cpn2Lin

Computes the Jacobian of a CPN1 MTI object around an operating point

Contents

Syntax

  cpn2Lin(obj,x)

Description

cpn2Lin(obj,x) Computes the Jacobian of an explicit multilinear model stored in the CP-decomposed norm-1 format obj around an operating point x. For further information on the implementation of the algorithm see [1].

Input Arguments

obj: CPN1 object

x : operating point, scalar or vector

Output Arguments

J: Jacobian matrix

Example:

Assume we have the following thrird-order explicit MTI model $\dot{\mathbf{x}}=\left(\begin{array}{cc} x_2 + x_1x_2\\ 2x_2 + 3x_3 + 2x_1x_2 - 3x_1x_3 \\ 4x_3 - 4x_1x_3 \end{array}\right)$. We write the explicit MTI model as a CPN1 object by defining the structural matrix S to form the monomial

    S=[0.5 -0.5; 1 0; 0 1];

and the parameter matrix with corresponding coefficients of the summands:

    phi=[2 0; 4 6; 0 8];

Then we can create explicit MTI model as a CPN1 object

    obj=CPN1(S,phi);

and assume the operating point

    x_op=[-1;1;3];

Then we can calcute the Jacobian

    J = cpn2Lin(obj,x_op)
J =

     1     0     0
    -7     0     6
   -12     0     8

References

[1] C. Kaufmann, D. Crespí, G. Lichtenberg, G. Pangalos, and C. Cateriano Yáñez, "Efficient Linearization of Explicit Multilinear Systems using Normalized Decomposed Tensors," IFAC-PapersOnLine, vol. 56, no. 2, pp. 7312–7317, Jan. 2023, doi: https://doi.org/10.1016/j.ifacol.2023.10.344.

See also

jacobian, cpn2LinSparse, linearize