Wolfram Language Paclet Repository

Community-contributed installable additions to the Wolfram Language

ZigangPan/ NonlinearSystems

This is a paclet on nonlinear systems with the ultimate goal of robust MRAC for linear systems

Contributed by: Zigang Pan

This paclet introduces a ten-item list to represent a nonlinear time-invariant system in state space representation. With this special format, one can do all sorts of things for a nonlinear system, such as convert a linear system in special format (as described in ZigangPan`LinearSystems`) to a nonlinear system, linearize a nonlinear system around an operating point to obtain a LTI system, do system operations on the nonlinear system just as for a LTI system, block diagonal, concatenate, parallel, and feedback interconnect two nonlinear systems, etc. One can calculate the relative degree of the nonlinear system and dynamically extend a nonlinear system to one with vector relative degree.

Installation Instructions

To install this paclet in your Wolfram Language environment, evaluate this code:
PacletInstall["ZigangPan/NonlinearSystems"]


To load the code after installation, evaluate this code:
Needs["ZigangPan`NonlinearSystems`"]

Details

Version 3.0: Removed dependency on ResourceFunction: LinearlyIndependent. So, the paclets are self-contained. No Cloud support needed.
Version 2.0: Introduces new functions: NLKarmanDecomposition, NLcontrollability, NLobservability, myMatrixRank, frobenius.
Version 1.1: Speed up in simulation of nonlinear systems using the RungeKutta45 method using the function simulationNLsystem.

Paclet Guide

Examples

Initialization for Examples

In[1]:=
Needs["ZigangPan`NonlinearSystems`"];

Basic Examples

In[2]:=
nlsystem1 = InterpretationBox[FrameBox[TagBox[TooltipBox[PaneBox[GridBox[List[List[GraphicsBox[List[Thickness[0.0025`], List[FaceForm[List[RGBColor[0.9607843137254902`, 0.5058823529411764`, 0.19607843137254902`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3]]], List[List[List[205.`, 22.863691329956055`], List[205.`, 212.31669425964355`], List[246.01799774169922`, 235.99870109558105`], List[369.0710144042969`, 307.0436840057373`], List[369.0710144042969`, 117.59068870544434`], List[205.`, 22.863691329956055`]], List[List[30.928985595703125`, 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Out[2]=
In[3]:=
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Out[3]=
In[4]:=
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Out[4]=
In[5]:=
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Out[5]=
In[6]:=
sol = RungeKutta45[nlsystem2[[4, 1]], 0, {1, 1}, 20, 0.1]
Out[6]=
In[7]:=
Plot[sol[t], {t, 0, 20}, PlotStyle -> Blue, PlotRange -> All]
Out[7]=
In[8]:=
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In[9]:=
nlsystem3 = InterpretationBox[FrameBox[TagBox[TooltipBox[PaneBox[GridBox[List[List[GraphicsBox[List[Thickness[0.0025`], List[FaceForm[List[RGBColor[0.9607843137254902`, 0.5058823529411764`, 0.19607843137254902`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3]]], List[List[List[205.`, 22.863691329956055`], List[205.`, 212.31669425964355`], List[246.01799774169922`, 235.99870109558105`], List[369.0710144042969`, 307.0436840057373`], List[369.0710144042969`, 117.59068870544434`], List[205.`, 22.863691329956055`]], List[List[30.928985595703125`, 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Out[9]=
In[10]:=
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Out[10]=

Publisher

Zigang Pan

Disclosures

Compatibility

Wolfram Language Version 14.2

Version History

  • 3.0.2 – 06 October 2025
  • 3.0.1 – 11 August 2025
  • 3.0.0 – 07 August 2025
  • 2.0.6 – 06 August 2025
  • 2.0.4 – 06 August 2025
  • 2.0.2 – 06 August 2025
  • 2.0.1 – 12 July 2025
  • 2.0.0 – 10 July 2025
  • 1.1.0 – 27 February 2025
  • 1.0.0 – 04 November 2024

License Information

MIT License

Paclet Source

Source Metadata

  • Citation: Isidori, A. (1995). Nonlinear Control Systems. 3rd ed. Springer-Verlag, London.

See Also