Formation control of multiple underwater vehicles subject to communication faults and uncertainties     

《Applied Ocean Research》2019

This paper proposes a novel approach to analyze and design the formation keeping control protocols for multiple underwater vehicles in the presence of communication faults and possible uncertainties. First, we formulate the considered vehicle model as the Port-controlled Hamiltonian form, and introduce the spring-damping system based formation control. Next, the dynamics of multiple underwater vehicles under uncertain relative information is reformulated as a network of Lur’e systems. Moreover, the agents under unknown disturbances generated by an external system are considered, where the internal model is applied to tackle the uncertainties, which still can be regulated as the Lur’e systems. In each case, the formation control is derived from solving LMI problems. Finally, a numerical example is introduced to illustrate the effectiveness of the proposed theoretical approach.  相似文献   

Forced secondary resonances at the 3 : 1 commensurability     

Yi-Sui Sun  Ji-Lin Zhou  Tian-Ling Zhang  Chong-Qing Cheng 《Celestial Mechanics and Dynamical Astronomy》1994,59(4):313-325

For the 3 : 1 Jovian resonance problem, the time scales of the two degrees of freedom of the resonant Hamiltonian are well-separated [5]. With the adiabatic approximation, the solution for the fast oscillations can be found in terms of the slowly varying variables. Thus the rapidly oscillating terms in the slow oscillation equations can be treated as forced terms. We refer to the resonance between the forcing and intrinsic frequencies as a forced secondary one in this paper. We discuss the forced secondary resonances in asteroidal motion at the 3 : 1 commensurability by using Wisdom's method. The results show that the orbits situated originally near the resonance will leave the neighbourhood of resonance and tend to the separatrices and critical points for different energies, respectively. We have not found any stochastic web as expected in this case. Moreover, we study the problem of validity on the approximation of a system.The Project Supported by the National Natural Science Foundation of China.  相似文献   

Effective Hamiltonian for the D'Alembert Planetary Model Near a Spin/Orbit Resonance     

Luca Biasco  Luigi Chierchia 《Celestial Mechanics and Dynamical Astronomy》2002,83(1-4):223-237

The D'Alembert model for the spin/orbit problem in celestial mechanics is considered. Using a Hamiltonian formalism, it is shown that in a small neighborhood of a p:q spin/orbit resonance with (p,q) different from (1,1) and (2,1) the 'effective' D'Alembert Hamiltonian is a completely integrable system with phase space foliated by maximal invariant curves; instead, in a small neighborhood of a p:q spin/orbit resonance with (p,q) equal to (1,1) or (2,1) the 'effective' D'Alembert Hamiltonian has a phase portrait similar to that of the standard pendulum (elliptic and hyperbolic equilibria, separatrices, invariant curves of different homotopy). A fast averaging with respect to the 'mean anomaly' is also performed (by means of Nekhoroshev techniques) showing that, up to exponentially small terms, the resonant D'Alembert Hamiltonian is described by a two-degrees-of-freedom, properly degenerate Hamiltonian having the lowest order terms corresponding to the 'effective' Hamiltonian mentioned above.  相似文献   

Mass-Weighted Symplectic Forms for the N-Body Problem     

F. Varadi  M. Ghil  W. M. Kaula 《Celestial Mechanics and Dynamical Astronomy》1998,72(3):187-199

Mass-weighted symplectic forms provide a unified framework for the treatment of both finite and vanishingly small masses in the N-body problem. These forms are introduced, compared to previous approaches, and their properties are discussed. Applications to symplectic mappings, the definition of action-angle variables for the Kepler problem, and Hamiltonian perturbation theory are outlined This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

Normalization and the detection of integrability: The generalized Van Der Waals potential     

David Farrelly  T. Uzer 《Celestial Mechanics and Dynamical Astronomy》1995,61(1):71-95

Deprit and Miller have conjectured that normalization of integrable Hamiltonians may produce normal forms exhibiting degenerate equilibria to very high order. Several examples in the class of coupled elliptic oscillators are known. In order to test the utility of normalization as a detector of integrability we normalize, to high order, a perturbed Keplerian system known to have several integrable limits; the generalized van der Waals Hamiltonian for a hydrogen atom. While the separable limits give rise to high order degeneracy we find a non-separable, integrable limit for which the normal form does not exhibit degeneracy. We conclude that normalization may, in certain cases, indicate integrability but is not guaranteed to uncover all integrable limits.  相似文献   

一类广义Hamilton系统的辛格式     

Zhao Ying  Wang Bin  Ji Zhongzhen 《大气科学进展》2002,19(4):719-726

通过引人泊松括号，分析了无限维Hamilton的性质，并将其推广到广义Hamilton系统，且从理论和实用角度讨论了这类广义Hamilton系统的辛格式构造问题，从而为辛几何算法在一般的时间发展方程的数值求解提供新的具体途径。  相似文献   

Global Bifurcations of Periodic solutions of the Hill Lunar Problem*     

A.J. Maciejewski  S.M. Rybicki 《Celestial Mechanics and Dynamical Astronomy》2001,81(4):279-297

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The Relegation Algorithm     

André Deprit  Jesúus Palacián  Etienne Deprit 《Celestial Mechanics and Dynamical Astronomy》2001,79(3):157-182

The relegation algorithm extends the method of normalization by Lie transformations. Given a Hamiltonian that is a power series = ₀+ ₁+ ... of a small parameter , normalization constructs a map which converts the principal part ₀into an integral of the transformed system — relegation does the same for an arbitrary function [G]. If the Lie derivative induced by [G] is semi-simple, a double recursion produces the generator of the relegating transformation. The relegation algorithm is illustrated with an elementary example borrowed from galactic dynamics; the exercise serves as a standard against which to test software implementations. Relegation is also applied to the more substantial example of a Keplerian system perturbed by radiation pressure emanating from a rotating source.This revised version was published online in October 2005 with corrections to the Cover Date.  相似文献   

Integrability of the Yang-Mills Hamiltonian system     

S. Kasperczuk 《Celestial Mechanics and Dynamical Astronomy》1994,58(4):387-391

This paper considers the integrability of generalized Yang-Mills system with the HamiltonianH _a (p, q)=1/2(p ₁ ² +p ₂ ² +a ₁ q ₁ ² +a ₂ q ₂ ² )+1/4q ₁ ⁴ +1/4a ₃ q ₂ ⁴ + 1/2a ₄ q ₁ ² q ₂ ² . We prove that the system is integrable for the cases: (A)a ₁=a ₂,a ₃=a ₄=1; (b)a ₁=a ₂,a ₃=1,a ₄=3; (C)a ₁=a ₂/4,a ₃=16,a ₄=6. Our main result is the presentation of these integrals. Only for cases A and B does the Yang-Mills Hamiltonian possess the Painlevé property. Therefore the Painlevé test does not take account of the integrability for the case C.  相似文献   

Escapes and Recurrence in a Simple Hamiltonian System     

G. Contopoulos  K. Efstathiou 《Celestial Mechanics and Dynamical Astronomy》2004,88(2):163-183

Many physical systems can be modeled as scattering problems. For example, the motions of stars escaping from a galaxy can be described using a potential with two or more escape routes. Each escape route is crossed by an unstable Lyapunov orbit. The region between the two Lyapunov orbits is where the particle interacts with the system. We study a simple dynamical system with escapes using a suitably selected surface of section. The surface of section is partitioned in different escape regions which are defined by the intersections of the asymptotic manifolds of the Lyapunov orbits with the surface of section. The asymptotic curves of the other unstable periodic orbits form spirals around various escape regions. These manifolds, together with the manifolds of the Lyapunov orbits, govern the transport between different parts of the phase space. We study in detail the form of the asymptotic manifolds of a central unstable periodic orbit, the form of the escape regions and the infinite spirals of the asymptotic manifolds around the escape regions. We compute the escape rate for different values of the energy. In particular, we give the percentage of orbits that escape after a finite number of iterations. In a system with escapes one cannot define a Poincaré recurrence time, because the available phase space is infinite. However, for certain domains inside the lobes of the asymptotic manifolds there is a finite minimum recurrence time. We find the minimum recurrence time as a function of the energy.This revised version was published online in October 2005 with corrections to the Cover Date.  相似文献