We present an efficient computational procedure for finite abstraction of discrete-time mixed monotone systems by considering a rectangular partition of the state space. Mixed monotone systems are decomposable into increasing and decreasing components, and significantly generalize the well known class of monotone systems. We tightly overapproximate the one-step reachable set from a box of initi...

This paper presents a framework for situated design optimization that expands the traditional view of design optimization. It is based on the notion of interaction providing the potential for modifications of various aspects of the optimization process: problem formulation, the optimization tool, the designer and ultimately the result. In contrast to other approaches, these modifications can dr...

: This paper deals with the comparison between two control strategies for the optimal operation of Activated Sludge Processes (ASPs). The first approach describes an industrial control strategy composed of two decentralized Proportional Integral controllers (PIs) while the second approach is based on a state space model of the system together with the Disturbance Modeling Principle (Johnson, 19...

A direct and inverse scattering theory on the full line is developed for a class of firstorder selfadjoint 2n • 2n systems of differential equations with integrable potential matrices. Various properties of the corresponding scattering matrices including unitarity and canonical Wiener-Hopf factorization are established. The Marchenko integral equations are derived and their unique solvability i...

This paper treats absorption problems for the one-dimensional quantum walk determined by a 2 × 2 unitary matrix U on a state space {0, 1, . . . , N} where N is finite or infinite by using a new path integral approach based on an orthonormal basis P,Q,R and S of the vector space of complex 2× 2 matrices. Our method studied here is a natural extension of the approach in the classical random walk.

α∈R (∣∣〈ρk, α∨〉+ kα + 1 2kα/2∣∣)! (∣∣〈ρk, α∨〉+ 1 2kα/2∣∣)! • Also in 1982, A. Koranyi uses the Selberg formula to compute the volumes of bounded symmetric domains. • In 1987, K. Aomoto studies a slight generalization of the Selberg integral arising from work on Fock space representations of the Virasoro algebra. Here a connection with hypergeometric functions, specifically Jacobi polynomials is...

A theoretical framework that is based on a generalization of state space systems is proposed. The resulting transfer function connection matrix model describes both subsystem interconnections and dynamics in an integrated mathematical formulation, yet ensures that the dynamic and the connection aspects of the system are separated into two sets of equations that are relatively independent. The s...

This paper follows 3] where a new notion of state aggregation for nite machines was introduced via the concept of the dynamical consistency (DC) relation between the blocks of states in any given state space partition. This formulation results in a deenition of high level dynamics on the nite (partition) machine M whose states correspond to the given partition elements. This paper treats the mo...

In this paper a quantum stochastic integral representation theorem is obtained for unbounded regular martingales with respect to multidimensional quantum noise. This simultaneously extends results of Parthasarathy and Sinha to unbounded martingales and those of the author to multidimensions.

In this article it is shown how non-holonomic constraints can be included in the formulation of the dynamic equations of flexible multibody systems. The equations are given in state space form with the degrees of freedom, their derivatives and the kinematic coordinates as state variables, which circumvents the use of Lagrangian multipliers. With these independent state variables for the system ...