Information-based controlNetworked cyber-physical systems often involve digital components connected via communication networks to regulate physical processes in an ongoing interaction of measurement, data processing and actuation. Use of digital channel (finite bandwidth) between sensor and controller prevents the instantaneous transmission of an infinite amount of state information. One of the most fundamental research questions in this context is: What is the minimal data rate of the channel so that a given control goal is achievable? Or equivalently: What is the amount of state information (measured in bits per sampling-time) necessarily available to any controller that enforces a given control task in the closed loop? In this context information measures, which are known from the theory of dynamical systems and which are often referred to as entropy, have proven to be extremely useful. For example, the invariance entropy of deterministic control systems characterizes the minimal data rate of a communication channel between the sensor and the controller, which is necessary to control a given subset of the state space invariant with respect to the system behavior. Previous theories have been limited to linear control systems and deterministic, nonlinear control systems. Data rate constraints for nondeterministic, nonlinear control systems that take model uncertainties and disturbances into account cannot be explained with those theories so far. Here, we mainly aim at designing and analysizing information measures for nondeterministic (a.k.a. uncertain) control systems to explain minimal data rates that are necessary for the realization of control properties in the closed loop. Active lab Members
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