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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...
In this paper the problem of designing a second-order sliding mode controller for nonlinear systems with bounded uncertainties is addressed. The adding a power integrator technique is applied to develop a new second-order sliding mode control algorithm. It is shown that under the controller thus designed, the resulting closed-loop system can achieve the finite-time Lyapunov stability, which is superior...
We aim to design in the present paper an adaptive output feedback control scheme to address the tracking problem of an uncertain system having full relative degree in the presence of neglected dynamics and modelling errors. Then, the obtained controller is augmented by an online radial basis function neural network (RBF NN) that is used to adaptively compensate for the nonlinearity existing in the...
This paper deals with the problem of designing a new iterative learning control (ILC) for a class of strict-feedback nonlinear systems subject to both structured and unstructured uncertainties and dynamic disturbances. These systems are assumed to perform the same task repeatedly under alignment condition. Simple learning mechanisms are proposed to approximate the unknown nonlinear state-dependent...
The robust decentralized tracking control problem for a class of uncertain multi-input multi-output (MIMO) nonlinear systems in block-triangular form is investigated in this paper. A control design method combining backstepping technique and signal compensation method is proposed to deal with the nonlinear uncertainties, external disturbances and strongly coupled interconnections in this kind of systems...
In this paper, some of the now well established results from the area of parametric robust control are combined with the describing function method to analyze the stability problem of uncertain discrete time systems with separable nonlinearities. Numerical examples are given to illustrate application of the proposed method.
For nonlinear systems in output injection feedback form with a scalar uncertainty on the nonlinear term, we give necessary and sufficient conditions for the observability with unknown input. The known approach of building an observer decoupled from the disturbances is not possible. Under the additional assumption that the uncertainty is bounded, we build practical observers whose error converges exponentially...
Variable Structure Control(VSC) with sliding mode is a special type of control technique that is capable of making a control system very robust with respect to system parameter variations and external disturbances. The chattering of the VSC signal can be reduced by several methods. One way is to augment the system with an integrator to isolate the system from the VSC control signal which causes the...
This paper addresses the inverse optimal robust control problem for uncertain nonlinear systems. A new version of robust backstepping is proposed in which inverse optimality is achieved through the selection of generalized state-dependent scaling factors. The design procedure is always successful for uncertain nonlinear systems in strict-feedback form. The class of cost functionals allowed in the...
This work presents and compares a set of active and passive adaptive predictive controllers based on orthonormal series representations. The controllers are designed according to the receding horizon principle, where the parameters of the predictive model are considered as random variables. This general framework allows the design of active and passive adaptive controllers, according to the assumptions...
In this paper a digital variable structure control algorithm, directly derived from a continuous one, previously presented by the authors, is considered. The proposed algorithm is able to perform the second order sliding mode control of a large class of uncertain second order nonlinear SISO systems. The discretization effects of the control law on the system behaviour are analyzed, and the sufficient...
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...
A robust MPC for constrained nonlinear system with uncertainties is presented. Uncertain evolution sets are used to predict the evolution of the system under any admisible uncertainty. The robust stability is guaranteed by a terminal and contractive constraint that drives the system to a robust positively invariant set. A new method to calculate the uncertain evolution sets is used. The method uses...
This paper proposes a novel design method for the adaptive robust Ho, control problem of a class of nonlinear systems with parametric uncertainties and external disturbances, which combines adaptive control and robust H∞, control techniques. By the use of the parameter projection method in adaptive control, the adaptive control laws are derived. Based on Hamilton-Jacobi inequalities, the adaptive...
In this paper, we consider robust regulation of a class of nonlinear systems, via H∞ controller using singular perturbation approach. First, using normal form equations, we eliminate the nonlinear part of the system matrix of equations of system and transform it to a linear diagonal form. Separating new equations to slow and fast subsystems, due to the singular perturbation approach and with the assumption...
The focal point of this paper is to develop a measure of closed-loop nonlinearity. In this work, the Vinnicombe metric and the quasi-linear parameter varying (quasi-LPV) representation of nonlinear systems are exploited for this purpose. The proposed measure can serve as a decision making tool for control engineers when deciding whether a linear or nonlinear control strategy should be employed to...
In this paper the robust positivity of polynomials under coefficient perturbation is investigated. This robust positivity of polynomials can be used for polynomial systems in order to determine the robust asymptotic stability of the system. We assume that the polynomials under investigation depend linearly on some parameters. Our aim is to determine the parameter perturbation region as a hypercube,...
Adaptive control schemes are developed, which provide global asymptotic stability property with respect to state space vector of the plant with functional uncertainty. In the presence of disturbance these schemes ensure boundedness of all trajectories of the system. A switching modification of proposed schemes is considered.
A class of memoryless feedback controls is designed to asymptotically stabilize a class of imperfectly known, nonlinear, descriptor systems with time-delays. Each descriptor system, consisting of dynamic and static subsystems, contains discrete and distributed delays, and each dynamic subsystem is a time-delay system of the retarded type. A deterministic methodology based on Lyapunov theory and Lyapunov-Krasovskii...
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...
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