Results 151 to 160 of about 34,893 (179)

Control design with Lipschitz switching surfaces based on new contingent cone criteria

International Journal of Modelling, Identification and Control, 2011
In this paper, a control design method for a class of non-linear uncertain systems is proposed based on the new contingent cone criteria, which are used to estimate the relation between the phase trajectories and an arbitrary Lipschitz continuous surface.
Xin Huo, Yu Yao, Kai Zheng
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Sliding mode control design via piecewise smooth Lipschitz surfaces based on contingent cone criteria

International Journal of Control, Automation and Systems, 2014
In order to improve flexibility of sliding mode control (SMC) for a class of nonlinear systems, a new control design method is proposed in this paper. The sliding surface is extended to be a generic Lipschitz continuous surface instead of a smooth one, with which different characteristics of sliding motion may be realized.
Xin Huo, Kai Zheng, Kemao Ma
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Contingent cone to a set defined by equality and inequality constraints at a Fréchet differentiable point

Journal of Optimization Theory and Applications, 1994
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Di, S., Poliquin, R.
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Optimality conditions of the set-valued optimization problem with generalized cone convex set-valued maps characterized by contingent epiderivative

Acta Mathematicae Applicatae Sinica, English Series, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhou, Zhi-ang, Yang, Xin-min, Qiu, Qiu-sheng   +2 more
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On the intersection of contingent cones

Journal of Optimization Theory and Applications, 1991
A new condition that ensures the equality \[ (1)\quad T_{K\cap L}(x)=T_ K(x)\cap T_ L(x),\quad x\in K\cap L, \] \[ T_ K(x)=\{v\in X| \quad \liminf_{h\downarrow 0+}[dist(K,x+hv)/h]=0\} \] for convex closed subsets K, L of a Hilbert space X is established.
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Tangent cone and contingent cone to the intersection of two closed sets

Nonlinear Analysis: Theory, Methods & Applications, 2010
Let \(X\) be a normed vector space and \(C\subset X\) a nonempty closed set; let \(T_C(x)\) denote the tangent cone to \(C\) at \(x\in C\). For \(X=\mathbb R^n\), \textit{R. T. Rockafellar} [Nonlinear Anal., Theory Methods Appl.\ 3, 145--154 (1979; Zbl 0443.26010)] has shown that, if \(x\in C_1\cap C_2\), then \[ T_{C_1}(x)\cap T_{C_2}(x)\subset T_{C_1\
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Cone-directed contingent derivatives and generalized preinvex set-valued optimization

Acta Mathematica Scientia, 2007
Abstract By using cone-directed contingent derivatives, the unified necessary and sufficient optimality conditions are given for weakly and strongly minimal elements respectively in generalized preinvex set-valued optimization.
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Corrigendum to "Convex Subcones of the Contingent Cone in Nonsmooth Calculus and Optimization"

Transactions of the American Mathematical Society, 1989
This is a correction to the paper ibid. 302, 661-682 (1987; Zbl 0629.58007).
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OPTIMALITY OF GLOBAL PROPER EFFICIENCY FOR CONE-ARCWISE CONNECTED SET-VALUED OPTIMIZATION USING CONTINGENT EPIDERIVATIVE

Asia-Pacific Journal of Operational Research, 2013
This note deals with the optimality conditions of set-valued unconstraint optimization problem in real normed linear spaces. Based upon the concept of contingent epiderivative, the unified necessary and sufficient optimality conditions for global proper efficiency in vector optimization problem involving cone-arcwise connected set-valued mapping are ...
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Contingent Cones to Reachable Sets of Control Systems

1988
The author studies high order necessary conditions for optimality for an optimal control problem via properties of contingent cones to reachable sets along the optimal trajectory. It is shown that the adjoint vector of Pontryagin's maximum principle is normal to the set of variations of reachable sets.
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