2016/01/05 by Shankar Mohan, Mohan, Shankar, Victor Shia +3
Biochemistry, Genetics and Molecular Biology · Engineering · #FOS: Electrical engineering #FOS: Mathematics #Gene Regulatory Network Analysis #Optimization and Control (math.OC) #Robotic Locomotion and Control #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1601.01019
openalex publication_date 2016/01/05 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
To verify the correct operation of systems, engineers need to determine the\nset of configurations of a dynamical model that are able to safely reach a\nspecified configuration under a control law. Unfortunately, constructing models\nfor systems interacting in highly dynamic environments is difficult. This paper\naddresses this challenge by presenting a convex optimization method to\nefficiently compute the set of configurations of a polynomial hybrid dynamical\nsystem that are able to safely reach a user defined target set despite\nparametric uncertainty in the model. This class of models describes, for\nexample, legged robots moving over uncertain terrains. The presented approach\nutilizes the notion of occupation measures to describe the evolution of\ntrajectories of a nonlinear hybrid dynamical system with parametric uncertainty\nas a linear equation over measures whose supports coincide with the\ntrajectories under investigation. This linear equation with user defined\nsupport constraints is approximated with vanishing conservatism using a\nhierarchy of semidefinite programs that are each proven to compute an\ninner/outer approximation to the set of initial conditions that can reach the\nuser defined target set safely in spite of uncertainty. The efficacy of this\nmethod is illustrated on a collection of six representative examples.\n