无局部自交的轴变形新方法

提出了一种无局部自交的轴变形的新算法.不同于传统的方法,新方法通过调整轴曲线的控制顶点及形状来调整轴曲线的曲率,从而避免物体发生局部自交.另外,文中还给出了一种快速判断轴变形中物体发生局部自交的方法,并给出了快速求解交点并去除自交的算法.上述方法计算量少,效率高,能应用于实时的计算机动画和几何造型系统中,具有广泛的应用前景.     

Passivity and disturbance attenuation via output feedback foruncertain nonlinear systems

The authors address the problem of disturbance attenuation with internal stability via output feedback for a class of passive systems with uncertainties. The problem is approached by means of adaptive output feedback control which does not require any state observer. The results obtained extend an earlier result of Steinberg and Corless (1985). Sufficient conditions are proposed under which a nonlinear system can be made locally or globally passive via output feedback     

A constructive approach to local stabilization of nonlinear systems by dynamic output feedback

The note considers the problem of local stabilization of nonlinear systems by dynamic output feedback. A new concept, namely, local uniform observability of feedback control law, is introduced. The main result is that if a nonlinear system is Nth-order approximately stabilizable by a locally uniformly observable state feedback, then it is stabilizable by dynamic output feedback. Based on the approximate stability, a constructive method for designing dynamic compensators is presented. The design of the dynamic compensators is beyond the separation principle and can handle systems whose linearization might be uncontrollable and/or unobservable. An example of nonminimum phase nonlinear systems is presented to illustrate the utility of the results.     

Global tracking control of underactuated ships by Lyapunov's direct method

This paper studies the global tracking problem for an underactuated ship with only two propellers. Under sufficient conditions of persistent excitation, two constructive solutions are proposed by application of Lyapunov's direct method. Both solutions exploit the inherent cascade interconnected structure of the ship dynamics and generate explicit Lyapunov functions. A common feature of the second solution and the recent cascade approach of Lefeber (Tracking control of nonlinear mechanical systems, Ph.D. Thesis, University of Twente, 2000) is that global exponential tracking is achieved, but at the expense of transient performance. Extension to unmeasured thruster dynamics is also considered. Simulation results validate the proposed tracking methodology.     

Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems

In this paper, the problem of decentralized adaptive output-feedback stabilization is investigated for large-scale stochastic nonlinear systems with three types of uncertainties, including parametric uncertainties, nonlinear uncertain interactions and stochastic inverse dynamics. Under the assumption that the inverse dynamics of the subsystems are stochastic input-to-state stable, an adaptive output-feedback controller is constructively designed by the backstepping method. It is shown that under some general conditions, the closed-loop system trajectories are bounded in probability and the outputs can be regulated into a small neighborhood of the origin in probability. In addition, the equilibrium of interest is globally stable in probability and the outputs can be regulated to the origin almost surely when the drift and diffusion vector fields vanish at the origin. The contributions of the work are characterized by the following novel features: (1) even for centralized single-input single-output systems, this paper presents a first result in stochastic, nonlinear, adaptive, output-feedback asymptotic stabilization; (2) the methodology previously developed for deterministic large-scale systems is generalized to stochastic ones. At the same time, novel small-gain conditions for small signals are identified in the setting of stochastic systems design; (3) both drift and diffusion vector fields are allowed to be dependent not only on the measurable outputs but some unmeasurable states; (4) parameter update laws are used to counteract the parametric uncertainty existing in both drift and diffusion vector fields, which may appear nonlinearly; (5) the concept of stochastic input-to-state stability and the method of changing supply functions are adapted, for the first time, to deal with stochastic and nonlinear inverse dynamics in the context of decentralized control.     

Construction of Lyapunov–Krasovskii functionals for networks of iISS retarded systems in small-gain formulation

This paper tackles a problem of verifying stability of retarded dynamical networks in a dissipative formulation. Subsystems are assumed to be integral input-to-state stable (iISS). Time-delays are allowed to reside in both subsystems and interconnection channels, and may be both discrete and distributed. No assumption is made on the interconnection topology. A small-gain methodology is developed for constructing a Lyapunov–Krasovskii functional to establish iISS of such a network.     

Robust global stabilization with ignored input dynamics: aninput-to-state stability (ISS) small-gain approach

This paper presents a re-design for global asymptotic stabilization in the presence of ignored input dynamics, restricted to be minimum-phase and relative degree zero. Using nonlinear small-gain arguments, we design a static feedback control law to achieve global asymptotic stabilization. In the absence of full-state information, an observer-based stabilizing controller is proposed     

A Lyapunov characterization of robust policy optimization

In this paper, we study the robustness property of policy optimization (particularly Gauss–Newton gradient descent algorithm which is equivalent to the policy iteration in reinforcement learning) subject to noise at each iteration. By invoking the concept of input-to-state stability and utilizing Lyapunov’s direct method, it is shown that, if the noise is sufficiently small, the policy iteration algorithm converges to a small neighborhood of the optimal solution even in the presence of noise at each iteration. Explicit expressions of the upperbound on the noise and the size of the neighborhood to which the policies ultimately converge are provided. Based onWillems’ fundamental lemma, a learning-based policy iteration algorithm is proposed. The persistent excitation condition can be readily guaranteed by checking the rank of the Hankel matrix related to an exploration signal. The robustness of the learning-based policy iteration to measurement noise and unknown system disturbances is theoretically demonstrated by the input-to-state stability of the policy iteration. Several numerical simulations are conducted to demonstrate the efficacy of the proposed method.