On evaluating optimality losses of greenhouse climate controllers

Optimal operation strategies for greenhouse crop cultivation can be computed with open loop dynamic optimization. These solutions are obtained off-line, and are valid under nominal weather conditions only. On-line, feed-back control is needed to cope with deviations from the nominal weather. One of the issues in practical control is how to link the off-line nominal solution to on-line control. One option is to use a receding horizon controller with the same goal function as used off-line, but enhanced with a term based on the co-state of the slow crop states to encapsulate the long term goals. Loss measures are introduced to evaluate this solution against various other approximate solutions proposed in the literature. To our knowledge this is the first time that various sub-optimal solutions are clearly listed and analysed. A simplified, but transparent, example is used to illustrate the various losses. One of the results is that receding horizon optimal control with an adapted goal function is superior to other more common control solutions