共查询到20条相似文献,搜索用时 15 毫秒
1.
《Automatica》2014,50(11):2918-2923
In this paper we consider the problem of global asymptotic stabilization with prescribed local behavior. We show that this problem can be formulated in terms of control Lyapunov functions. Moreover, we show that if the local control law has been synthesized employing an LQ approach, then the associated Lyapunov function can be seen as the value function of an optimal problem with some specific local properties. We illustrate these results on two specific classes of systems: backstepping and feedforward systems. Finally, we show how this framework can be employed when considering the orbital transfer problem. 相似文献
2.
This paper investigates the finite‐time stabilization problem for a class of cascade nonlinear switched systems. Using the average dwell time and multiple Lyapunov function technologies, some sufficient conditions to guarantee that the corresponding closed‐loop system is finite‐time stabilized are derived for the switched systems. Via multiple Lyapunov functions, the state feedback controller is designed to finite‐time stabilize a cascade nonlinear switched system, and the conditions are formulated in terms of linear matrix inequalities. An example is given to illustrate the efficiency of the proposed methods. 相似文献
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《Automatic Control, IEEE Transactions on》2009,54(3):498-511
5.
Lijun Long 《国际强度与非线性控制杂志
》2017,27(18):4808-4824
》2017,27(18):4808-4824
The problem of global stabilization is investigated for a class of switched nonlinear feedforward systems in this paper where the solvability of the stabilization problem for individual subsystem is not assumed. Some sufficient condition for the stabilization problem to be solvable is derived for the first time by exploiting the multiple Lyapunov functions method and the forwarding technique. Also, we design a switching law and construct bounded state feedback controllers of subsystems explicitly by a recursive design algorithm to achieve global asymptotic stability. The provided technique permits removal of a common restriction in which all subsystems in switched nonlinear feedforward systems are globally asymptotically stable. Finally, a numerical example is provided to demonstrate the feasibility of the theoretical result. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
6.
This paper shows how the nonsmooth but continuous feedback design approach developed recently for global stabilization of nonlinear systems with uncontrollable unstable linearization, and the notion and properties of the input-to-state stability Lyapunov function can be effectively coupled, resulting in globally stabilizing C/sup 0/ partial-state feedback controllers for a class of cascade systems which may not be smoothly stabilizable, even locally. 相似文献
7.
《Fuzzy Systems, IEEE Transactions on》2006,14(5):640-653
We propose a new approach for the stability analysis of discrete Sugeno Types II and III fuzzy systems. The approach does not require the existence of a common Lyapunov function. We introduce the concept of fuzzy positive definite and fuzzy negative definite functions. This new concept is used to replace classical positive and negative definite functions in arguments similar to those of traditional Lyapunov stability theory. We obtain the equivalent fuzzy system for a cascade of two Type II/III fuzzy systems. We use the cascade of a system and a fuzzy Lyapunov function candidate to derive new conditions for stability and asymptotic stability for discrete Type II and Type III fuzzy systems. To demonstrate the new approach, we apply it to numerical examples where no common Lyapunov function exists. 相似文献
8.
S. Battilotti 《Mathematics of Control, Signals, and Systems (MCSS)》1997,10(2):188-202
In this paper we discuss the construction of “universal” controllers for a class of robust stabilization problems. We give a general theorem on the construction of these controllers, which requires that a certain nonlinear inequality is solvablepointwisely or, equivalently, that arobust control Lyapunov function does exist. The constructive procedure producesalmost smooth controllers. The robust control Lyapunov functions extend to uncertain systems the concept of control Lyapunov functions. If such a robust control Lyapunov function also satisfies a small control property, the resulting stabilizing controller is also continuous in the origin of the state space. Applications of our results range from optimal to robust control. 相似文献
9.
The problem of global stabilization for a class of switched nonlinear feedforward systems under arbitrary switchings is investigated in this paper. Based on the integrator forwarding technique and the common Lyapunov function method, we design bounded state feedback controllers of individual subsystems to guarantee asymptotic stability of the closed-loop system. A common coordinate transformation of all subsystems is exploited to avoid individual coordinate transformations for subsystems that are required when applying the forwarding recursive design scheme. An example is provided to demonstrate the effectiveness of the proposed design method. 相似文献
10.
This paper addresses stability analysis and stabilization for Takagi-Sugeno fuzzy systems via a so-called fuzzy Lyapunov function which is a multiple Lyapunov function. The fuzzy Lyapunov function is defined by fuzzily blending quadratic Lyapunov functions. Based on the fuzzy Lyapunov function approach, we give stability conditions for open-loop fuzzy systems and stabilization conditions for closed-loop fuzzy systems. To take full advantage of a fuzzy Lyapunov function, we propose a new parallel distributed compensation (PDC) scheme that feedbacks the time derivatives of premise membership functions. The new PDC contains the ordinary PDC as a special case. A design example illustrates the utility of the fuzzy Lyapunov function approach and the new PDC stabilization method. 相似文献
11.
Global stabilization via nested saturation function for high‐order feedforward nonlinear systems with unknown time‐varying delays
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We consider the global stabilization problem for a class of high‐order feedforward time‐delay nonlinear systems. The nested saturation function method is inherently improved to develop a continuous controller, without the requirements on the memory of the past input and the prior information of the time‐varying delays. The proposed controller is less conservative in terms of the level of nonlinearities whose upper bounds include high‐order, low‐order, and linear terms. The design procedures are provided based on the sign function technique, the homogeneous domination idea, and the search of Lyapunov function. Finally, a simulation example is used to demonstrate the application of the obtained theoretical results. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
12.
The objective of this paper is to solve the problem of tracking trajectories of feedforward systems. A family of time-varying state feedbacks that globally, uniformly, asymptotically and locally exponentially stabilize trajectories which are not necessarily periodic functions of time is exhibited. The control design is based on the construction of a strict Lyapunov function. 相似文献
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F. Mazenc 《Systems & Control Letters》1997,32(4):734
We prove that, for any odd integer p and any strictly positive integer n, feedforward systems which are approximated at the origin by a chain of integrators of degree p and length n can be globally asymptotically stabilized by bounded smooth time-invariant state feedbacks. Our proof is based on the construction of a Lyapunov function and the feedback laws we obtain are given by explicit formulas. 相似文献
14.
In this paper, we discuss global stabilization procedure for convergence of a more general feedforward nonlinear systems. Our stabilizer consists of a nested saturation function, which is a nonlinear combination of saturation functions. We extend the existing stabilization results and prove that our stabilizer is exponential convergent. 相似文献
15.
Hybrid mechanical systems with switched force fields, whose motions are described by differential second-order equations are
considered. We propose two approaches to solving problems of analysis of stability and stabilization of an equilibrium position
of the named systems. The first approach is based on the decomposition of an original system of differential equations into
two systems of the same dimension but of the first order. The second approach is in direct specifying a construction of a
general Lyapunov function for a mechanical system with switching. 相似文献
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17.
Our study relates to systems whose dynamics generalize x˙=h(y,u), y˙=f(y,u), where the state components x integrate functions of the other components y and the inputs u. We give sufficient conditions under which global asymptotic stabilizability of the y subsystem (respectively, by saturated control) implies global asymptotic stabilizability of the overall system (respectively, by saturated control). It is obtained by constructing explicitly a control Lyapunov function and provides feedback laws with several degrees of freedom which can be exploited to tackle design constraints. Also, we study how appropriate changes of coordinates allow us to extend its domain of application. Finally, we show how the proposed approach serves as a basic tool to be used, in a recursive design, to deal with more complex systems. In particular the stabilization problem of the so-called feedforward systems is solved this way 相似文献
18.
This paper studies the problem of finite-time stabilization for nonlinear systems. We prove that global finite-time stabilizability of uncertain nonlinear systems that are dominated by a lower-triangular system can be achieved by Hölder continuous state feedback. The proof is based on the finite-time Lyapunov stability theorem and the nonsmooth feedback design method developed recently for the control of inherently nonlinear systems that cannot be dealt with by any smooth feedback. A recursive design algorithm is developed for the construction of a Hölder continuous, global finite-time stabilizer as well as a C1 positive definite and proper Lyapunov function that guarantees finite-time stability. 相似文献
19.
We present a construction of a (strong) Lyapunov function whose derivative is negative definite along the solutions of the system using another (weak) Lyapunov function whose derivative along the solutions of the system is negative semidefinite. The construction can be carried out if a Lie algebraic condition that involves the (weak) Lyapunov function and the system vector field is satisfied. Our main result extends to general nonlinear systems the strong Lyapunov function construction presented in a previous paper that was valid only for homogeneous systems. 相似文献