【正文】 temperature humidity and CO2 concentration of the inside air the amount of water and fertilizers supplied by irrigation pests and diseases and culture labors such as pruning and pesticide treatments among others A greenhouse is ideal for crop growing since it constitutes a closed environment in which climatic and Fertilizer irrigation variables can be controlled Climate and Fertilizer irrigation are two independent systems with different control problems and objectives Empirically the water and nutrient requirements of the different crop species are known and in fact the first automated systems were those that control these variables On the other hand the market price fluctuations and the environment rules to improve the wateruse efficiency or reduce the fertilizer residues in the soil such as the nitrate contents are other aspects to be taken into account Therefore the optimal production process in a greenhouse agrosystem may be summarized as the problem to reaching the following objectives an optimal crop growth a bigger production with a better quality reduction of the associate costs mainly fuel electricity and fertilizers reduction of residues mainly pesticides and ions in soil and the improvement of the water use efficiency Many approaches have already been applied to this problem for instance dealing with the management of greenhouse climate in the optimal control field eg Challa and van 2 MO optimization in crop production An MO optimization problem can be defined as finding a vector of decision variables which satisfies constraints and optimizes a vector whose elements represent objective functions The problems characterized by peting measures of performance or objectives are considered as MO optimization problems where n objectives Ji p in the vector of variables p∈ P are simultaneously minimized or imized The problem often has no optimal solution that simultaneously optimize all objectives but it has a set of suboptimal or nondominated alternative solutions known as a Pareto optimal set where a promise solution may be selected from that set by a decision process Different criteria such as physical yield crop quality product quality timing of the production process or production costs and risks can be formulated within greenhouse crop management These criteria will often give rise to controversial climate and 肥料灌溉 requirements which have to be solved explicitly or implicitly at the socalled tactical level where the grower has to make decisions about several conflicting objectives The solution of this MO optimization process p∈ P is the optimal diurnal and nocturnal present and future reference trajectories of temperature Xta and electrical conductivity XEC for the rest of the crop cycle That is where is a vector of the inside air temperature along the optimization intervals and is a vector of the electrical conductivity EC along the optimization intervals Notice that the plants grow under the influence of the PAR radiation diurnal conditions performing the photosynthesis process Furthermore the temperature influences the speed of sugar production by photosynthesis and thus radiation and temperature have to be in balance in the way that a higher radiation level corresponds to a higher temperature So under diurnal conditions it is necessary to maintain the temperature at a high level In nocturnal conditions the plants are not active the crop does not grow so it is not necessary to maintain such a high temperature For this reason two temperature setpoints are usually considered diurnal and nocturnal It is necessary to highlight that although the process optimization is presented in continuous time it is solved in discrete time intervals for an optimization horizon Nf k this horizon is variable and represents the remaining intervals until the end of the agricultural season Thus the solution vectors and are obtained as where k is the current discrete time instant Notice that for the proposed optimization problem a greenhouse crop production model is required in order to estimate the inner climate behavior and the crop growth through the different steps of the algorithm and relate the different function objectives to the decision variables The dynamic behavior of the microclimate inside the greenhouse is a bination of physical processes involving energy transfer radiation and heat and mass balance water vapor fluxes and CO2 concentration On the other hand the crop growth and yield mainly depend among other conditions such as irrigation and fertilizers on the inside temperature of the greenhouse the PAR radiation and the CO2 concentration Thus both climate conditions and crop growth influence each other and their dynamic behavior can be characterized by different time scales Hence the crop growth in response to the environment can be described by