This paper is an attempt to tackle the problem of the characterization of the response of a dynamical system submitted to inputs represented by intervals, its initial state and some of its parameters also possibly being described in that way. Such a problem may occur when some parts of a complex device are modelized numerically and receive as inputs some signals provided by the qualitative simulation of other—often ill-known—parts. The proposed approach imbeds it in optimal control problems with constraints. This allows a full treatment of continuous time-invariant systems and leads to a well-posed optimization problem in the general case. Some application results for elementary systems with interval-valued parameters are given, and a first stage in the treatment of QSIM-like inputs is discussed. All the required theoretic background in optimal control theory is detailed so that the paper is self-contained.