Stabilization of a class of multi-inputs nonlinear systems

In this paper, we investigate the local stabilization of affine analytic systems with n − 1 inputs. We state a sufficient condition on the first approximation of f for which the local asymptotic stabilizability can be achieved; furthermore, we give explicitly the stabilizing feedback.     

Stabilization of a class of switched nonlinear systems

The stabilization of a class of switched nonlinear systems is investigated in the paper. The systems concerned are of （generalized） switched Byrnes-Isidori canonical form, which has all switched models in （generalized） Byrnes- Isidori canonical form. First, a stability result of switched systems is obtained. Then it is used to solve the stabilization problem of the switched nonlinear control systems. In addition, necessary and sufficient conditions are obtained for a switched affine nonlinear system to be feedback equivalent to （generalized） switched Byrnes-Isidori canonical systems are presented. Finally, as an application the stability of switched lorenz systems is investigated.     

Stabilization of a class of switched nonlinear systems

The stabilization of a class of switched nonlinear systems is investigated in the paper. The systems con- cerned are of (generalized) switched Byrnes-Isidori canonical form, which has all switched models in (generalized) Byrnes- Isidori canonical form. First, a stability result of switched systems is obtained. Then it is used to solve the stabilization prob- lem of the switched nonlinear control systems. In addition, necessary and sufficient conditions are obtained for a switched affine nonlinear system to be feedback equivalent to (generalized) switched Byrnes-Isidori canonical systems are presented. Finally, as an application the stability of switched lorenz systems is investigated.     

Robust stabilization of one class of nonlinear systems

We consider the robust linear stabilization problem for a family of nonlinear controllable systems that contains functional-parametric uncertainties and depends on the control nonlinearly. We obtain sufficient conditions for robust stabilization and synthesize state linear controllers that perform robust stabilization. We also obtain necessary conditions for robust stabilization that are close to sufficient. The synthesis is based on the method of Lyapunov functions.     

Controllability of one class of nonlinear singularly perturbed systems

Sufficient conditions of complete controllability are derived for quasilinear singularly perturbed systems.Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 61–66, July–August, 1992.     

Stabilization of a class of nonlinear systems by adaptive output feedback

In recent years, several results have been proposed on global stabilization of a class of nonlinear systems that are dominated by a triangular system satisfying the linear growth condition. However, in these works, at least the linear growth bound is assumed to be known in designing stabilizing controllers. In our work, we propose an adaptive output feedback control scheme in which the high-gain parameter is tuned on-line. Thus, a priori knowledge on the linear growth bound of system nonlinearities is not required in our scheme.     

On absolute stability of one class of nonlinear switched systems

A certain class of nonlinear switched systems is considered. Methods of developing Lyapynov functions for the systems under study are suggested. Conditions are defined, in the fulfillment of which the asymptotic stability of the zero solution will take place for any witching laws and for any admissible nonlinearities entering into right sides of the equations under discussion.     

Stabilization of a class of cascade nonlinear switched systems with application to chaotic systems

In this study, the problem of finite‐time practical control of a class of nonlinear switched systems in the presence of input nonlinearities is investigated. The subsystems of the switched system are considered as complex nonlinear systems with a cascade structure. Each subsystem is fluctuated by lumped uncertainties. Moreover, some parts of the system's dynamics are considered to be unknown in advance. This paper sets no restrictive assumption on the switching logic of the system. Therefore, the aim is to propose a controller to work under any arbitrary switching signals. After providing a smooth sliding manifold, a simple adaptive control input is developed such that the system trajectories approach the prescribed sliding mode dynamics in finite‐time sense. The adopted control signal does not use the upper bounds of the lumped uncertainties, and it is robust against unknown nonlinear parts of the subsystems. It is proved that the origin is the (practical) finite‐time stable equilibrium point of the overall closed‐loop system. Subsequently, the proposed control rule is modified to handle the same switched system with no input nonlinearities. Computer simulations via 2 chaotic electric direct current machines demonstrate the robust performance of the derived variable structure control algorithm against system fluctuations and nonlinear inputs.     

Stabilization of a class of nonlinear systems by a smooth feedback control

We consider the stabilizability problem for systems of the form in the neighborhood of an equilibrium point of f(x). First, by means of center manifold theory, a lower order system is introduced. If this system is stabilizable, then so is the original system. Results on the stabilization of the low order system are presented. No resort is taken to Liapunov theory. The relation between stabilizability and controllability is discussed.     

Stabilization for a class of nonlinear systems: A fuzzy logic approach

In this paper, the problem of stabilization for the class of continuous time nonlinear systems which are discretized in closed form is addressed. By using the Takagi–Sugeno model approach, a discrete controller capable of stabilizing the discrete Takagi–Sugeno model and the continuous model as well, is obtained. This scheme allows using a digital controller for stabilizing an analog plant.     

Stabilization of a class of uncertain nonlinear affine systems subject to control constraints

Practical and asymptotic stabilization is investigated for a class of uncertain nonlinear affine control systems subject to constraints on the control inputs. The uncertain systems are modelled as non‐linear perturbations to a known non‐linear idealized system and a problem formulation based on differential inclusions is adopted. A class of constrained generalized state‐feedback controls (containing both continuous and discontinuous selections) is developed, which guarantees stabilization with a specified region of attraction. In the presence of residual uncertainty, sufficient conditions for global stabilizability are presented, whilst local results are obtained by relaxing these conditions. Copyright © 2001 John Wiley & Sons, Ltd.     

Stabilization of continuous-time switched nonlinear systems

The paper considers three problems for continuous-time nonlinear switched systems. The first result of this paper is a open-loop stabilization strategy based on dwell time computation. The second considers a state switching strategy for global stabilization. The strategy is of closed loop nature (trajectory dependent) and is designed from the solution of what we call nonlinear Lyapunov–Metzler inequalities from which the stability condition is expressed. Finally, results on the stabilization of nonlinear time varying polytopic systems are provided.     

Stabilization of nonlinear systems with uncontrollablelinearization

The problem of local stabilization of nonlinear control systems with linearizations that contain uncontrollable modes on the imaginary axis is considered. A methodology of designing a stabilizing control is investigated. It involves the following steps: (1) reduction of the stability problem to the stability of the center manifold system, (2) simplification of the vector field on the center manifold using the theory of normal forms, and (3) finding conditions under which the simplified vector field is asymptotically stable. Three cases of degeneracies in the linearized system are treated, and sufficient conditions for the existence of stabilizing controls are given in each case. A theorem is presented regarding the robustness of the above control strategies     

Stabilization of nonlinear systems with moving equilibria

This note provides a new method for the stabilization of nonlinear systems with parametric uncertainty. Unlike traditional techniques, our approach does not assume that the equilibrium remains fixed for all parameter values. The proposed method combines different optimization techniques to produce a robust control that accounts for uncertain parametric variations, and the corresponding equilibrium shifts. Comparisons with analytical gain scheduling are provided.     

Stabilization of nonlinear discrete-time systems using statedetection

Some recent results concerning stabilization of continuous-time systems using state detection are extended to the case of discrete-time nonlinear systems. It is shown that if a discrete-time locally detectable system can be stabilized by a state feedback law, then it can also be stabilized by a feedback law that depends on the output of a weak detector     

符号网络下一类非线性二分一致性系统的跟踪控制

研究具有对抗交互的一类非线性多智能体系统的二分一致性跟踪控制问题,借助有向符号图刻画智能体之间的通信关系,并假定符号图是结构平衡的.进一步,借助符号图网络对二分一致性跟踪问题进行公式化描述.基于最近邻原则,结合拉普拉斯矩阵、牵制矩阵、符号函数、耦合增益参数等,设计分布式控制律.利用Barbalat引理和李亚谱诺夫函数证明整个闭环系统的渐近稳定性,在保持闭环系统稳定的条件下推导出耦合增益的下界.最后通过仿真验证所提出方法的有效性.     

Stabilization for nonlinear fractional-order time-varying switched systems

This paper deals with the global asymptotic stabilization problem for discontinuous nonlinear time-varying switched systems in the sense of fractional-order. Via the designed periodic switching law, some criteria are firstly developed. It is shown that the derivatives of the constructed Lyapunov functions are allowed to be indefinite. Several corollaries are further derived, and some existing results can be regarded as special cases of our obtained results. Finally, our findings are verified by three numerical examples and one experiment.     

Stabilization of unknown nonlinear systems using neural networks

This paper deals with stabilization of unknown nonlinear systems using a nonlinear controller made with a backpropagation neural network. Control strategies based on an inverse state neural model built from an off-line learning step are proposed. The proposed strategies can be implemented following two approaches. The first one consists on computing control horizon based on actual state vector and desired one at a future instant. The second approach applies control action in the sense of a receding horizon. Adaptive control has been considered where the updating of the neural controller is accomplished to optimize different control objectives.     

Stabilization of collocated systems by nonlinear boundary control

We design control laws for a class of dissipative infinite-dimensional systems using nonlinear boundary control action. The applications are to saturated control of SCOLE-type models.