Optimal control for maximal accuracy with an arbitrary control space metric

The finite dimensional theory of minimal sensitivity design is extended to infinite dimensions. The high accuracy control of the state vector of a system is a practical application of this problem. First the discrete time high accuracy control problem is solved for a single input system with fixed bound on the relative error of the control. The optimal steering is characterized as one that is zero for the longest possible time. The continuous time problem is solved via the maximum principle and the example of the rocket car with relative control error is solved in detail. The maximum accuracy and the accuracy/time problem have a solution of bang-zero-bang type. The accuracy/energy problem also exhibits a coasting period