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The primary focus of this thesis is the numerical investigation of chaos in Hamiltonian models describing charged particle orbits in plasma, star motions in barred galaxies, and orbits' diffusion in multidimensional maps. We systematically…

This paper considers Hamiltonian identification for a controllable quantum system with non-degenerate transitions and a known initial state. We assume to have at our disposal a single scalar control input and the population measure of only…

Patterns arise spontaneously in a range of systems spanning the sciences, and their study typically focuses on mechanisms to understand their evolution in space-time. Increasingly, there has been a transition towards controlling these…

We present a method for the computation of the Generalized Alignment Index (GALI), a fast and effective chaos indicator, using a multi-particle approach that avoids variational equations. We show that this approach is robust and accurate by…

We reveal the escape mechanism of orbits in a Hamiltonian system with four exit channels composed of two-dimensional perturbed harmonic oscillators. We distinguish between trapped chaotic, non-escaping regular and escaping orbits by…

This paper investigates a distributed formation tracking control law for large-scale networks of mechanical systems. In particular, the formation network is represented by a directed communication graph with leaders and followers, where…

In real-world robotics applications, accurate models of robot dynamics are critical for safe and stable control in rapidly changing operational conditions. This motivates the use of machine learning techniques to approximate robot dynamics…

We consider the motion of a particle on a surface which is a small perturbation of the standard sphere. One may qualitatively describe the motion by means of a precessing great circle of the sphere. The observation is employed to derive a…

The question of open-loop control in the Gaussian regime may be cast by asking which Gaussian unitary transformations are reachable by turning on and off a given set of quadratic Hamiltonians. For compact groups, including finite…

The escape mechanism of orbits in a star cluster rotating around its parent galaxy in a circular orbit is investigated. A three degrees of freedom model is used for describing the dynamical properties of the Hamiltonian system. The…

A method to reduce or enhance chaos in Hamiltonian flows with two degrees of freedom is discussed. This method is based on finding a suitable perturbation of the system such that the stability of a set of periodic orbits changes (local…

Robust control design for quantum systems has been recognized as a key task in the development of practical quantum technology. In this paper, we present a systematic numerical methodology of sampling-based learning control (SLC) for…

We consider finite-dimensional Markovian open quantum systems, and characterize the extent to which time-independent Hamiltonian control may allow to stabilize a target quantum state or subspace and optimize the resulting convergence speed.…

Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…

Supersymmetry allows one to build a hierarchy of Hamiltonians that share the same spectral properties and which are pairwise connected through common superpotentials. The iso-spectral properties of these Hamiltonians imply that the dynamics…

The basic module for the solution of the minimum time optimal control of a car-like vehicle is herein presented. The vehicle is subject to the effect of laminar (linear) and aerodynamic (quadratic) drag, taking into account the asymmetric…

We investigate the possibility to control localization properties of the asymptotic state of an open quantum system with a tunable synthetic dissipation. The control mechanism relies on the matching between properties of dissipative…

The first-order optimality conditions for a generic nonlinear optimization problem are generated as part of the terminal transversality conditions of an optimal control problem. It is shown that the Lagrangian of the optimization problem is…

By combining a standard symmetric, symplectic integrator with a new step size controller, we provide an integration scheme that is symmetric, reversible and conserves the values of the constants of motion. This new scheme is appropriate for…

Synchronization forms the basis of many coordination phenomena in natural systems, enabling them to function cohesively and support their fundamental operations. However, there are scenarios where synchronization disrupts a system's proper…