forked from oxfordcontrol/SOSTOOLS
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Contents.m
executable file
·79 lines (78 loc) · 4.1 KB
/
Contents.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
% SOSTOOLS --- Sum of Squares Toolbox
% Version 4.00, 14 September 2021.
%
% Monomial vectors construction:
% MONOMIALS --- Construct a vector of monomials with prespecified
% degrees.
% MPMONOMIALS --- Construct a vector of multipartite monomials with
% prespecified degrees.
%
% General purpose sum of squares program (SOSP) solver:
% SOSPROGRAM --- Initialize a new SOSP.
% SOSDECVAR --- Declare new decision variables in an SOSP.
% SOSPOLYVAR --- Declare a new polynomial variable in an SOSP.
% SOSSOSVAR --- Declare a new sum of squares variable in an SOSP.
% SOSPOLYMATRIXVAR --- Declare a new matrix of polynomial variables in an SOSP.
% SOSSOSMATRIXVAR --- Declare a new matrix of sum of squares polynomial
% variables in an SOSP.
% SOSPOSMATR --- Declare a new positive semidefinite matrix variable in an SOSP
% SOSPOSMATRVAR --- Declare a new symbolic positive semidefinite matrix
% variable in an SOSP
% SOSQUADVAR --- Declare a polynomial/SOS decision variable with
% customized structure.
% SOSEQ --- Add a new equality constraint to an SOSP.
% SOSINEQ --- Add a new inequality constraint to an SOSP.
% SOSMATRIXINEQ --- Add a new matrix inequality constraint to an SOSP.
% SOSSETOBJ --- Set the objective function of an SOSP.
% SOSPSIMPLIFY --- Perform simplification of an SOSP.
% SOSSOLVE --- Solve an SOSP.
% SOSGETSOL --- Get the solution from a solved SOSP.
%
% Customized functions:
% FINDSOS --- Find a sum of squares decomposition of a given polynomial.
% FINDLYAP --- Find a Lyapunov function for a dynamical system.
% FINDBOUND --- Find a global/constrained lower bound for a polynomial.
%
% Demos:
% SOSDEMO1 and SOSDEMO1S --- Sum of squares test.
% SOSDEMO2 and SOSDEMO2S --- Lyapunov function search.
% SOSDEMO3 and SOSDEMO3S --- Bound on global extremum.
% SOSDEMO4 and SOSDEMO4S --- Matrix copositivity.
% SOSDEMO5 and SOSDEMO5S --- Upper bound for the structured singular value mu.
% SOSDEMO6 and SOSDEMO6S --- MAX CUT.
% SOSDEMO7S --- Chebyshev polynomials.
% SOSDEMO8S --- Bound in probability.
% SOSDEMO9 and SOSDEMO9S --- Matrix SOS decomposition.
% SOSDEMO10 and SOSDEMO10S --- Set containment.
% This file is part of SOSTOOLS - Sum of Squares Toolbox ver 4.00.
%
% Copyright (C)2002, 2004, 2013, 2016, 2018, 2021 A. Papachristodoulou (1), J. Anderson (1),
% G. Valmorbida (2), S. Prajna (3),
% P. Seiler (4), P. A. Parrilo (5)
% M. Peet (6), D. Jagt (6)
% (1) Department of Engineering Science, University of Oxford, Oxford, U.K.
% (2) Laboratoire de Signaux et Systmes, CentraleSupelec, Gif sur Yvette,
% 91192, France
% (3) Control and Dynamical Systems - California Institute of Technology,
% Pasadena, CA 91125, USA.
% (4) Aerospace and Engineering Mechanics Department, University of
% Minnesota, Minneapolis, MN 55455-0153, USA.
% (5) Laboratory for Information and Decision Systems, M.I.T.,
% Massachusetts, MA 02139-4307
% (6) Cybernetic Systems and Controls Laboratory, Arizona State University,
% Tempe, AZ 85287-6106, USA.
%
% Send bug reports and feedback to: [email protected]
%
% This program is free software; you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 2 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.