TY - CHAP
T1 - Some recent directions in algebraic methods for optimization and lyapunov analysis
AU - Ahmadi, Amir Ali
AU - Parrilo, Pablo A.
PY - 2017
Y1 - 2017
N2 - Exciting recent developments at the interface of optimization and control have shown that several fundamental problems in dynamics and control, such as stability, collision avoidance, robust performance, and controller synthesis can be addressed by a synergy of classical tools from Lyapunov theory and modern computational techniques from algebraic optimization. In this chapter, we give a brief overview of our recent research efforts (with various coauthors) to (i) enhance the scalability of the algorithms in this field, and (ii) understand their worst case performance guarantees as well as fundamental limitations. The topics covered include the concepts of “dsos and sdsos optimization”, path-complete and non-monotonic Lyapunov functions, and some lower bounds and complexity results for Lyapunov analysis of polynomial vector fields and hybrid systems. In each case, our relevant papers are tersely surveyed and the challenges/opportunities that lie ahead are stated.
AB - Exciting recent developments at the interface of optimization and control have shown that several fundamental problems in dynamics and control, such as stability, collision avoidance, robust performance, and controller synthesis can be addressed by a synergy of classical tools from Lyapunov theory and modern computational techniques from algebraic optimization. In this chapter, we give a brief overview of our recent research efforts (with various coauthors) to (i) enhance the scalability of the algorithms in this field, and (ii) understand their worst case performance guarantees as well as fundamental limitations. The topics covered include the concepts of “dsos and sdsos optimization”, path-complete and non-monotonic Lyapunov functions, and some lower bounds and complexity results for Lyapunov analysis of polynomial vector fields and hybrid systems. In each case, our relevant papers are tersely surveyed and the challenges/opportunities that lie ahead are stated.
UR - http://www.scopus.com/inward/record.url?scp=85018459165&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85018459165&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-51547-2_5
DO - 10.1007/978-3-319-51547-2_5
M3 - Chapter
AN - SCOPUS:85018459165
T3 - Springer Tracts in Advanced Robotics
SP - 89
EP - 112
BT - Springer Tracts in Advanced Robotics
PB - Springer Verlag
ER -