This manuscript is divided into two main parts, associated with two quite different types of applications. In the first part, which includes the first two chapters, I am interested in control and estimation problems in quantum physics and in the second part (the third chapter of the manuscript), I study the propagation of the electrical waves along the classical wires in a network of transmission lines, and I consider some parameter identification problems. In the first chapter we study the problem of motion planning for closed quantum systems modeled by bilinear Schrödinger equations. We then demonstrate some approximate stabilization results in the case of an infinite quantum potential well, as well as for the case of a decaying potential. In both cases, the lack of pre-compactness of trajectories in appropriate functional spaces leads us to propose Lyapunov-based methods that avoid mass-loss type phenomena at infinity. In the second chapter we study the problem of stabilization of quantum systems under observation. This observation requires opening the system to its environment. Relevant models for the evolution of such systems are stochastic models based on quantum Monte Carlo trajectories. We study some stabilization problems that are raised by physical experiments. Finally, in Chapter 3 we consider the problem of estimating parameters for a network of electrical wires. For this purpose, we consider two approaches: the time-domain approach and the frequency-domain approach. In the time-domain approach, we consider the simplest network that consists of a single transmission line and we propose an algorithm for the identification of associated wave equation which is based on the application of asymptotic observers. In the frequency domain approach, we consider a more complicated star-shaped network. We then propose some identifiability results based on inverse scattering techniques.
