Design of of model-based controllers via parametric programming

Imperial Users onl

Nonautonomous Hamiltonians

We present a theory of resonances for a class of non-autonomous Hamiltonians to treat the structural instability of spatially localized and time-periodic solutions associated with an unperturbed autonomous Hamiltonian. The mechanism of instability is radiative decay, due to resonant coupling of the discrete modes to the continuum modes by the time-dependent perturbation. This results in a slow transfer of energy from the discrete modes to the continuum. The rate of decay of solutions is slow and hence the decaying bound states can be viewed as metastable. The ideas are closely related to the authors' work on (i) a time dependent approach to the instability of eigenvalues embedded in the continuous spectra, and (ii) resonances, radiation damping and instability in Hamiltonian nonlinear wave equations. The theory is applied to a general class of Schr\"odinger equations. The phenomenon of ionization may be viewed as a resonance problem of the type we consider and we apply our theory to find the rate of ionization, spectral line shift and local decay estimates for such Hamiltonians.Comment: To appear in Journal of Statistical Physic

Statistical modelling of algorithms for signal processing in systems based on environment perception

One cornerstone for realising automated driving systems is an appropriate handling of uncertainties in the environment perception and situation interpretation. Uncertainties arise due to noisy sensor measurements or the unknown future evolution of a traffic situation. This work contributes to the understanding of these uncertainties by modelling and propagating them with parametric probability distributions