Centrala begrepp
Efficient conservative reachability analysis for nonlinear systems using linear envelopes and antagonistic error.
Sammanfattning
The article discusses a method to efficiently analyze reachability in high-dimensional systems using conservative linear envelopes and antagonistic error. It introduces the concept of Hamilton-Jacobi reachability analysis and its applications in various domains. The authors propose a novel approach to overcome the curse of dimensionality by utilizing the Hopf formula for linear time-varying systems. By transforming nonlinear system errors into bounded artificial disturbances, they achieve guaranteed conservative reachability analysis and control synthesis. Several technical methods are presented to reduce conservativeness in the analysis, demonstrated through examples like the Van der Pol system and pursuit-evasion games with Dubins cars.
- Introduction to Hamilton-Jacobi reachability analysis.
- Challenges posed by exponential computation growth with state dimension.
- Utilization of the Hopf formula for efficient space-parallelizable solutions.
- Transformation of nonlinear system errors into adversarial disturbances.
- Demonstration of theory through controlled Van der Pol system and multi-agent games.
Statistik
The recently favored Hopf formula mitigates the curse of dimensionality by providing an efficient approach for solving reachability problems.
Systems of dimension 4000 have been solved efficiently using the Hopf formula.
Linearization introduces error in solutions but guarantees optimality with respect to true dynamics.
Citat
"The strength of DI methods is that they scale to dimensions greater than 100."
"Applying Bellman’s principle of optimality leads to viscosity solutions."