We propose in this paper a new method for the quantisation of systems with first-class constraints. This method is a combination of the coherent-state-path-integral quantisation developed by Klauder, with the ideas of reduced state space quantisation. The key idea is that the physical Hilbert space may be defined by a coherent-state path-integral on the reduced state space and that the metric o...

In Chapter 5, we discussed how to design digital controllers using transform techniques, methods now commonly designated as "classical design." The goal of this chapter is to solve the identical problem using the state-space formulation. The difference in the two approaches is entirely in the design method; the end result, a set of difference equations providing control, is identical. In fact, ...

Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert space, whereas in phase space they are described by real, true representations. Equivalence of the formulations requires that the former representations can b...

In this paper firstly, the dynamics of LC-circuits without excess elements is expressed in terms of contact systems encompassing in a single formulation the Hamiltonian formulation and the pseudo-gradient formulation called the Brayton-Moser equations. Indeed the contact formulation encompasses both the Hamiltonian system and its the adjoint variational system. Secondly we express the dynamics ...

The polarized Gowdy T 3 vacuum spacetimes are characterized, modulo gauge, by a " point particle " degree of freedom and a function ϕ that satisfies a linear field equation and a non-linear constraint. The quantum Gowdy model has been defined by using a representation for ϕ on a Fock space F. Using this quantum model, it has recently been shown that the dynamical evolution determined by the lin...

To enable the use of traditional tools for analysis of multivariable controllers such as model predictive control (MPC), we develop a state space formulation for the resulting controller for MPC without constraints or assuming that the constraints are not active. Such a derivation was not found in the literature. The formulation includes a state estimator. The MPC algorithm used is a receding h...