Abstract: In this paper by using the port-controlled Hamiltonian
(PCH) systems theory, a full-order nonlinear controlled model is first
developed. Then a nonlinear passivity-based robust adaptive control
(PBRAC) of switched reluctance motor in the presence of external
disturbances for the purpose of torque ripple reduction and
characteristic improvement is presented. The proposed controller
design is separated into the inner loop and the outer loop controller.
In the inner loop, passivity-based control is employed by using
energy shaping techniques to produce the proper switching function.
The outer loop control is employed by robust adaptive controller to
determine the appropriate Torque command. It can also overcome the
inherent nonlinear characteristics of the system and make the whole
system robust to uncertainties and bounded disturbances. A 4KW 8/6
SRM with experimental characteristics that takes magnetic saturation
into account is modeled, simulation results show that the proposed
scheme has good performance and practical application prospects.
Abstract: Let G be a Hamiltonian graph. A factor F of G is called
a Hamiltonian factor if F contains a Hamiltonian cycle. In this paper,
two sufficient conditions are given, which are two neighborhood
conditions for a Hamiltonian graph G to have a Hamiltonian factor.
Abstract: We propose the use of magneto-optic Kerr effect (MOKE) to realize single-qubit quantum gates. We consider longitudinal and polar MOKE in reflection geometry in which the magnetic field is parallel to both the plane of incidence and surface of the film. MOKE couples incident TE and TM polarized photons and the Hamiltonian that represents this interaction is isomorphic to that of a canonical two-level quantum system. By varying the phase and amplitude of the magnetic field, we can realize Hadamard, NOT, and arbitrary phase-shift single-qubit quantum gates. The principal advantage is operation with magnetically non-transparent materials.
Abstract: Star graphs are Cayley graphs of symmetric groups of permutations, with transpositions as the generating sets. A star graph is a preferred interconnection network topology to a hypercube for its ability to connect a greater number of nodes with lower degree. However, an attractive property of the hypercube is that it has a Hamiltonian decomposition, i.e. its edges can be partitioned into disjoint Hamiltonian cycles, and therefore a simple routing can be found in the case of an edge failure. The existence of Hamiltonian cycles in Cayley graphs has been known for some time. So far, there are no published results on the much stronger condition of the existence of Hamiltonian decompositions. In this paper, we give a construction of a Hamiltonian decomposition of the star graph 5-star of degree 4, by defining an automorphism for 5-star and a Hamiltonian cycle which is edge-disjoint with its image under the automorphism.
Abstract: In this paper smooth trajectories are computed in the Lie group SO(2, 1) as a motion planning problem by assigning a Frenet frame to the rigid body system to optimize the cost function of the elastic energy which is spent to track a timelike curve in Minkowski space. A method is proposed to solve a motion planning problem that minimize the integral of the square norm of Darboux vector of a timelike curve. This method uses the coordinate free Maximum Principle of Optimal control and results in the theory of integrable Hamiltonian systems. The presence of several conversed quantities inherent in these Hamiltonian systems aids in the explicit computation of the rigid body motions.
Abstract: In the closed quantum system, if the control system is
strongly regular and all other eigenstates are directly coupled to the
target state, the control system can be asymptotically stabilized at the
target eigenstate by the Lyapunov control based on the state error.
However, if the control system is not strongly regular or as long as
there is one eigenstate not directly coupled to the target state, the
situations will become complicated. In this paper, we propose an
implicit Lyapunov control method based on the state error to solve the
convergence problems for these two degenerate cases. And at the same
time, we expand the target state from the eigenstate to the arbitrary
pure state. Especially, the proposed method is also applicable in the
control system with multi-control Hamiltonians. On this basis, the
convergence of the control systems is analyzed using the LaSalle
invariance principle. Furthermore, the relation between the implicit
Lyapunov functions of the state distance and the state error is
investigated. Finally, numerical simulations are carried out to verify
the effectiveness of the proposed implicit Lyapunov control method.
The comparisons of the control effect using the implicit Lyapunov
control method based on the state distance with that of the state error
are given.
Abstract: In this study the regional stability of a rotor system which is supported on rolling bearings with radial clearance is studied. The rotor is assumed to be rigid. Due to radial clearance of bearings and dynamic configuration of system, each rolling elements of bearings has the possibility to be in contact with both of the races (under compression) or lose its contact. As a result, this change in dynamic of the system makes it to be known as switching system which is a type of Hybrid systems. In this investigation by adopting Multiple Lyapunov Function theorem and using Hamiltonian function as a candidate Lyapunov function, the stability of the system is studied. The purpose of this study is to inspect the regional stability of rotor-roller bearing and rotor-ball bearing systems.
Abstract: Mathematical models of dynamics employing exterior calculus are mathematical representations of the same unifying principle; namely, the description of a dynamic system with a characteristic differential one-form on an odd-dimensional differentiable manifold leads, by analysis with exterior calculus, to a set of differential equations and a characteristic tangent vector (vortex vector) which define transformations of the system. Using this principle, a mathematical model for economic growth is constructed by proposing a characteristic differential one-form for economic growth dynamics (analogous to the action in Hamiltonian dynamics), then generating a pair of characteristic differential equations and solving these equations for the rate of economic growth as a function of labor and capital. By contracting the characteristic differential one-form with the vortex vector, the Lagrangian for economic growth dynamics is obtained.
Abstract: The crossed cube is one of the most notable variations of hypercube, but some properties of the former are superior to those of the latter. For example, the diameter of the crossed cube is almost the half of that of the hypercube. In this paper, we focus on the problem embedding a Hamiltonian cycle through an arbitrary given edge in the crossed cube. We give necessary and sufficient condition for determining whether a given permutation with n elements over Zn generates a Hamiltonian cycle pattern of the crossed cube. Moreover, we obtain a lower bound for the number of different Hamiltonian cycles passing through a given edge in an n-dimensional crossed cube. Our work extends some recently obtained results.
Abstract: Traveling salesman problem (TSP) is hard to resolve
when the number of cities and routes become large. The frequency
graph is constructed to tackle the problem. A frequency graph
maintains the topological relationships of the original weighted graph.
The numbers on the edges are the frequencies of the edges emulated
from the local optimal Hamiltonian paths. The simplest kind of local
optimal Hamiltonian paths are computed based on the four vertices
and three lines inequality. The search algorithm is given to find the
optimal Hamiltonian circuit based on the frequency graph. The
experiments show that the method can find the optimal Hamiltonian
circuit within several trials.
Abstract: The hypercube Qn is one of the most well-known
and popular interconnection networks and the k-ary n-cube Qk
n is
an enlarged family from Qn that keeps many pleasing properties
from hypercubes. In this article, we study the panpositionable
hamiltonicity of Qk
n for k ≥ 3 and n ≥ 2. Let x, y of V (Qk
n)
be two arbitrary vertices and C be a hamiltonian cycle of Qk
n.
We use dC(x, y) to denote the distance between x and y on the
hamiltonian cycle C. Define l as an integer satisfying d(x, y) ≤ l ≤ 1
2 |V (Qk
n)|. We prove the followings:
• When k = 3 and n ≥ 2, there exists a hamiltonian cycle C
of Qk
n such that dC(x, y) = l.
• When k ≥ 5 is odd and n ≥ 2, we request that l /∈ S
where S is a set of specific integers. Then there exists a
hamiltonian cycle C of Qk
n such that dC(x, y) = l.
• When k ≥ 4 is even and n ≥ 2, we request l-d(x, y) to be
even. Then there exists a hamiltonian cycle C of Qk
n such
that dC(x, y) = l.
The result is optimal since the restrictions on l is due to the
structure of Qk
n by definition.
Abstract: The deterministic quantum transfer-matrix (QTM)
technique and its mathematical background are presented. This
important tool in computational physics can be applied to a class of
the real physical low-dimensional magnetic systems described by the
Heisenberg hamiltonian which includes the macroscopic molecularbased
spin chains, small size magnetic clusters embedded in some
supramolecules and other interesting compounds. Using QTM, the
spin degrees of freedom are accurately taken into account, yielding
the thermodynamical functions at finite temperatures.
In order to test the application for the susceptibility calculations to
run in the parallel environment, the speed-up and efficiency of
parallelization are analyzed on our platform SGI Origin 3800 with
p = 128 processor units. Using Message Parallel Interface (MPI)
system libraries we find the efficiency of the code of 94% for
p = 128 that makes our application highly scalable.
Abstract: This paper is concerned with the existence and unique¬ness of pseudo-almost periodic solutions to the chaotic delayed neural networks (t)= —Dx(t) ± A f (x (t)) B f (x (t — r)) C f (x(p))dp J (t) . t-o Under some suitable assumptions on A, B, C, D, J and f, the existence and uniqueness of a pseudo-almost periodic solution to equation above is obtained. The results of this paper are new and they complement previously known results.
Abstract: Many well-known interconnection networks, such as kary n-cubes, recursive circulant graphs, generalized recursive circulant graphs, circulant graphs and so on, are shown to belong to the family of cycle composition networks. Recently, various studies about mutually independent hamiltonian cycles, abbreviated as MIHC-s, on interconnection networks are published. In this paper, using an improved construction method, we obtain MIHC-s on cycle composition networks with a much weaker condition than the known result. In fact, we established the existence of MIHC-s in the cycle composition networks and the result is optimal in the sense that the number of MIHC-s we constructed is maximal.
Abstract: A mathematical model for the Dynamics of Economic
Profit is constructed by proposing a characteristic differential oneform
for this dynamics (analogous to the action in Hamiltonian
dynamics). After processing this form with exterior calculus, a pair of
characteristic differential equations is generated and solved for the
rate of change of profit P as a function of revenue R (t) and cost C (t).
By contracting the characteristic differential one-form with a vortex
vector, the Lagrangian is obtained for the Dynamics of Economic
Profit.
Abstract: The balanced Hamiltonian cycle problemis a quiet new topic of graph theorem. Given a graph G = (V, E), whose edge set can be partitioned into k dimensions, for positive integer k and a Hamiltonian cycle C on G. The set of all i-dimensional edge of C, which is a subset by E(C), is denoted as Ei(C).
Abstract: The position and momentum space information entropies
of hydrogen atom are exactly evaluated. Using isospectral
Hamiltonian approach, a family of isospectral potentials is constructed having same energy eigenvalues as that of the original potential. The information entropy content is obtained in position
space as well as in momentum space. It is shown that the information
entropy content in each level can be re-arranged as a function of deformation parameter.