Global Practical Stability Research Articles

H∞ Adaptive tracking control for switched systems based on an average dwell-time method

This paper investigates the H∞ state tracking model reference adaptive control (MRAC) problem for a class of switched systems using an average dwell-time method. First, a stability criterion is established for a switched reference model. Then, an adaptive controller is designed and the state tracking control problem is converted into the stability analysis. The global practical stability of the error switched system can be guaranteed under a class of switching signals characterised by an average dwell time. Consequently, sufficient conditions for the solvability of the H∞ state tracking MRAC problem are derived. An example of highly manoeuvrable aircraft technology vehicle is given to demonstrate the feasibility and effectiveness of the proposed design method.

Switching‐based state tracking of model reference adaptive control systems in the presence of intermittent failures of all actuators

SUMMARYThis paper investigates the state tracking problem for a class of model reference adaptive control systems with intermittent failures of all actuators. We consider the case that all actuators may suffer failures simultaneously. The concepts of failure frequency and unavailability rate are introduced to describe the failures. Because of the actuator failures, the error system is modeled as a switched system. Then, the notion of global practical stability of switched systems is presented, and sufficient conditions are provided to guarantee the global practical stability of the error system. An example of HiMAT vehicle and the simulation results demonstrate the feasibility and effectiveness of the proposed design method. Copyright © 2013 John Wiley & Sons, Ltd.

Global exact tracking for uncertain MIMO linear systems by output feedback sliding mode control

This paper presents a solution to the problem of global exact output tracking for uncertain MIMO (multiple-input–multiple-output) linear plants with non-uniform arbitrary relative degree using output feedback sliding mode control. The key idea to overcome the relative degree obstacle is to generalize our previous hybrid estimation scheme to a multivariable version by combining, through switching, a standard linear lead filter with a non-linear one based on robust exact differentiators, achieving uniform global exponential practical stability and exact tracking.

Global Practical Stabilization for Non-holonomic Mobile Robots with Uncalibrated Visual Parameters by Using a Switching Controller

Global Practical Stabilization for Non-holonomic Mobile Robots with Uncalibrated Visual Parameters by Using a Switching Controller

State Tracking of MRAC Systems in the Presence of Controller Temporary Failure Based on a Switching Method

The state tracking problem for a class of model reference adaptive control (MRAC) systems in the presence of controller temporary failures is studied. Due to the controller temporary failure, the considered system is viewed as an error switched system. The properties of Lyapunov function candidates without switching are described. Then the notion of global practical stability of switched systems is presented, and sufficient conditions for global practical stability of the error system under the restrictions of controller failure frequency and unavailability rate are provided. An example is presented to demonstrate the feasibility and effectiveness of the proposed method.

On the Robust Practical Global Stability of Nonlinear Time-varying Systems

The goal of this paper is twofold. The first part presents a Lyapunov statement and proof of the concept of robust global practical exponential stability (RpGES) for nonlinear time varying systems. A RpGES-Lyapunov function for the overall system is exhibited. Its proof is a consequence of some results on converse Lyapunov theorems obtained by Tsinias in 19. The second part provides sufficient conditions for the robust practical globally uniformly asymptotically stability (RpGUAS).

The Practical Stabilization for a Class of Networked Systems with Actuator Saturation and Input Additive Disturbances

The practical stabilization problem is investigated for a class of linear systems with actuator saturation and input additive disturbances. Firstly, the case of the input additive disturbance being a bounded constant and a variety of different situations of system matrices are studied for the three‐dimensional linear system with actuator saturation, respectively. By applying the Riccati equation approach and designing the linear state feedback control law, sufficient conditions are established to guarantee the semiglobal practical stabilization or oscillation for the addressed system. Secondly, for the case of the input additive disturbances being time‐varying functions, a more general class of systems with actuator saturation is investigated. By employing the Riccati equation approach, a low‐and‐high‐gain linear state feedback control law is designed to guarantee the global or semiglobal practical stabilization for the closed‐loop systems.

Global Exact Tracking for Uncertain Multivariable Systems by Switching Adaptation

AbstractIn this paper, we propose an output feedback sliding mode controller to solve the problem of global exact output tracking for uncertain multivariable linear plants with non-uniform arbitrary relative degree. The controller is based on a hybrid estimation scheme, which adapts the relative degree compensation through switching between a high-gain observer and a set of locally exact differentiators. As a result, uniform global exponential practical stability and exact tracking are achieved with peaking free control signal.

A Lie Bracket Approximation for Extremum Seeking Vehicles

AbstractIn this paper we propose a novel methodology for the analysis of autonomous vehicles seeking the extremum of an arbitrary smooth nonlinear map in the plane. By interpreting the extremum seeking schemes as input-affine systems with periodic excitations and by using the methodology of Lie brackets, we calculate a simplified system which approximates the qualitative behavior of the original one better than existing methods. By examining this approximate Lie bracket system, we are able to directly derive properties of the original one. Thus, by showing that the Lie bracket direction is directly related to the unknown gradient of the objective function we prove global uniform practical asymptotic stability of the extremum point for vehicles modeled as single integrators and non-holonomic unicycles. We illustrate the proposed method through simulations.

Practical Uniform Stability of Nonlinear Differential Delay Equations

In this paper, we investigate the problem of global uniform practical exponential stability of a general nonlinear non autonomous differential delay equations. Using the global uniform practical exponential stability of the corresponding differential equation without delay, we show that the differential delay equation will remain globally uniformly practically exponentially stable provided that the time-lag is small enough. Finally, some illustrative examples are given to demonstrate the validity of the results.

Controle por realimentação de saída para sistemas incertos fortemente não-lineares

Um controlador livre de peaking baseado em modos deslizantes e realimentação de saída é introduzido para o rastreamento de uma classe de sistemas não-lineares incerta utilizando observadores de alto ganho e o conceito de tempo de espera na ativação do sinal de controle. Estabilidade exponencial global (semi-global) e bom comportamento transitório são obtidos. Um esquema de monitoração é também proposto para lidar com o fenômeno de peaking do HGO induzido por perturbações de saída.

Global Exact Tracking for Uncertain Systems Using Output-Feedback Sliding Mode Control

This note presents a solution to the problem of global exact output tracking for uncertain linear plants with arbitrary relative degree using output-feedback sliding mode control. The key idea to overcome the relative degree obstacle is to introduce a hybrid compensator by combining, through switching, a standard lead filter with a robust exact differentiator, based on higher-order sliding modes, achieving uniform global exponential practical stability and asymptotic exact tracking.

On the Practical Output Feedback Stabilization for Nonlinear Uncertain Systems

In this paper, we treat the problem of output feedback stabilization of nonlinear uncertain systems. We propose an output feedback controller that guarantees global uniform practical stability of the closed loop system.

Practical Stability of Nonlinear Time-Varying Cascade Systems

In this paper, we investigate the practical stability problem of nonlinear time-varying cascade systems. We give some sufficient conditions that guarantee practical global uniform asymptotic stability and practical global uniform exponential stability of such dynamical systems.

Practical Stabilization of a Quantum Particle in a One-Dimensional Infinite Square Potential Well

We consider a nonrelativistic charged particle in a one-dimensional infinite square potential well. This quantum system is subjected to a control, which is a uniform (in space) time-depending electric field. It is represented by a complex probability amplitude solution of a Schrödinger equation on a one-dimensional bounded domain, with Dirichlet boundary conditions. We prove the almost global practical stabilization of the eigenstates by explicit feedback laws.

Global Practical Stabilization of Planar Linear Systems in the Presence of Actuator Saturation and Input Additive Disturbance

In this note, we revisit the problem of global practical stabilization for planar linear systems subject to actuator saturation and input additive disturbances. A parameterized linear state feedback law is designed such that, by tuning the value of the parameter, all trajectories of the closed-loop system converge to an arbitrarily small neighborhood of the origin in a finite time and remain in there.

Uniform Global Practical Asymptotic Stability for Time-varying Cascaded Systems*

This paper aims to give sufficient conditions for a cascade composed of nonlinear time-varying systems that are uniformly globally practically asymptotically stable (UGPAS) to be UGPAS. These conditions are expressed as relations between the Lyapunov function of the driven subsystem and the interconnection term. Our results generalise previous theorems that establish the uniform global asymptotic stability of cascades and its application is illustrated by characterising the effect of smoothing control laws in disturbance rejection.

A scaled feedback stabilization of power integrator triangular systems

Using unbounded time-varying scaling of the states we design C 1 feedback laws for power integrator triangular systems which globally asymptotically stabilize (GAS) the origin despite the uncontrollability of the linearization. With bounded scaling the feedback laws achieve global practical stability (GPS). For a trade-off between GAS/GPS of the origin and unboundedness/boundedness of the scaling we construct a dynamic version of these feedback laws.

Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems

Motivated by control Lyapunov functions and Razumikhin theorems on stability of time delay systems, we introduce the concept of control Lyapunov-Razumikhin functions (CLRF). The main reason for considering CLRFs is construction of robust stabilizing control laws for time delay systems. Most existing universal formulas that apply to CLFs, are not applicable to CLRFs. It turns out that the domination redesign control law applies, achieving global practical stability and, under an additional assumption, global asymptotic stability. This additional assumption is satisfied in the practically important case when the quadratic part of a CLRF is itself a CLRF for the Jacobian linearization of the system. The CLRF based domination redesign possesses robustness to input unmodeled dynamics including an infinite gain margin. While, in general, construction of CLRFs is an open problem, we show that for several classes of time delay systems a CLRF can be constructed in a systematic way.

Global Practical Stabilization and Tracking for an Underactuated Ship - A Combined Averaging and Backstepping Approach

Global Practical Stabilization and Tracking for an Underactuated Ship - A Combined Averaging and Backstepping Approach