This paper addresses a new differential game problem with forward-backward doubly stochastic differential equations. There are two distinguishing features. One is that our game systems are initial coupled, rather than terminal coupled. The other is that the admissible control is required to be adapted to a subset of the information generated by the underlying Brownian motions. We establish a necessary condition and a sufficient condition for an equilibrium point of nonzero-sum games and a saddle...
A graph is said to be symmetric if its automorphism group acts transitively on its arcs. In this paper, all connected valency seven symmetric graphs of order are classified, where , are distinct primes. It follows from the classification that there is a unique connected valency seven symmetric graph of order , and that for odd primes and , there is an infinite family of connected valency seven one-regular graphs of order with solvable automorphism groups, and there are four sporadic ones...
This paper highlights the role of the rank of a differential one-form in the solution of such nonlinear control problems via measurement feedback as disturbance decoupling problem of multi-input single output (MISO) systems. For the later problem, some necessary conditions and sufficient conditions are given.
Global finite-time observers are designed for a class of nonlinear systems with bounded varying rational powers imposed on the increments of the nonlinearities whose solutions exist and are unique for all positive time. The global finite-time observers designed in this paper are with two homogeneous terms. The global finite-time convergence of the observation error system is achieved by combining global asymptotic stability and local finite-time stability.
In this paper differential forms and differential algebra are applied to give a new definition of realization for multivariable nonlinear systems consistent with the linear realization theory. Criteria for the existence of realization and the definition of minimal realization are presented. The relations of minimal realization and accessibility and finally the computation of realizations are also discussed in this paper.
In this paper, we consider two kinds of sampled-data observer design for a class of nonlinear systems. The system output is sampled and transmitted under two kinds of truncations. Firstly, we present definitions of the truncations and the globally uniformly ultimately bounded observer, respectively. Then, two kinds of observers are proposed by using the delayed measurements with these two truncations, respectively. The observers are hybrid in essence. For the first kind of observers, by constructing...
Let be a finite simple undirected graph with a subgroup of the full automorphism group . Then is said to be -transitive for a positive integer , if is transitive on -arcs but not on -arcs, and -transitive if it is -transitive. Let be a stabilizer of a vertex in . Up to now, the structures of vertex stabilizers of cubic, tetravalent or pentavalent -transitive graphs are known. Thus, in this paper, we give the structure of the vertex stabilizers of connected hexavalent -transitive...
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