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Invariance Principle (invariance + principle)
Selected AbstractsTHE ECONOMICS OF ACHIEVING COMPETITIVE BALANCE IN THE AUSTRALIAN FOOTBALL LEAGUE, 1897,2004ECONOMIC PAPERS: A JOURNAL OF APPLIED ECONOMICS AND POLICY, Issue 4 2004Ross Booth This paper summarises some key aspects of a theoretical and empirical analysis of whether various labour market devices and revenue-sharing rules used in the Victorian Football League/Australian Football League (VFL/AFL) since its inception in 1897 have increased competitive balance by reducing the inequality in the distribution of player talent between clubs. The history of labour market intervention and revenue sharing in the VFL/AFL is discussed, with six different periods between 1897 and 2004 identified for analysis. Fort and Quirk's (1995) model of US professional team sports leagues is used to analyse the effectiveness of the various devices that have been used in the VFL/AFL, but only after adapting the model to allow for VFL/AFL clubs being win maximisers (subject to a budget constraint) rather than profit maximisers. The various devices used by the VFL/AFL are assessed in terms of their likely impact on competitive balance, with some significantly different theoretical predictions than under profit maximisation. It is found that free agency results in a less equal distribution of player talent under win maximisation, whilst both gate sharing and increases in shared league-revenue tend to equalise playing strengths (which is not the case under profit maximisation). Moreover, the invariance principle, that the effect of a player draft will be undermined by the sale (and/or trade) of player talent, is found not necessarily to hold under win maximisation and can be reduced or eliminated with a team salary cap. Whether the trade of players and draft choices can undermine a player draft is also considered. The conclusion reached is that a player draft, a team salary cap, and revenue sharing is the combination most likely to succeed in achieving higher levels of competitive balance. The evidence of competitive balance in the VFL/AFL is consistent with these predictions. [source] Stabilization of an underactuated bottom-heavy airship via interconnection and damping assignmentINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 18 2007Zili Cai Abstract This paper focuses on feedback stabilization of a neutrally buoyant and bottom-heavy airship actuated by only five independent controls (with the rolling motion underactuated). The airship is modelled as an eudipleural submerged rigid body whose dynamics is formulated as a Hamiltonian system with respect to a Lie,Poisson structure. By exploiting the geometrical structure and using the so-called interconnection and damping assignment (IDA) passivity-based methodology for port-controlled Hamiltonian systems, state feedback control laws asymptotically stabilizing two typical motions are designed via La Salle invariance principle and Chetaev instability theorem. Simulation results verify the control laws. Copyright © 2007 John Wiley & Sons, Ltd. [source] Least-squares Estimation of an Unknown Number of Shifts in a Time SeriesJOURNAL OF TIME SERIES ANALYSIS, Issue 1 2000Marc Lavielle In this contribution, general results on the off-line least-squares estimate of changes in the mean of a random process are presented. First, a generalisation of the Hajek-Renyi inequality, dealing with the fluctuations of the normalized partial sums, is given. This preliminary result is then used to derive the consistency and the rate of convergence of the change-points estimate, in the situation where the number of changes is known. Strong consistency is obtained under some mixing conditions. The limiting distribution is also computed under an invariance principle. The case where the number of changes is unknown is then addressed. All these results apply to a large class of dependent processes, including strongly mixing and also long-range dependent processes. [source] Stabilization of the inverted spherical pendulum via Lyapunov approach,ASIAN JOURNAL OF CONTROL, Issue 6 2009O. Octavio Gutiérrez F. Abstract In this paper a nonlinear controller is presented for the stabilization of the spherical inverted pendulum system. The control strategy is based on the Lyapunov approach in conjunction with LaSalle's invariance principle. The proposed controller is able to bring the pendulum to the unstable upright equilibrium point with the position of the movable base at the origin. The obtained closed-loop system has a very large domain of attraction, that can be as large as desired, for any initial position of the pendulum which lies above the horizontal plane. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] A new adaptive backstepping Coulomb friction compensator for servo control systems,ASIAN JOURNAL OF CONTROL, Issue 1 2009Jen-te Yu Abstract A new Coulomb friction compensator is proposed for servo control systems in this paper. The novelty of the new approach lies in its capability of assigning the eigenvalues of the resulting closed loop system while attacking the problem. First, based on the standard backstepping methodology, an implicit Lyapunov function, with part of the components being only symbolically constructed at the very beginning, is utilized. To increase the robustness of the system against disturbance and model inaccuracy, an integral term is employed in the design. Using part of the variable gradient method, we are able to turn the implicit Lyapunov function into an explicit one, which is positive definite, and whose time-derivative is negative definite. Second, it will be shown that the resulting closed loop error system is a switched linear system with two possible active modes that share the same set of eigenvalues, which is at our disposal. Unlike the common adaptive control design methods, such as the Control Lyapunov Function approach, in which the gains are typically positive but otherwise arbitrary, and are hence difficult to choose and have a lack of connection with the system's performance, our new scheme imposes two further constraints on the gains. It turns out that we can then match these gains with the coefficients of the desired characteristic equation of the closed loop system. In this respect, the gains are linked to the system's overall performance, which is a new and very appealing feature for such a scheme. Finally, a procedure of constructing a common Lyapunov function is provided to prove exponential stability of the aforementioned switched linear system. In addition, using the invariance principle, we will show the convergence of the estimated Coulomb friction coefficient to its real value. Numerical simulations are given to validate the effectiveness of the design and its robustness against friction time-variations. Compared to existing results, the proposed scheme is much simpler, hence, much more advantageous computationally. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] Nonequilibrium scaling limit for a tagged particle in the simple exclusion process with long jumpsCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 2 2009Milton Jara We prove an invariance principle for a tagged particle in a simple exclusion process with long jumps out of equilibrium. © 2008 Wiley Periodicals, Inc. [source] | |||||||||||||