Criterion Function ODEVAL

Syntax

=ODEVAL(col1, exprn, opr, pt, [options])


  • Use ODEVAL to compute a single value from a solution array obtained by any of the ordinary differential equations solvers. ODEVAL computes the value using a specified calculus operation including interpolation, differentiation or integration.

  • In a dynamical optimization problem, ODEVAL can be used to define dynamic constraints on the solution array of the ordinary differential equations solver. A constraint formula is typically defined as the difference between the computed value by ODEVAL and a target value. The constraint formulas are input to NLSOLVE.

Required Inputs

col1 a reference to the first column in the solution array. This defines the time or spatial range for the calculus operation.

You may select a sub range of column 1 although this reduces the accuracy of the calculus operation.

exprn a reference to the operand for the calculus operation.

The reference may be to single variable or a formula implicating mulutiple variables. If your operand is a single variable, just pass its name in this argument.

opr a string value specifying the calculus operation to perform. Supported values are INTERP, DERIV, and INTEG.

pt defines the point of interpolation or differentiation for the calculus operation.

Not required if the calculus operation is INTEG.

Optional Inputs

order controls the calculus operation as described below:

  • If opr is INTERP or INTEG
    Enter 1 to use linear splines, or 3 to use cubic splines. Default is 3.

  • If opr is DERIV
    Enter the derivative order: 1, 2 or 3. Default is 1.

Consider the array result shown in Table 1 from the simulation of an initial value pendulum problem with IVSOLVE

With the following parameters:


Table 1
A B C
6 T1 theta omega
7 0 0 0.1
8 0.066667 0.006619 0.097835
9 0.133333 0.012949 0.091411
10 0.2 0.018719 0.081034
11 0.266667 0.023675 0.067133
12 0.333333 0.027606 0.050324
13 0.4 0.030336 0.031328
14 0.466667 0.031752 0.010976
15 0.533333 0.031789 -0.00985
16 0.6 0.030448 -0.03025
17 0.666667 0.027784 -0.04934
18 0.733333 0.023917 -0.06629
19 0.8 0.01901 -0.08036
20 0.866667 0.013279 -0.09095
21 0.933333 0.006971 -0.09759
22 1 0.000361 -0.09999

You can use ODEVAL() to extract or compute values of interest from the simulation result:

Objective Formula Result
Find derivative of omega at t = 0.5 =ODEVAL(A7:A22,omega,"deriv",0.5) -0.313005332
Integrate theta from 0 to 1 =ODEVAL(A7:A22,theta,"integ") 0.020409729
Interpolate theta at t = 0.5 =ODEVAL(A7:A22,theta,"interp",0.5) 0.031944316
Integrate the square of omega from 0 to 1 =ODEVAL(A7:A22,H21,"integ") 0.004982081
H21 =omega^2  

When solving a parametrized dynamical optimization problem, ODEVAL is used to define constraints on the dynamical system solution typically as the difference between a computed value by ODEVAL and a target value. You can then use the nonlinear solver NLSOLVE to find optimal values for the design parameters that will minimize the differences your defined constraints.

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