| Abstract: |
Ensuring safety through set invariance has proven to be a valuable method in various robotics and control applications. This talk will introduce a comprehensive framework for the safe probabilistic invariance verification of both discrete- and continuous-time stochastic dynamical systems over an infinite time horizon. The objective is to ascertain the lower and upper bounds of safety probabilities for a given safe set and set of initial states. The safety probability signifies the likelihood of the system remaining within the safe set indefinitely, starting from a state in the initial set. To address this problem, we propose optimizations for verifying safe probabilistic invariance in discrete-time and continuous-time stochastic dynamical systems. These optimizations are constructed via either using the Doob’s nonnegative supermartingale inequality-based method or relaxing the equations proposed in our previous works, which can precisely characterize the probability of reaching a target set while avoiding unsafe states. Finally, we demonstrate the effectiveness of these optimizations through several examples using semi-definite programming tools. |
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