model.options.IMODE defines the problem type. Each problem type treats variable classes differently and builds equations behind the scenes to meet the particular objective inherit to each problem type. The modes are:
|Non-Dynamic||1 Sys of Eq||2 MPU||3 RTO|
|Dynamic Simultaneous||4 ODE Solver||5 MHE||6 MPC|
|Dynamic Sequential||7 ODE Solver||8 MHE||9 MPC|
Ordinary differential equations are specified by differentiation a variable with the dt() method. For example, velocity v is the derivative of position x:
m.Equation( v == x.dt() )
Discretization is determined by the model time attribute. For example, m.time = [0,1,2,3] will discretize all equations and variable at the 4 points specified. Only ordinary differential equations discretized by time are available internally. Other discretization must be performed manually.
Simultaneous methods use orthogonal collocation on finite elements to implicitly solve the DAE system. Non-simulation simultaneous methods (modes 5 and 6) simultaneously optimize the objective and implicitly calculate the model/constraints. Simultaneous methods tend to perform better for problems with many degrees of freedom.
Sequential methods separate the NLP optimizer and the DAE simulator. Sequential methods will satisfy the differential equations, even when the solver is unable to find a feasible optimal solution.
Non-Dynamic modes sets all differential terms to zero to calculate steady-state conditions.
Simulation just solves the given equations. These modes provide little benefit over other ODE integrator packages. However, successful simulation of a model within GEKKO helps debug the model and greatly facilitates the transition from model development/simulation to optimization.
Model Parameter Update is parameter estimation for non-dynamic conditions. This mode implements the special variable types as follows:
Moving Horizon Estimation is for dynamic estimation, both for states and parameter regression. The horizon to match is the discretized time horizon of the model m.time. m.time should be discretized and regular intervals. New measurements are added at the end of the horizon m.time[-1] and the oldest measurements (m.time) is dropped off.
m.options.TIMESHIFT enables automatic shifting of all variables and parameters with each new solve of a model. The frequency of new measurements should match the discretization of m.time.
Fixed variables are fixed through the horizon.
STATUS adds one degree of freedom for the optimizer, i.e. a fixed parameter for fit.
FSTATUS allows giving a fixed measurement.
Manipulated variables are like FVs, but discretized with time.
STATUS adds one degree of freedom for each time point for the optimizer, i.e. a dynamic parameter for fit.
FSTATUS allows giving a measurements for each time.
Controlled variables are the measurement to match.
If FSTATUS is on (FSTATUS=1), an objective function is added to minimize the model prediction to the measurements. The error is either squared or absolute depending on if m.options.EV_TYPE is 2 or 1, respectively. FSTATUS enables receiving measurements through the MEAS attribute.
If m.options.EV_TYPE = 1, CV.MEAS_GAP=v will provide a dead-band of size v around the measurement to avoid fitting to measurement noise.
STATUS is ignored in MHE.
Model Predictive Control
Controlled variables are the objective to match. When STATUS=1 for a CV, the objective includes a minimization between model predictions and the setpoint.
If m.options.CV_TYPE=1, the objective is an l1-norm (absolute error) with a dead-band. The setpoint range should be specified with SPHI and SPLO. If m.options.CV_TYPE=2, the objective is an l2-norm (squared error). The setpoint should be specified with SP.