Risk Analysis of Stochastic Nonlinear Dynamical Networks Via Lifting Operators
Abstract
In this project, we developed operator theoretic tools to study convergence of Carleman lifting of time-varying nonlinear systems. We quantified explicit error bounds for finite-section of the lifted system and proved that the truncation error converges exponentially to zero as the truncation length increases. We utilized our findings to study Hamilton-Jacobi-Bellman (HJB) equation and proposed a quadrization method to lift and represent the HJB equation as a semi-Riccati operator equation. An exact iterative algorithm to calculate the sub-blocks of the solution to the semi-Riccati operator equation up to an arbitrary precision was proposed. Furthermore, we developed a methodology to study and quantify systemic risk measures in various dynamical networks subject to Gaussian or stable non-Gaussian noise. More specifically, our findings show that for a class of nonlinear dynamical networks one can quantify the value of a family of risk measures using spectral mode decomposition techniques. Our theoretical results have been applied to various applications including platoon of autonomous vehicles, swarm of multiple robots, rendezvous and synchronization in multi-agent systems, and power networks.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 11, 2022
- Accession Number
- AD1230408
Entities
People
- Nader Motee
Organizations
- Lehigh University