"There are two main goals that must be achieved in any physical implementation of Quantum Information. The first one is the ability to perform a desired unitary operation on a selected quantum system with very high fidelity, the second is to preserve system coherence while performing the operation. The aim of the proposed project is to investigate how to accomplish both tasks by means of Optimal Control Theory. Indeed this is a relatively new tool to be exploited within the Quantum Information perspective.Our goal is to derive a general theoretical framework for the application of Optimal Control to open quantum systems used in Quantum Information. The Surrogate Hamiltonian method developed within the context of chemical physics by C. Koch (Freie Universitity, Berlin) allows to investigate decoherence resorting neither to weak coupling, nor to the Markovian approximation, and to take into account a microscopic description of the bath. We will use this approach to study how decoherence affects Quantum Information processes, such as single and two-qubit gates, for different strength and type of system-bath coupling. The environment will be described in terms of a spin bath, as it allows for a more general and accurate description of decoherence processes than a bath of harmonic oscillators. After having formulated a general model of spin-bath decoherence for a quantum register, we will investigate control strategies allowing to perform a selected quantum operation while balancing decoherence effects, for different dynamical regimes. The understandings of control achieved in the abstract treatment will be applied to trapped ions, one of the most promising realisations of Quantum Information. Extensions to further approaches that are formally related to the trapped ion Hamiltonian such as the Jaynes-Cummings Hamiltonian will be explored."