Invariance Feedback Entropy of Nondeterministic Control Systems.

We introduce a notion of invariance feedback entropy for discrete-time, nondeterministic control systems as a measure of necessary state information to enforce a given subset of the state space to be invariant. We provide conditions that guarantee finiteness and show that the well-known notion of invariance feedback entropy for deterministic systems is recovered in the deterministic case. We establish the data rate theorem which shows that the entropy equals the largest lower bound on the data rate of any coder-controller that achieves invariance. For finite systems, the invariance feedback entropy is characterized by the value function of an appropriately designed mean-payoff game. We use several examples throughout the paper to instantiate the various definitions and results.