Direct adaptive fuzzy control based on integral-type Lyapunov function

A new scheme of direct adaptive fuzzy controller for a class of nonlinear systems with unknown triangular control gain structure is proposed. The design is based on the principle of sliding mode control and the approximation capability of the first type fuzzy systems. By introducing integral-type Lyapunov function and adopting the adaptive compensation term of optimal approximation error, the closed-loop control system is proved to be globally stable, with tracking error converging to zero. Simulation results demonstrate the effectiveness of the approach.

ROBUST CONTROL OF A CLASS OF NONLINEAR SYSTEM WITH TIME-VARYING PAR AMETRIC UNCERTAINTIES

A class of triangular non li near system with disturbances which has unknown multiplicative time varying par ametric uncertainties in each virtual control is treated by a backstepping techn ique. The controller designed for all admissible uncertainties can guarantee tha t all states of its closed loop system are uniformly bounded. The robust contro ller design algorithm and a sufficient condition of the system stability are giv en. In addition, the closed loop system has an ISS property when the multiplica tive time varying parametric uncertainties are viewed as inputs to the system. Thus, this design provides a way to prevent a destabilizing effect of the multip licative time varying parametric uncertainties. Finally, simulational example i s given and simulational result shows that the controller exhibits effectiveness and excellent robustness.

Exponential stabilization of distributed parameter switched systems under dwell time constraints

The exponential stabilization problem for finite dimensional switched systems is extended to the infinite dimensional distributed parameter systems in the Hilbert space. Based on the semigroup theory, by applying the multiple Lyapunov function method, the exponential stabilization conditions are derived. These conditions are given in the form of linear operator inequalities where the decision variables are operators in the Hilbert space; while the stabilization properties depend on the switching rule. Being applied to the two-dimensional heat switched propagation equations with the Dirichlet boundary conditions, these linear operator inequalities are transformed into standard linear matrix inequalities. Finally, two examples are given to illustrate the effectiveness of the proposed results.

Adaptive variable structure control based on backstepping for spacecraft with reaction wheels during attitude maneuver

An adaptive variable structure control method based on backstepping is proposed for the attitude maneuver problem of rigid spacecraft with reaction wheel dynamics in the presence of uncertain inertia matrix and external disturbances. The proposed control approach is a combination of the backstepping and the adaptive variable structure control. The cascaded structure of the attitude maneuver control system with reaction wheel dynamics gives the advantage for applying the backstepping method to construct Lyapunov functions. The robust stability to external disturbances and parametric uncertainty is guaranteed by the adaptive variable structure control. To validate the proposed control algorithm, numerical simulations using the proposed approach are performed for the attitude maneuver mission of rigid spacecraft with a configuration consisting of four reaction wheels for actuator and three magnetorquers for momentum unloading. Simulation results verify the effectiveness of the proposed control algorithm.

Approximation Properties of a Special Class of Mathematical Expectation Operators

In this paper we study the local measure of approximation of a class of special mathematical expectation operators to Lipschitz class of functions by probabilistic method. The some well known operators (e. g., the Bernstein, Bascakov and Szasz-Mirakjan operators etc) are special cases of a class of the mathematical expetation operators.

Boundedness of the Maximal Operator on Lip_α(R^n) (0<α<1)

It provides the boundary proof of the maximal operator on Lipschitz space. i.e.,if f ∈Lip α(R n) (0<α<1) and inf x∈R nM(f)(x) <∞, then almost every x∈R n has M(f)(x) <∞ and exists a constant C independent of f and x ,such that ‖M(f)‖ ∧ α ≤C‖f‖ ∧ α .

Control Lyapunov Stabilization of Nonlinear Systems with Structural Uncertainty

This paper deals with global stabilization problem for the nonlinear systems with structural uncertainty. Based on control Lyapunov function, a sufficient and necessary condition for the globally and asymptotically stabilizing the equailibrium of the closed system is given. Moreovery, an almost smooth state feedback control law is constructed. The simulation shows the effectiveness of the method.

Stabilization of nonlinear systems based on robust control Lyapunov function

This paper deals with the robust stabilization problem for a class of nonlinear systems with structural uncertainty. Based on robust control Lyapunov function, a sufficient and necessary condition for a function to be a robust control Lyapunov function is given. From this condition, simply sufficient condition for the robust stabilization （robust practical stabilization） is deduced. Moreover, if the equilibrium of the closed-loop system is unique, the existence of such a robust control Lyapunnv function will also imply robustly globally asymptotical stabilization. Then a continuous state feedback law can be constructed explicitly. The simulation shows the effectiveness of the method.

Instability Theorems for Fuzzy Differential Equations

Some instability results of the trivial solution of fuzzy differential equations via Lyapunov functions is elaborated.

Adaptive Tracking Control for Diffractive Film Based on Nonlinear Sliding Mode

A nonlinear sliding mode adaptive controller for a thin-film diffractive imaging system is designed to achieve accurate pointing direction over the attitude of subarrays in large-diameter mirror arrays.The kinematics and dynamics equations based on error quaternion and angular velocity are derived,and a diffractive thin-film sub-mirror array controller is designed to point precisely.Moreover,the global stability of the controller is proved by the Lyapunov method.Since the controller can adaptively identify the inertia matrix of each sub-mirror system,it is robust to bounded disturbances and changes in inertia parameters.At the same time,the continuous arctangent function is introduced,which is effectively anti-chattering.The simulation results show that the designed controller can ensure the accurate tracking of the diffractive film in each sub-mirror in the presence of rotational inertia matrix uncertainty and various disturbances.

Robust L_2-L_∞ filtering with pole constraint in a disk via parameter-dependent Lyapunov functions

Addresses the design problems of robust L2-L∞ filters with pole constraint in a disk for uncertain continuous-time linear systems. The uncertain parameters are assumed to belong to convex bounded domains. The aim is to determine a stable linear filter such that the filtering error system possesses a prescribed L2-L∞ noise attenuation level and expected poles location. The filtering strategies are based on parameter-dependent Lyapunov stability results to derive new robust L2-L∞ performance criteria and the regional pole placement conditions. From the proposed multi-objective performance criteria, we derive sufficient conditions for the existence of robust L2-L∞ filters with pole constraint in a disk, and cast the filter design into a convex optimization problem subject to a set of linear matrix inequality constraints. This filtering method exhibits less conservativeness than previous results in the quadratic framework. The advantages of the filter design procedures are demonstrated by means of numerical examples.

T-S Fuzzy Stochastic Bilinear Model and Fuzzy Controller Design Based on Switching Piecewise Lyapunov Functions

Based on a piecewise quadratic lyapunov function （PQLF）, this paper presents stochastic stability analysis and synthesis methods for ItO and discrete T-S fuzzy bilinear stochastic systems. Two improved stochastic stability conditions have been established in terms of linear matrix inequalities （LMIs）. It is shown that the stability in the mean square for T-S fuzzy bilinear stochastic systems can be established if a PQLF can be constructed. Considering the established stability criterion, the controller can be designed by solving a set of （LMIs）, and the closed loop system is asymptotically stable in the mean square. Two illustrative examples are provided to demonstrate the effectiveness of the results proposed in this paper.

Symmetry Reductions of Two-Dimensional Variable Coefficient Burgers Equation

By use of a direct method, we discuss symmetries and reductions of the two-dimensional Burgers equation with variable coefficient (VCBurgers). Five types of symmetry-reducing VCBurgers to (1+1)-dimensional partial differential equation and three types of symmetry reducing VCBurgers to ordinary differential equation are obtained.

《通俗编》版本考略

《通俗编》无不宜斋本38卷是作者翟灏的定本,《函海》本25卷所据仅是作者的未定稿。《函海》本错讹很多,加之李调元丧失编辑底线,掺入非《通俗编》内容,因而合理的界线是:凡是不见于无不宜斋38卷本的条目及话语,一概不得归入《通俗编》。《函海》光绪重刊本后出转劣,《丛书集成初编》择此本排印是一失策。

Conditional Stability of Stochastic Volterra Equationswith Anticipating Kernel

This paper introdnces some concepts of conditional stability of stochasticVolterra equations with anticipating kernel. Snfficient conditions of these types of sta-bility are established via Lyapunov funciton.

我的“毒舌”闺密

六六,大名李函汝,是我的闺密。黑白分明的眼睛,瘦瘦的身材,头发扎成马尾,声音清脆。更多的时候,我称她为'老六',她叫我'老邱'。

STABILITY OF IMPULSIVE LINEAR HYBRID SYSTEMS WITH TIME DELAY

This paper investigates the stability of impulsive linear hybrid systems with time delay.And a number of delay-independent/delay-dependent stability criteria are obtained by using Lyapunovfunctions or Lyapunov functionals.Two examples are also presented to illustrate the effectiveness ofthe obtained results or to compare with the existing results.

Stabilization of an Euler-Bernoulli Beam with a Tip Mass Under the Unknown Boundary External Disturbances

This paper studies the stabilization problem of an Euler-Bernoulli beam with a tip mass,which undergoes unknown but uniform bounded disturbance at tip mass. Here the nonlinear feedback control law is used to cancel the effects of the external disturbances. For the controlled nonlinear system,the authors prove the well-posedness by the maximal monotone operator theory and the variational principle. Further the authors prove that the controlled nonlinear system is exponential stable by constructing a suitable Lyapunov function. Finally, some numerical simulations are given to support these results.

A novel LMI criterion for power system stability with multiple time-delays

This paper presents a novel LMI criterion for electric power system stability with multiple time-delays.Initially,the linear time-invariant model of the power system with multiple delays is constructed,subsequently,the former criteria and the novel criterion of this paper are demonstrated in this paper,and the novel criterion is fully proved according to Lyapunov direct method.Specifically,the proposed criterion utilizes a properly simplified Lyapunov-Krasovskii functional,and no free-weighting matrix is introduced in the formation of new criterion,as a consequence,the calculation efficiency is remarkably enhanced.A typical second-order delay system,a single-generator-infinite-bus system and the WSCC 3-generator-9-bus delay system are taken to validate the effectiveness and efficiency enhancement of the proposed criterion.The numerical results indicate that the criterion of this paper can generate the same stability margin with the former ones.Further,the numerical results also verify that the proposed criterion’s efficiency is substantially boosted and calculation time is greatly curtailed.

ROBUST CONSENSUS FOR MULTI-AGENT SYSTEMS OVER UNBALANCED DIRECTED NETWORKS

In this paper,a distributed consensus protocol is proposed for discrete-time single-integer multi-agent systems with measurement noises under general fixed directed topologies.The time-varying control gains satisfying the stochastic approximation conditions are introduced to attenuate noises,thus the closed-loop multi-agent system is intrinsically a linear time-varying stochastic difference system.Then the mean square consensus convergence analysis is developed based on the Lyapunov technique,and the construction of the Lyapunov function especially does not require the typical balanced network topology condition assumed for the existence of quadratic Lyapunov function.Thus,the proposed consensus protocol can be applicable to more general networked multi-agent systems,particularly when the bidirectional and/or balanced information exchanges between agents are not required.Under the proposed protocol,it is proved that the state of each agent converges in mean square to a common random variable whose mathematical expectation is the weighted average of agents' initial state values;meanwhile,the random variable's variance is bounded.