Explicit Conditions (explicit + condition)

Distribution by Scientific Domains


Selected Abstracts


Feedback stabilization of bifurcations in multivariable nonlinear systems,Part II: Hopf bifurcations

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 4 2007
Yong Wang
Abstract In this paper we derive necessary and sufficient conditions of stabilizability for multi-input nonlinear systems possessing a Hopf bifurcation with the critical mode being linearly uncontrollable, under the non-degeneracy assumption that stability can be determined by the third order term in the normal form of the dynamics on the centre manifold. Stabilizability is defined as the existence of a sufficiently smooth state feedback such that the Hopf bifurcation of the closed-loop system is supercritical, which is equivalent to local asymptotic stability of the system at the bifurcation point. We prove that under the non-degeneracy conditions, stabilizability is equivalent to the existence of solutions to a third order algebraic inequality of the feedback gains. Explicit conditions for the existence of solutions to the algebraic inequality are derived, and the stabilizing feedback laws are constructed. Part of the sufficient conditions are equivalent to the rank conditions of an augmented matrix which is a generalization of the Popov,Belevitch,Hautus (PBH) rank test of controllability for linear time invariant (LTI) systems. We also apply our theory to feedback control of rotating stall in axial compression systems using bleed valve as actuators. Copyright © 2006 John Wiley & Sons, Ltd. [source]


Stochastic optimization for the ruin probability

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003
Manfred Schäl Prof. Dr. rer. nat.
The Cramér-Lundberg insurance model is studied where the risk process can be controlled by reinsurance and by investment in a financial market. The performance criterion is the ruin probability. The problem can be imbedded in the framework of discrete-time stochastic dynamic programming. Basic tools are the Howard improvement and the verification theorem. Explicit conditions are obtained for the optimality of employing no reinsurance and of not investing in the market. [source]


L2 -absolute and input-to-state stabilities of equations with nonlinear causal mappings

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 2 2009
M. I. Gil'
Abstract Nonlinear scalar equations with causal mappings are considered. These equations include differential, difference, differential-delay, integro-differential and other traditional equations. Estimates for the L2 -norms of solutions are established. These estimates give us explicit conditions for the absolute and input-to-state stabilities of the considered equations. The Aizerman-type problem from the theory of absolute stability is also discussed. The suggested approach enables us to consider various classes of systems from the unified point of view. Copyright © 2008 John Wiley & Sons, Ltd. [source]


Some nonlinear optimal control problems with closed-form solutions

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 14 2001
Michael Margaliot
Abstract Optimal controllers guarantee many desirable properties including stability and robustness of the closed-loop system. Unfortunately, the design of optimal controllers is generally very difficult because it requires solving an associated Hamilton,Jacobi,Bellman equation. In this paper we develop a new approach that allows the formulation of some nonlinear optimal control problems whose solution can be stated explicitly as a state-feedback controller. The approach is based on using Young's inequality to derive explicit conditions by which the solution of the associated Hamilton,Jacobi,Bellman equation is simplified. This allows us to formulate large families of nonlinear optimal control problems with closed-form solutions. We demonstrate this by developing optimal controllers for a Lotka,Volterra system. Copyright © 2001 John Wiley & Sons, Ltd. [source]


Computerized Task-Based Exposure, Explicitness, Type of Feedback, and Spanish L2 Development

MODERN LANGUAGE JOURNAL, Issue 2 2004
Elena M. Rosa
This study examined whether exposure to second/foreign language (L2) data under different computerized task conditions had a differential impact on learners' ability to recognize and produce the target structure immediately after exposure to the input and over time. Learners' L2 development was assessed through recognition and controlled-production tests containing old and new exemplars of the target structure. Adult learners of Spanish were exposed to past conditional sentences under 1 of 6 conditions premised on different degrees of explicitness. The degree of explicitness was manipulated by combining 3 features: (a) a pretask providing explicit grammatical information, (b) feedback concurrent to input processing, and (c) variation in the nature (i.e., implicit or explicit) of the feedback in those cases in which it was provided. The advantages of processing input under explicit conditions were evident (a) in production more than in recognition and (b) in new exemplars more than in old exemplars. [source]