11 citations · 17 across the 14 of their papers we have counts for
14 papers
Sublevel Set Approximation in The Hausdorff and Volume Metric with Application to Path Planning and Obstacle Avoidance
Morgan Jones
Under what circumstances does the ``closeness" of two functions imply the ``closeness" of their respective sublevel sets? In this paper, we answer this question by showing that if…
Existence of Partially Quadratic Lyapunov Functions That Can Certify The Local Asymptotic Stability of Nonlinear Systems
Morgan Jones, Matthew M. Peet
This paper proposes a method for certifying the local asymptotic stability of a given nonlinear Ordinary Differential Equation (ODE) by using Sum-of-Squares (SOS) programming to se…
Combining Trajectory Data with Analytical Lyapunov Functions for Improved Region of Attraction Estimation
Lucas Lugnani, Morgan Jones, Luís F. C. Alberto +2
The increasing uptake of inverter based resources (IBRs) has resulted in many new challenges for power system operators around the world. The high level of complexity of IBR genera…
A Converse Sum of Squares Lyapunov Function for Outer Approximation of Minimal Attractor Sets of Nonlinear Systems
Morgan Jones, Matthew M. Peet
Many dynamical systems described by nonlinear ODEs are unstable. Their associated solutions do not converge towards an equilibrium point, but rather converge towards some invariant…
Converse Lyapunov Functions and Converging Inner Approximations to Maximal Regions of Attraction of Nonlinear Systems
Morgan Jones, Matthew M. Peet
This paper considers the problem of approximating the "maximal" region of attraction (the set that contains all asymptotically stable sets) of any given set of locally exponentiall…
Polynomial Approximation of Value Functions and Nonlinear Controller Design with Performance Bounds
Morgan Jones, Matthew M. Peet
For any suitable Optimal Control Problem (OCP) there exists a value function, defined as the unique viscosity solution to the Hamilton-Jacobi-Bellman (HJB) Partial-Differential-Equ…
A Generalization of Bellman's Equation with Application to Path Planning, Obstacle Avoidance and Invariant Set Estimation
Morgan Jones, Matthew Peet
The standard Dynamic Programming (DP) formulation can be used to solve Multi-Stage Optimization Problems (MSOP's) with additively separable objective functions. In this paper we co…
Relaxing The Hamilton Jacobi Bellman Equation To Construct Inner And Outer Bounds On Reachable Sets
Morgan Jones, Matthew M. Peet
We consider the problem of overbounding and underbounding both the backward and forward reachable set for a given polynomial vector field, nonlinear in both state and input, with a…
Using SOS and Sublevel Set Volume Minimization for Estimation of Forward Reachable Sets
Morgan Jones, Matthew M. Peet
In this paper we propose a convex Sum-of-Squares optimization problem for finding outer approximations of forward reachable sets for nonlinear uncertain Ordinary Differential Equat…
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 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…
Solving Dynamic Programming with Supremum Terms in the Objective and Application to Optimal Battery Scheduling for Electricity Consumers Subject to Demand Charges
Morgan Jones, Matthew M. Peet
In this paper, we consider the problem of dynamic programming when supremum terms appear in the objective function. Such terms can represent overhead costs associated with the unde…
Estimating the Region of Attraction Using Polynomial Optimization: a Converse Lyapunov Result
Hesameddin Mohammadi, Matthew M. Peet
In this paper, we propose an iterative method for using SOS programming to estimate the region of attraction of a polynomial vector field, the conjectured convergence of which nece…