A controller, particularly for setting a desired or randomized polarization state of an output light beam derived from an input, has more than the minimum number of controllable optical elements needed to determine the state of the output. The controller applies control input values to obtain a desired output state. The controller also selects among plural alternative sets of control values that could obtain the desired output state, so as to minimize other error conditions. The concurrent error conditions can be associated finite control range limits, for example to keep the input values near a middle of their ranges. Additional error conditions can include minimizing the incremental change in the values from one set to the next. The control is particularly useful to avoid problems associated with using finite range control elements such as liquid crystals for differential retardation or orthogonal light components, when controlling an endless or periodic parameter such as polarization. In the preferred arrangement, six retardation cells are used to control two independent variables determining polarization state.