Class Of Continuous Nonlinear Systems Research Articles

Q-Learning-Based Model Predictive Control for Nonlinear Continuous-Time Systems

In this paper, a Q-learning-based model predictive control using the Lyapunov technique (Q-LMPC) is proposed for the control of a class of continuous nonlinear systems with complicated dynamics, wh...

A Special Kind of Sliding Mode Control for Nonlinear System With State Constraints

This paper presents a control strategy named auxiliary surfaces sliding mode control (AS-SMC) by using Positive Invariant Set (PIS) to control a class of continuous nonlinear systems with state constraints. The PIS can be regarded as a special kind of sliding surface, and its invariance ensures that the system state can satisfy the constraints in the convergence process. The stability analysis and a PIS theory proof are given. The control strategy is successfully tested in numerical simulations and even effectively applied to the coaxial unmanned helicopter flight control system on hardware in the loop (HIL) platform. The results verify the effectiveness of the proposed control strategy for the experimental set-up.

Design of interval observer for a class of uncertain unobservable nonlinear systems

This paper investigates the interval observer design for a class of nonlinear continuous systems, which can be represented as a superposition of a uniformly observable nominal subsystem with a Lipschitz nonlinear perturbation. It is shown in this case there exists an interval observer for the system that estimates the set of admissible values for the state consistent with the output measurements. An illustrative example of the observer application is given with simulation results.

Estimation of sampling interval based on Churilova's circle criterion systems with time-varying delay

A class of nonlinear continuous systems with discrete control is considered. Applying the input delay approach the system is transformed to system with time-varying sawtooth delay. Then an approach to estimate maximum upper bound of sampling interval using circle criterion for time-varying systems proposed by Churilova (1995) is described. Effectiveness and advantages of the method are illustrated by some numerical examples.

Convergence of a parameter switching algorithm for a class of nonlinear continuous systems and a generalization of Parrondo’s paradox

In this paper, we prove the convergence of a numerical algorithm that switches in some deterministic or random manner, the control parameter of a class of continuous-time nonlinear systems while the underlying initial value problem is numerically integrated. The numerically obtained attractor is a good approximation of the attractor obtained when the control parameter is replaced with the average of the switched values. In this way, a generalization of Parrondo’s paradox can be obtained. As an application, the Lorenz and Rabinovich–Fabrikant systems are used for illustration.

Observer-based Sampled-data Control for a Class of Continuous Nonlinear Systems

摘要: 首先使用反演方法分别设计了系统的连续时间状态反馈控制器、连续时间观测器和基于连续时间观测器的连续时间控制器. 接下来, 利用零阶保持法对连续时间状态反馈控制器进行离散化, 获得了状态反馈采样控制器; 利用零阶保持法对基于连续时间观测器 的连续时间控制器离散化, 获得了基于连续时间观测器的采样控制器; 利用Euler法对连续时间观测器离散化, 同时利用零阶保持法对控制器离散化, 从而获得了采样观测器和基于采样观测器的采样控制器. 本文论证了上述状态反馈采样控制器和基于连续时间观测器的采样控制器可以保证闭环系统渐近稳定, 而基于采样观测器的采样控制器可以保证被控对象的状态是有界的, 其最终边界依赖于设计参数与采样周期. 最后, 通过选择适当的采样周期, 完成了闭环采样控制系统的设计. 一个船舶航向控制的例子表明应用本文 所提方法设计出的三种采样控制器具有良好的控制效果. 关键词: 非线性系统 / 采样控制 / 观测器 / 输出反馈 / 离散化

A Design Method of LS-SVM Based Stable Adaptive Controller for a Class of Nonlinear Systems

A design method of LS-SVM based stable adaptive controller is proposed for a class of nonlinear continuous systems with unknown nonlinear function in this paper. Due to the fact that the control law is derived based on the Lyapunov stability theory, the scheme can not only solve the tracking problem of this class of nonlinear systems, but also it can guarantee the asymptotic stability of the closed systems, which is superior to many LS-SVM based control schemes. The effectiveness of the proposed scheme is demonstrated by simulation results.

An advanced fuzzy logic gain scheduling trajectory control for nonlinear systems

This paper investigates a novel fuzzy control approach developed for a class of nonlinear continuous systems. We combine an input–output feedback linearization (IOFL) method and a gain scheduling (GS) approach to obtain a tracking control structure. The latter is mainly based on the reversing trajectory method which allows us to estimate the asymptotic stability region around operating points. Needless to say that the limitation of this analytical approach lies in the challenge of determining the intermediate operating points in order to ensure a smooth transition from actual operating conditions to desired ones. This happens when there is no intersection between successive stability regions. The proposed fuzzy logic controller (FLC) is synthesized in order to determine the intermediate operating points which, in turn, will allows us to online implement the tracking control for nonlinear systems. Finally, the effectiveness of the fuzzy gain scheduling schema is demonstrated through its simulation to a temperature control problem in a CSTR.

Robust output-feedback stabilization of a class of nonlinear systems with the nonlinearities of varied form

The back-stepping designs based on confine functions are suggested for the robust output-feedback global stabilization of a class of nonlinear continuous systems; the proposed stabilizer is efficient for the nonlinear continuous systems confined by a bound function, the nonlinearities of the systems may be of varied forms or uncertain; the designed stabilizer is robust means that a class of nonlinear continuous systems can be stabilized by the same output feedback stabilization schemes: numerical simulation examples are given.

Global finite-time stabilization by dynamic output feedback for a class of continuous nonlinear systems

This note studies the problem of global finite-time stabilization by dynamic output feedback for a class of continuous but nonsmooth nonlinear systems. By extending the adding-a-power-integrator technique and a special continuous observer design, a dynamic output feedback controller is explicitly constructed to render the systems globally finite-time stable. The novelty of the note is the development of a recursive design procedure, which takes full advantage of the continuous structure of the systems in constructing the state feedback stabilizer and the continuous observer with rigorously selected gains.

Fuzzy sliding mode control for a class of non-linear continuous systems

In this work, a fuzzy sliding mode control for a non-linear uncertain and disturbed system is presented. Two adaptive fuzzy systems are used to determine the equivalent control signal. To overcome the design constraints in the classical sliding mode control, an adaptive fuzzy system and an attenuation term are introduced in the control law. A PID adaptation law is used to update the adjustable parameters of this fuzzy system. The synthesised controller efficiently eliminates the chattering phenomenon without requiring any particular knowledge about the upper bounds of either the external disturbances or the approximation errors. The simulation results illustrate the tracking performances of the proposed method.

Discrete Abstractions for Two-Dimensional Nearly Integrable Continuous Systems

Many manufacturing processes involve an interplay of logical and continuous objectives. Hybrid Control Systems are well-suited for studying interactions between continuous and logical control goals. A technique for generating the interfaces of a family of Hybrid Control Systems is presented. It amounts to extracting (untimed and specification-independent) abstractions for a class of nonlinear continuous systems satisfying an integrability property. Here we focus on the special case of two-dimensional systems. An example illustrates the theory.

A PMGOP method of parameter identification for a class of continuous nonlinear systems

A series of piecewise multiple general orthogonal polynomials (PMGOPs) is introduced and applied to the parameter identication problem for a class of continuous nonlinear systems. After introducing PMGOPs and discussing their main properties, an effective procedure for the parameter identification of a large class of continuous systems, called parameter separable systems, is proposed. Some relevant algorithms are presented. The procedure given in the paper has the following advantages compared with other methods: the identification algorithm (IA) obtained is computationally fast and accurate; the IA can be implemented in a recursive fashion; the IA is effective for a small number of data points; the IA does not require a priori knowledge of the estimated parameters; the IA is tolerant to choices of expanding orders when PMGOPs are applied. Some numerical examples, together with an experimental example taken from a biochemical fermentation process, are given for illustrative purposes.

Lyapunov Design of Sampled-Data Stabilising Feedback Control for Nonlinear Continuous-Time Systems

The problem of deriving sampled-data control laws for a class of nonlinear continuous systems is considered. The concept of approximate state-feedback (Lyapunov exponentially) stabilizing control is defined for sampled-data models arising from the sampling of continuous-time systems. Conditions for the existence of such control are explicited. A stability and asymptotic performance analysis is provided.

Sampled-data adaptive control of a class of continuous nonlinear systems

The problem is addressed of deriving sampled-data control laws for a class of nonlinear continuous systems. The concept of approximate state-feedback linearizing control is defined for sampled-data models arising from the sampling of continuous-time systems. Such control laws are then designed for both non-adaptive and adaptive cases and a detailed performance analysis is performed.

Discrete Time Adaptive Control for a Class of Nonlinear Continuous Systems

It is shown that adaptive approximate state feedback linearization can be achieved for a class of sampled-data non linear models which arise from the sampling of state feedback linearizable and linearly parametrized continuous time systems.

Multiple Solutions for a Class of Continuous Nonlinear Systems

A nonlinear state space representation of a nonlinear system implies that the system has a unique solution for a given set of initial conditions and system controls. But not all nonlinear systems have unique solutions for a given set of initial conditions and system controls. This paper presents an algebraic theory for solving continuous nonlinear systems equations that have multiple solutions.

Estimation of states and parameters in continuous non-linear systems with discrete observations

We consider a class of continuous non-linear systems defined by the ordinary differential equation x = f( x, t) + g( x, t) u, where u is an unknown input representing noise or disturbances. The object is to estimate states and parameters in these systems by means of a fixed number of discrete observations y i = h( x( t i ), t i ) + v i , 1 ⩽ i ⩽ m, where the v i represents unknown errors in the measurements y i . No statistical assumptions are made concerning the nature of the unknown input u or the unknown measurement errors v i . A weighted least squares criterion is defined as a measure of the optimal estimate. A result concerning the existence of solutions of the differential equation which minimize the criterion is presented. The necessary conditions for an optimal estimate, a set of Euler-Lagrange equations and multi-point discontinuous non-linear boundary conditions, are given. The multi-point problem is converted to an equivalent continuous two-point boundary value problem of larger dimension in the case in which the observations are assumed to be linear functions of the state. A pair of equivalent quasilinearization algorithms is defined for the two-point system and the multi-point system. Quadratic convergence for these algorithms is proved.

Series-Parallel and Parallel Identification Schemes for a Class of Continuous Nonlinear Systems

This technical brief deals with the identification of a single-input, single-output nonlinear system which is composed of a nonlinear static part and a linear dynamic part. A series-parallel identification algorithm and a parallel identification algorithm are presented; they require the input, output, and the order of the linear dynamic portion of the system. The stability of the algorithms is assured by Popov’s hyperstability theorem. The effectiveness of the identification schemes developed is demonstrated by computer simulation.

On the stability of a class of non-linear continuous systems†

Abstract A procedure to find the existence and domain of asymptotic stability for a class of systems described by a set of non-linear partial differential equations is presented in the context of semigroup theory. No a priori bound is imposed on the non-linearity which is assumed to be a quad ratic (bilinear) or multilinear form. The linearized system can be non-self-adjoint and need not be asymptotically stable equation by equation. The solution of the stability problem is carried out. in two steps : (a) the development of an L2-like norm that bounds above the sup norm, a requirement to obtain a useful estimate of the non-linear term, and (a)the computation of an estimate of the L2-likc norm of the semigroup generated by the linearized system in terms of its usual L2 norm.