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In this paper, a sliding mode control based on backstepping (BSMC) and feedback linearization (FLSMC) are proposed to solve disturbances, nonlinearity and chattering problems for a class of uncertain systems in strict feedback form. Based on backstepping technique, the proposed control strategy has fast response and good disturbance rejection capability. The stability analysis of the closed-loop system...
This paper presents a treatment of variable structure discrete systems. Firstly, in order to control nonlinear single-input single-output (SISO) systems, the first sliding mode controller using the classical surface is considered. Then, a robust discrete second order sliding mode controller is investigated to overcome the effect of the chattering phenomenon. The controllers designed using the above...
This paper present a combined field orientation and backstepping control. This method is an elegant approach for nonlinear super twisting sliding-mode control of an induction motor. The objective is to improve the speed control, the rotor flux control and the rejection of load torque disturbances and parameter variations. Simulation results are given to show the performance obtained with this kind...
This article is concerned with the problem of robust H∞ noise-attenuation for switched linear discrete-time systems with polytopic uncertainties based on homogeneous parameter dependent quadratic Lyapunov function. We give the condition of robustly asymptotically stable for uncertain switched system by homogeneous parameter dependent quadratic Lyapunov function. This method is more feasible and effective...
We present an approach to high-level control for bipedal walking exemplified with a 2D point-mass inextensible-legs inverted-pendulum model. Balance control authority here is only from step position and trailing-leg push-off, both of which are bounded to reflect actuator limits. The controller is defined implicitly as the solution of an optimization problem. The optimization robustly avoids falling...
A discontinuous control law exponentially stabilizing a simple nonholonomic system is discussed and analyzed in detail. Basic properties, such as existence and uniqueness of the closed loop system trajectories, and simple robustness issues are studied. Continuous modifications of the considered discontinuous control law are proposed and discussed in detail. The considered controller is representative...
Our objective in this paper is to extend as much as possible the dissipativity approach for the study of robustness of stability in the presence of known/unknown but ignored input dynamics. This leads us to: • give a new characterization of control Lyapunov functions (CLF) where LfV is upper-bounded by a function of LgV, • define the dissipativity approach as : — assuming the ignored dynamics are...
This paper deals with an inverse optimal Η∞, disturbance attenuation of the Euler Lagrange systems. The ISS control Lyapunov function is constructed by the energy function of full Lagrangian dynamics, i.e. the Euler-Lagrange systems are input-to-state stabilizability. The ISS-CLF gives us an inverse optimal H∞ control law. Further, we discuss that the inverse optimal H∞ controller has robustness against...
The robust stabilization problem is solved by constructing variable structure state-feedback control laws based on a conic partition of the state-space. The control Lyapunov function candidate and the conic partition are induced by a polyhedral region of interest. Nonlinear systems are approximated as piecewise affine in every sub-region of the partition. The partition has a simple and systematic...
The problem of bounded disturbance rejection for linear impulsive systems with polytopic uncertainties is considered in this paper. By using the Lyapunov function and positively invariant set method, a sufficient condition for robustly internal stability and L1-performance of the impulsive systems is obtained in terms of linear matrix inequalities. A simple algebraic approach to the design of a linear...
The existing methods of decentralized control suffer from two major restrictions. First, almost all of them hinge on Lyapunov's method, and second, they do not address the problem of performance robustness. A novel methodology to overcome the above defects is presented in this paper. Central to this approach is the notion of a finite-spectrum-equivalent descriptor system in the input-output decentralized...
A wheel slip controller for Anti-lock Brake Systems (ABS) is designed using LQ-optimal control. The controller gain matrices are gain scheduled on the vehicle speed. A parameter dependent Lyapunov function for the nominal linear parameter varying (LPV) closed loop system is found by solving a linear matrix inequality (LMI) problem. This Lyapunov function is used to investigate robustness with respect...
In this paper, one method of robust control based on sliding mode and fuzzy logic techniques is presented. It combines hierarchical control with high gain approach for multivariable and nonlinear systems; in order to eliminate chattering in presence of disturbances. Simulation results are presented to illustrate the applicability of the approach.
In this note we study the robustness of Generalized PI (GPI) control with respect to parametric uncertainties. We present two cases of study: a second order linear system and the inertia wheel pendulum. We propose a step by step procedure which may be used in each particular application.
An iterative procedure is proposed for robust H2 controller design. This method improves a previously reported technique, where optimization over two variables — the controller and a scaling matrix — was carried out by keeping one fixed at a time and minimizing the worst-case H2 norm over the other. In this paper, it is shown how optimization over both parameters at the same time can be formulated...
In this paper, we address the robust reduced-order filtering problem for linear parameter-varying (LPV) systems using an H∞-setting. The stability and the performance in a L2-gain sense of the filtering error is based on the existence of an affine parameter-dependent Lyapunov function. Our synthesis method gives sufficient conditions for the filter design which are expressed as new easily tractable...
In this paper, we consider a modification design of a class of Lyapunov-based robust controllers subject to bounded input. Our modification shows benefits in enhancing the input utilization and in retaining the stability and the robustness of the original control. An estimation of the stabilization region is proposed to explore region where the control is modified. It results in an estimate showing...
The stability robustness analysis for a class of nonlinear systems with bounded structured uncertainties is characterized by Nonlinear Matrix Inequalities (NLMI). By introducing scaling to reduce conservatism arising from the uncertainty structure, the problem turns out to be still convex. However, it is shown that it is as hard as Lyapunov stability analysis. In this paper, it is proposed a new way...
This paper considers the nonlinear optimization problems arising in robust control synthesis for discrete linear systems with polytopic time-varying uncertainty. Here a linear objective function is minimized under nonlinear matrix-valued function constraints. An iterative semidefinite programming (SDP) method is used to this class of problems. The benefit of the new approach is that the sub-problems...
The problem of stabilization of a polytope of matrices in a sub-region DR of the complex plane is revisited. A new sufficient condition of robust DR stabilization is given. It implies the solution of an LMI involving matrix variables constrained by a nonlinear algebraic relation. A cone complementarity formulation of this condition allows to associate an efficient iterative numerical procedure which...
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