of planar switched systems with an asymmetric output constraint. A fraction-type asymmetric barrier Lyapunov function (BLF) is constructed firstly. Based on relaxed assumptions on system nonlinearities together with the developed BLF, a set of finite-time state feedback controllers are designed systematically by revamping the technique of adding a power integrator. By incorporating the state controllers with switched reduced-order observers developed delicately, the task of finite-time stabilization for planar switched systems can be realized by the resultant output feedback controllers in consideration of asymmetric output constraints imposed on switched systems simultaneously. The proposed method enjoys the unification property such that it is workable for the scenarios of constrained and unconstrained cases, without the need of changing/redesigning the structures of controllers and observers. Finally, simulation results are presented to verify the proposed scheme.