The typical formulation of an optimal control or dynamic optimization problem is to optimize a scalar performance functional; less frequently, also vectors of performance functionals are considered in multiobjective optimization. However, there are many practical problems where the objectives are stated in terms of desirable trajectories. If the goal would be to approximate the desired trajectory from both sides, then the problem could be equivalently stated as a typical approximation problem. However, in many cases the desired trajectories have the meaning of aspiration levels: if possible, they should be exceeded.

The paper presents a mathematical formulation of a multiobjective trajectory optimization problem, an interpretation as a semi-regularization procedure for ill-posed problems, and examples of actual applications.