Stochastic control: theory and applications

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Most of practical systems are stochastic and nonlinear. Dynamical systems of this type must in their functioning meet performance requirements and maintain acceptable behavior even in the presence of abrupt changes in their dynamics due, to random component failures or repairs, abrupt environmental disturbances, changes in subsystems interconnections, abrupt changes in the operating point of nonlinear plant, etc. Systems with this behavior may be modeled as hybrid ones, that is, to the state variable usually used in system theory, a discrete random variable called the mode, or regime is appended. The mode describes the random jumps of the systems parameters and the occurrence of the discontinuities. One of the most important hybrid class of systems is the one called systems with Markovian jumping parameters, in which the mode-process is a Markov chain taking values in a finite set.