{'fraction_non_alphanumeric': 0.01882845188284519, 'fraction_numerical': 0.0, 'mean_word_length': 5.73943661971831, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Constrained optimal control of stochastic switched affine systems using randomization

We consider a finite-horizon optimal control problem for a switched affine system with controlled switches, affected by uncertainty and subject to input and/or state constraints. We show how the logical statements that govern the underlying switching mechanism can be transformed into robust mixed-integer inequalities, leading to an infinite dimensional linear program with robust constraints. Following a randomized methodology, based on enforcing the constraints only on a finite number of uncertainty instances/scenarios, we relax the infinite dimensional program to a mixed-integer linear program, which is amenable to existing numerical tools. We establish a probabilistic link between the infinite dimensional robust program and its scenario-based relaxation, showing that the optimal solution of the latter is feasible, in a probabilistic sense, for the former.