The quaternionic Grassmannian HGr(r, n) is the affine open subscheme of the ordinary Grassmannian parametrizing those 2r-dimensional subspaces of a 2n-dimensional symplectic vector space on which the symplectic form is nondegenerate. In particular there is HP = HGr(1, n+1). For a symplectically oriented cohomology theory A, including oriented theories but also hermitian K-theory, Witt groups an...

the objective of this article is to derive the necessary optimality conditions, known as pontryagin's minimum principle, for fuzzy optimal control problems based on the concepts of differentiability and integrability of a fuzzy mapping that may be parameterized by the left and right-hand functions of its $alpha$-level sets.

We study optimal control problems for hyperbolic equations (focusing on the multidimensional wave equation) with control functions in the Dirichlet boundary conditions under hard/pointwise control and state constraints. Imposing appropriate convexity assumptions on the cost integral functional, we establish the existence of optimal control and derive new necessary optimality conditions in the i...

This article treats two problems dealing with control of linear systems in the presence of a jammer that can sporadically turn off the control signal. The first problem treats the standard reachability problem, and the second treats the standard linear quadratic regulator problem under the above class of jamming signals. We provide necessary and sufficient conditions for optimality based on a n...

We study optimal control problems for hyperbolic equations (focusing on the multidimensional wave equation) with control functions in the Dirichlet boundary conditions under hard/pointwise control and state constraints. Imposing appropriate convexity assumptions on the cost integral functional, we establish the existence of optimal control and derive new necessary optimality conditions in the i...

This paper presents a global optimization approach to solving linear non-quadratic optimal control problems. The main work is to construct a differential flow for finding a global minimizer of the Hamiltonian function over a Euclid space. With the Pontryagin principle, the optimal control is characterized by a function of the adjoint variable and is obtained by solving a Hamiltonian differentia...

It seems intuitively reasonable that Gibbs' variational principle de­ termining the conditions of heterogeneous equilibrium can be gener­ alized to nonequilibrium conditions. That is, a nonequilibriurn steady state should be the one that makes some kind of generalized-entropy production stationary; and even in the presence of irreversible fluxes, the condition for migrational equilibrium should...

We provide a new, simpler, and more direct proof of the well known fact that for autonomous optimal control problems the Pontryagin extremals evolve on a level surface of the respective Pontryagin Hamiltonian. Given sets Ω ⊆ R and F ⊆ R, constants a < b, and two continuous functions L(x, u) : R × Ω → R and φ(x, u) : R ×Ω → R with continuous derivatives with respect to x, we define the autonomou...