where t h is a short-term finite horizon and v f are the short-term weather predictions, ^ xðs iþ1 Þ, i ¼ 0; 1; 2; . . . is the state estimate from the model and the measurements at each sampling instant s i in which all the measurements and control
are updated and a new optimal control problem is solved. It is apparent that
t 0 ¼ s iþ1 is required for i ¼ 0; 1; 2. . . and also the final time is updated using
t f ¼ s iþ1 þ t h . Therefore, a new optimal control problem is solved at each time
period T ¼ s iþ1 À s i . Tap (2000) applied a gradient-based algorithm to solve this
RHOC each minute. More recently, an RHOC has been applied to control a solar
greenhouse (van Ooteghem 2007) and the nutrients supply to greenhouse tomatoes
(van Straten et al. 2006). An extensive discussion on the so-called closed-loop
optimal control in greenhouse has been elaborated recently (van Straten et al.
2011).
14.2.4 Model Predictive Control
The model predictive control (MPC) approach has been applied to the greenhouse
system recently. According to the theory of model predictive control (Camacho
and Bordons 1998), the three main components of an MPC required to derive an
optimal control law of the system are a prediction model, an objective or cost
function, and an optimization algorithm. There are several options for the components of an MPC. In the case of the greenhouse system some researchers have
applied state-space models similar to the ones required in optimal control, for the
greenhouse climate (Blasco et al. 2007; Piñon et al. 2005; El Ghoumari et al.
2005), and autoregressive models (ARX) with external inputs (Coelho et al. 2005).
Regarding the cost function it has included the optimization of energy and water
consumption in the greenhouse (Blasco et al. 2007). Objective functions including
only the greenhouse climate have been used by other researchers. However, no one
has so far used a model of the crop growth and development. Several optimization
algorithms such as gradient-based methods (Piñon et al. 2005; El Ghoumari et al.
2005), but also global optimization approaches such as genetic algorithms (Blasco
et al. 2007) and particle swarm optimization (Coelho et al. 2005) have been
applied to solve the MPC in the greenhouse context. A model-based predictive
control was tested in order to optimize the efficiency of two heating systems in a
greenhouse: aerial pipes with hot water and air-fan heater. It was found that using
linearized models of the system around the predefined set points and a generalized
predictive control strategy, the performance was improved (Ramírez-Arias et al.
2005). Recently, a nonlinear model predictive control strategy was designed for
temperature control in a greenhouse using natural ventilation (Gruber et al. 2011).
The control strategy is based on a second-order Volterra series model coming from
experimental input/output data of a greenhouse.
14 Control Strategies of Greenhouse Climate
407
are updated and a new optimal control problem is solved. It is apparent that
t 0 ¼ s iþ1 is required for i ¼ 0; 1; 2. . . and also the final time is updated using
t f ¼ s iþ1 þ t h . Therefore, a new optimal control problem is solved at each time
period T ¼ s iþ1 À s i . Tap (2000) applied a gradient-based algorithm to solve this
RHOC each minute. More recently, an RHOC has been applied to control a solar
greenhouse (van Ooteghem 2007) and the nutrients supply to greenhouse tomatoes
(van Straten et al. 2006). An extensive discussion on the so-called closed-loop
optimal control in greenhouse has been elaborated recently (van Straten et al.
2011).
14.2.4 Model Predictive Control
The model predictive control (MPC) approach has been applied to the greenhouse
system recently. According to the theory of model predictive control (Camacho
and Bordons 1998), the three main components of an MPC required to derive an
optimal control law of the system are a prediction model, an objective or cost
function, and an optimization algorithm. There are several options for the components of an MPC. In the case of the greenhouse system some researchers have
applied state-space models similar to the ones required in optimal control, for the
greenhouse climate (Blasco et al. 2007; Piñon et al. 2005; El Ghoumari et al.
2005), and autoregressive models (ARX) with external inputs (Coelho et al. 2005).
Regarding the cost function it has included the optimization of energy and water
consumption in the greenhouse (Blasco et al. 2007). Objective functions including
only the greenhouse climate have been used by other researchers. However, no one
has so far used a model of the crop growth and development. Several optimization
algorithms such as gradient-based methods (Piñon et al. 2005; El Ghoumari et al.
2005), but also global optimization approaches such as genetic algorithms (Blasco
et al. 2007) and particle swarm optimization (Coelho et al. 2005) have been
applied to solve the MPC in the greenhouse context. A model-based predictive
control was tested in order to optimize the efficiency of two heating systems in a
greenhouse: aerial pipes with hot water and air-fan heater. It was found that using
linearized models of the system around the predefined set points and a generalized
predictive control strategy, the performance was improved (Ramírez-Arias et al.
2005). Recently, a nonlinear model predictive control strategy was designed for
temperature control in a greenhouse using natural ventilation (Gruber et al. 2011).
The control strategy is based on a second-order Volterra series model coming from
experimental input/output data of a greenhouse.
14 Control Strategies of Greenhouse Climate
407