Introducing SOSTOOLS: a general purpose sum of squares programming solver

By Stephen Prajna, Antonis Papachristodoulou, Pablo A. Parrilo. Proceedings of the 41st IEEE Conference on Decision and Control, 2002., 2002

612 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/2f556c89eefceb4057724d75c84230f9d92905c9

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Citations in the corpus

Analysis of Non-polynomial Systems using the Sum of Squares Decomposition (2005, methodology): “For this reason, conversion of SOS conditions to the corresponding SDP has been automated in SOSTOOLS [12], a software package developed for this purpose.”
Safety Verification of Hybrid Systems Using Barrier Certificates (2004, methodology): “also Remark 1). In this case, a barrier certicate fBl(x)g can be searched directly using semidenite programming, e.g. with the help of the software [ 20 ].”
Nonlinear control synthesis by convex optimization (2004, neutral): “In particular, a recently available software SOSTOOLS [ 13 ] can be used for this purpose.”
A tutorial on sum of squares techniques for systems analysis (2005, methodology): “See also another equivalent canonical form of SOS programs in [43], [44].”
Lyapunov Based Analysis and Controller Synthesis for Polynomial Systems using Sum-of-Squares Optimization (2003, methodology): “These computational improvements are set to appear in the next release of SOSTOOLS.”
On the construction of Lyapunov functions using the sum of squares decomposition (2002, methodology): “A Lyapunov function of this form is not found by SOS- TOOLS, so we will aim for a 4th order Lyapunov function; in this case, V will contain all monomials that have order between 2 and 4, and W = 6 k=1 ǫ 1k x 2 k + 6 k=1 ǫ 2k x 4 k with the ǫ 1k 's and ǫ 2k 's positive decision variables that satisfy”
A Framework for Worst-Case and Stochastic Safety Verification Using Barrier Certificates (2007, methodology): “When the vector fiel ds of the system are polynomials and the sets in the system description are semialgebraic (i.e., described by polynomial equalities and inequalities), a tractable computational m ethod called sum of squares optimization [31], [32], [ 38 ], [39] ca n be utilized for constructing ”
Recent developments on the stability of systems with aperiodic sampling: An overview (2017, methodology): “Last, note that alternatively to the LMI formulation, numerical stability criteria based on polynomial matrix functions P ( τ ) and Sum-of-Squares programming [222] have been proposed in [27].”
Geometric Programming for Communication Systems (2005, methodology): “Compared to the recently developed algebraic sum-ofsquares method using SDP relaxations [102, 101, 106] for constrained polynomial minimization (which becomes a special case of SP when the variables are restricted to the positive quadrant), this GP relaxation method still lacks a theoretical foundat”