This paper presents a generalization of the minimax state estimation approach for singular linear Differential-Algebraic Equations (DAE) with uncertain but bounded input and observation’s noise. We apply generalized Kalman Duality principle to DAE in order to represent the minimax estimate as a solution of a dual control problem for adjoint DAE. The latter is then solved converting the adjoint ...

We define an invariant of torsors under adjoint linear algebraic groups of type Cn—equivalently, central simple algebras of degree 2n with symplectic involution—for n divisible by 4 that takes values in H(k, μ2). The invariant is distinct from the few known examples of cohomological invariants of torsors under adjoint groups. We also prove that the invariant detects whether a central simple alg...

We give a lower bound for the essential dimension of a split simple algebraic group of “adjoint” type over a field of characteristic 2. We also compute the essential dimension of orthogonal and special orthogonal groups in characteristic 2.

Abstract Infinitesimal symmetries of a partial differential equation (PDE) can be defined algebraically as the solutions linearisation (Frechet derivative) holding on space to PDE, and they are well-known comprise linear having structure Lie algebra. Solutions adjoint PDE called adjoint-symmetries. Their algebraic for general systems is studied herein. This motivated by correspondence between v...

The paper investigates boundary optimal controls and parameter estimates to the well-posedness nonlinear model of dehydratation of thermic problems. We summarize the general formulations for the boundary control for initial-boundary value problem for nonlinear partial differential equations modeling the heat transfer and derive necessary optimality conditions, including the adjoint equation, fo...

We characterize possible spectra of rank-one perturbations B a self-adjoint operator A with discrete spectrum and, in particular, prove that the may include any number real or non-real eigenvalues arbitrary algebraic multiplicity

In this paper, we present an explicit one-step method for solving periodic initial value problems of second order ordinary differential equations. The method is P -stable, and of first algebraic order and high phase-lag order. To improve the algebraic order, we give a composition second order scheme with the proposed method and its adjoint. We report some numerical results to illustrate the eff...

We present and discuss the definition of the adjoint and dual of a switched differential-algebraic equation. Based on this definition, we prove duality between controllability/reachability and determinability/observability for switched differential-algebraic equations. The switched system is viewed as a (linear) time-varying system, i.e. the switching signal is assumed to be fixed. In particula...

Complex symplectic spaces, and their Lagrangian subspaces, are defined in accord with motivations from Lagrangian classical dynamics and from linear ordinary differential operators; and then their basic algebraic properties are established. After these purely algebraic developments, an Appendix presents a related new result on the theory of self-adjoint operators in Hilbert spaces, and this pro...