Hybrid systems are a modeling framework that allows for the combined consideration of continuous and discrete state dynamics. They are described by a finite collection of continuous systems, with each of these continuous dynamics corresponding to discrete modes of operation. Hidden mode hybrid systems are the special case when the mode is unknown or hidden and mode transitions are autonomous (i.e., there is no direct control over the switching process). In addition, by allowing unknown inputs in this framework, both deterministic and stochastic disturbance inputs and noise can also be considered. There are a large number of applications, such as urban transportation systems, human-automation systems as well as fault and attack identification in cyber-physical systems, in which it is not realistic to assume knowledge of the mode and disturbance inputs or they are simply impractical or too costly or unwieldy to measure. However, the literature on feedback control and estimation approaches for such systems is rather sparse.
In this talk, we first discuss a novel tracking control algorithm for uncertain hidden mode hybrid systems subject to input amplitude and rate constraints. This technique was applied to the dynamic landing of a helicopter without a ground contact sensor and the control of a car with automatic transmission. Then, we discuss the development of the first inference algorithms for simultaneously estimating states, unknown inputs and hidden modes of stochastic switched linear systems, along with an analysis of their properties. These inference algorithms provide the initial steps towards the realization of smart vehicles that can infer the hidden intention of other drivers without explicit communication, as well as smart power grids with reliable estimates despite faults or malicious attacks on its topology, actuators and sensors.