Estimation and Control for Discrete-Time Stochastic Systems with Semi-Markovian or Markovian Parameter Jumps

Currently research in the related areas of discrete-time stochastic estimation and control has been concerned with hybrid stochastic systems. These efforts have been motivated by the fact that hybrid stochastic system modeling is applicable to a diverse range of problems such as multiple-target tracking, failure detection, control of solar panels, control of large flexible structures in space, etc. Hybrid systems have parameters with values that may change from one time step to the next, as governed by a parameter switching process. The stochastic estimation algorithm presented was developed for hybrid systems with a "sojourn-time-dependent Markov," STDM, switching process. The STDM process is of semi-Markov type. This algorithm is real-time implementable and incorporates the recently developed interacting multiple model, IMM, algorithm. The two control algorithms presented were developed for Markovian hybrid systems. An interesting connection between the control of jump-linear systems and the IMM algorithm is shown to exist. Both control algorithms presented utilize the IMM algorithm for system state estimation and model identification.