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This paper presents a convex optimization approach to control the densitydistribution of autonomous mobile agents with two control modes: ON and OFF.The main new characteristic distinguishing this model from standard Markovdecision models is the existence of the ON control mode and its observedactions. When an agent is in the ON mode, it can measure the instantaneousoutcome of one of the actions corresponding to the ON mode and decides whetherit should take this action or not based on this new observation. If it does nottake this action, it switches to the OFF mode where it transitions to the nextstate based on a predetermined set of transitional probabilities, withoutmaking any additional observations. In this decision-making model, each agentacts autonomously according to an ON/OFF decision policy, and the discreteprobability distribution for the agent's state evolves according to adiscrete-time Markov chain that is a linear function of the stochasticenvironment (i.e., transition probabilities) and the ON/OFF decision policy.The relevant policy synthesis is formulated as a convex optimization problemwhere hard safety and convergence constraints are imposed on the resultingMarkov matrix. We first consider the case where the ON mode has a single actionand the OFF mode has deterministic transitions (rather than stochastic) todemonstrate the model and the ideas behind our approach, which is thengeneralized to the case where ON mode has multiple actions and OFF mode hasstochastic transitions.

Safe Markov Chains for Density Control of ON/OFF Agents with Observed Transitions