Abstract
We study the problem of synthesizing a control strategy to enforce safety of affine-in-control stochastic dynamical systems over finite time horizons. We use stochastic control barrier functions to quantify the probability that a system exits a given safe region of the state space in finite-time and consider both continuous-time and discrete-time systems. A barrier certificate condition that bounds the expected value of the barrier function over the time horizon is recast as a sum-of-squares optimization problem for efficient numerical computation. Unlike prior works, the proposed certificate condition includes a state-dependent upper bound on the evolution of the expectation, allowing for tighter probability bounds. Two examples are presented.
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