Kernekoncepter
State-augmented linear games with antagonistic error provide conservative approximations of the true value function in high-dimensional systems.
Resumé
The article discusses the application of state-augmented linear games with antagonistic error to solve high-dimensional, nonlinear Hamilton-Jacobi reachability problems. It introduces a method that offers conservative approximations of the true value function and guarantees success in the original dynamics. The content is structured as follows:
- Introduction to Hamilton-Jacobi Reachability (HJR) and its significance in analyzing dynamical systems.
- Challenges faced by traditional methods like Dynamic Programming (DP) due to dimensionality constraints.
- Application of the generalized Hopf formula for solving differential games with linear dynamics.
- Extension of conservative solutions to nonlinear systems using state-augmented spaces.
- Theoretical results and proofs demonstrating how linear game values with antagonistic error can approximate true values conservatively.
- Demonstration of results in slow manifold and Van der Pol system examples using various lifting functions.
- Conclusion highlighting the benefits and future extensions of the proposed method.
Statistik
Recently, the space-parallelizeable, generalized Hopf formula has shown a three-log increase in dimension limit.
Systems greater than three dimensions online and six offline pose scalability challenges for DP methods.
Citater
"Unlike previous methods, this result offers the ability to safely approximate reachable sets and their corresponding controllers."
"This approach provides necessary guarantees for safety-critical systems."