Research Directions and Ideas 3

Hybrid automata as system models and refinement to ROS programs an the simulation engine
 The reaction module is the abstraction of ROS programs. Consider Khan Process Network~(KPN) as the intermediate model for abstracting ROS nodes and publish/subscribe communication paradigm because KPN can be analyzed independently from communication delay and interleaving of ROS nodes.
 Need a model of the environment that can be refined to match real or simulated environments. An interesting topic is to allow failure reproduction. If the hybrid automaton exhibits a failing execution, how do we instantiate a witness execution in the ROS program with the simulator.
 Synthesize perception contracts in different templates
 Receding horizon with temporal evolution
 Synthesize invariant and perception contract with PropertyDirected Reachability
 Kohei Suenaga and Takuya Ishizawa, “Generalized PropertyDirected Reachability for Hybrid Systems”, VMCAI 2020, doi: 10.1007/9783030393229_14
 Setinduced Lyapunov function that is piecewise linear. For discrete dynamical systems first, then use Euler approximation for continuous systems.
 Franco Blanchini, “Ultimate boundedness control for uncertain discretetime systems via setinduced Lyapunov functions”, IEEE Transactions on Automatic Control, 1994, doi: 10.1109/9.272351.
 Franco Blanchini, “Nonquadratic Lyapunov functions for robust control”, Automatica, 1995, doi: 10.1016/00051098(94)001334.
 Hai Lin and Panos J. Antsaklis, “Uniformly Ultimate Boundedness Control for Uncertain Switched Linear Systems”, ISIS Technical Report, ISIS2003004, University of Notre Dame (2003).
 Synthesize the model of the environment using automata learning, e.g., L* algorithms.
 Amit Gurung, Masaki Waga, Kohei Suenaga, “Learning nonlinear hybrid automata from inputoutput timeseries data”, arXiv, 2023, doi: 10.48550/arXiv.2301.03915
 Iman Saberi, Fathiyeh Faghih, and Farzad Sobhi Bavil, “A Passive Online Technique for Learning Hybrid Automata from Input/Output Traces”, ACM Trans. Embed. Comput. Syst. 22, 1, Article 9, January 2023, doi: 10.1145/3556543