Name
Abstract | ||
|---|---|---|
We present a numerical method for computing backward reachable sets in differential games. A backward reachable set for time t is captured by the t sublevel set of the lower value function of the game, which coincides with the viscosity solution of a stationary Hamilton-Jacobi-Isaacs (HJI) equation. We solve the stationary HJI equation in a computationally efficient way that does not involve any numerical integration over time, which would otherwise be required for time-dependent HJI equations. Backward reachable sets for all time points can simultaneously be extracted from the solution. The performance of the method is demonstrated by investigating the growth of multicellular structures of non-malignant and malignant breast cells as a proof of principle. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1145/2461328.2461359 | HSCC |
Keywords | Field | DocType |
numerical method,time-dependent hji equation,stationary hji equation,differential game,lower value function,numerical integration,time point,viscosity solution,one-shot computation,stationary hamilton-jacobi-isaacs,reachable set | Applied mathematics,Mathematical optimization,Numerical integration,Bellman equation,Proof of concept,Numerical analysis,Viscosity solution,Mathematics,Computation | Conference |
Citations | PageRank | References |
1 | 0.40 | 20 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Insoon Yang | 1 | 35 | 9.17 |
| Sabine Becker-Weimann | 2 | 1 | 0.40 |
| Mina J. Bissell | 3 | 101 | 5.26 |
| Claire J. Tomlin | 4 | 1491 | 158.05 |