113 citations · 211 across the 57 of their papers we have counts for
5 papers · 2 filters
Representation and Stability Analysis of PDE-ODE Coupled Systems
Amritam Das, Sachin Shivakumar, Siep Weiland +1
In this work, we present a scalable Linear Matrix Inequality (LMI) based framework to verify the stability of a set of linear Partial Differential Equations (PDEs) in one spatial d…
Extensions of the Dynamic Programming Framework: Battery Scheduling, Demand Charges, and Renewable Integration
Morgan Jones, Matthew M. Peet
We consider a general class of Dynamic Programming (DP) problems with non-separable objective functions. We show that for any problem in this class, there exists an augmented-state…
Using SOS for Optimal Semialgebraic Representation of Sets: Finding Minimal Representations of Limit Cycles, Chaotic Attractors and Unions
Morgan Jones, Matthew M. Peet
In this paper we show that Sum-of-Squares optimization can be used to find optimal semialgebraic representations of sets. These sets may be explicitly defined, as in the case of di…
A New State-Space Representation of Lyapunov Stability for Coupled PDEs and Scalable Stability Analysis in the SOS Framework - with Lemma Proofs
Matthew M. Peet
In this paper, we present a framework for Stability Analysis of Systems of Coupled Linear Partial-Differential Equations. The class of PDE systems considered in this paper includes…
A Dynamic Programming Approach to Evaluating Multivariate Gaussian Probabilities
Morgan Jones, Matthew M. Peet
We propose a method of approximating multivariate Gaussian probabilities using dynamic programming. We show that solving the optimization problem associated with a class of discret…