55 citations · 141 across the 19 of their papers we have counts for
18 papers · 1 filter
A Hamilton-Jacobi-Bellman Approach to Ellipsoidal Approximations of Reachable Sets for Linear Time-Varying Systems
Vincent Liu, Chris Manzie, Peter M. Dower
Reachable sets for a dynamical system describe collections of system states that can be reached in finite time, subject to system dynamics. They can be used to guarantee goal satis…
A Tree Structure Approach to Reachability Analysis
Alessandro Alla, Peter M. Dower, Vincent Liu
Reachability analysis is a powerful tool when it comes to capturing the behaviour, thus verifying the safety, of autonomous systems. However, general-purpose methods, such as Hamil…
Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs
Jérôme Darbon, Peter M. Dower, Tingwei Meng
Solving high dimensional optimal control problems and corresponding Hamilton-Jacobi PDEs are important but challenging problems in control engineering. In this paper, we propose tw…
Exploiting characteristics in stationary action problems
V. Basco, P. M. Dower, W. M. McEneaney +1
Connections between the principle of stationary action and optimal control, and between established notions of minimax and viscosity solutions, are combined to describe trajectorie…
A two-player game representation for a class of infinite horizon control problems under state constraints
Vincenzo Basco, Peter M. Dower
In this paper we give feedback laws for a class of parametrized infinite horizon control problems under state constraints. We provide a two-player representation assuming time depe…
Verifying fundamental solution groups for lossless wave equations via stationary action and optimal control
Peter M. Dower, William M. McEneaney
A representation of a fundamental solution group for a class of wave equations is constructed by exploiting connections between stationary action and optimal control. By using a Yo…