  


Convex computation of extremal invariant measures of nonlinear dynamical systems and Markov processes
Milan Korda(milan.kordaengineering.ucsb.edu) Abstract: We propose a convexoptimizationbased framework for computation of invariant measures of polynomial dynamical systems and Markov processes, in discrete and con tinuous time. The set of all invariant measures is characterized as the feasible set of an infinitedimensional linear program (LP). The objective functional of this LP is then used to singleout a specific measure (or a class of measures) extremal with respect to the selected functional such as physical measures, ergodic measures, atomic measures (corresponding to, e.g., periodic orbits) or measures absolutely continuous w.r.t. to a given measure. The infinitedimensional LP is then approximated using a standard hierarchy of finitedimensional semidefinite programming problems (SDPs), the solutions of which are truncated moment sequences, which are then used to re construct the measure. In particular, we show how to approximate the support of the measure as well as how to construct a sequence of weakly converging absolutely continuous approximations. The presented framework, where a convex functional is minimized or maximized among all invariant measures, can be seen as a generalization of and a computational method to carry out the so called ergodic optimization, where linear functionals are optimized over the set of invariant measures. Finally, we also describe how the presented framework can be adapted to compute eigenmeasures of the PerronFrobenius operator. Keywords: Invariant measure, convex optimization, ergodic optimization, physical measure Category 1: Linear, Cone and Semidefinite Programming (Semidefinite Programming ) Category 2: Nonlinear Optimization (Systems governed by Differential Equations Optimization ) Citation: Download: [PDF] Entry Submitted: 07/17/2018 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  