Today, complex technological processes must maintain an acceptable behavior in the event of random structural perturbations, such as failures or component degradation. Aerospace engineering provides numerous examples of such situations: an aircraft has to pursue its mission even if some gyroscopes are out of order; a space shuttle has to succeed in its reentry trip with a failed on-board computer. Failed or degraded operating modes are parts of an embedded system history and should therefore be accounted for during the control synthesis.
These few basic examples show that complex systems are inherently vulnerable to failure of components and their reliability has to be improved through fault tolerant control. Complex systems require mathematical representations that are in essence dynamic, multi-model and stochastic. Thus the stochastic multi-model approach appears as a natural representation for complex systems. The behavior of the physical model is thus described for each different mode of operation of the system as, for instance, from nominal to failure states with intermediate dysfunctional regimes.
A general family of non-diffusion stochastic models was introduced for formulating many optimization problems in several areas of operations research, namely piecewise-deterministic Markov processes (PDMP’s). The key feature of this class of processes is that it naturally takes into account the stochastic multi-model approach and in particular it is more and more popular to study the reliability of complex systems. Another class of multi-model stochastic processes that lately has been receiving a great deal of attention is the so-called Markov jump linear systems (MJLS). In this case the motion of the process follows linear differential equations punctuated by exponential jump times.
Control systems theory may lead to relevant progress in new emergent quantum technologies, including magnetic resonance images (MRI), inertial navigation systems, optical telecommunications, high precision metrology, quantic communication, and circuits and quantum computer prototypes. For this it is necessary to develop extensions of traditional control concepts and their standard paradigms, such that optimality, feedback, stability, robustness, filtering and identification methods. Such extensions are now becoming key issues in the recent literature regarding quantum control.