Minimum attention control

In this paper we consider the question of how to trade-off the complexity of implementing a control law against the performance of the control system. We propose a measure of complexity and formulate optimization problems involving both a measure of the desirability of the trajectories and the difficulty of implementing the control law. By introducing criteria of the type proposed here it is possible to strike a balance between the performance of the system and the difficulty involved in implementing the control. The optimization problems coming from this formulation are similar to those arising in the variational description of fields in physics.