Variance-Constrained Multi-Objective Stochastic Control and Filtering

Chapter 12Mixed H₂/H_∞ Control with Markovian Jump Parameters and Probabilistic Sensor Failures: The Finite-Horizon Case

Recently, quite a lot of research interest has been devoted to Markovian jump systems (MJSs) whose dynamics may experience abrupt changes in their structure and parameters caused by phenomena such as component failures or repairs, changing subsystem interconnections, and environmental disturbance. It is worth mentioning that most of the literature relevant to MJSs have been about linear systems, and the respective results for nonlinear Markovian jump systems have been scattered. Several methods including the linear matrix inequality approach and the T-S fuzzy algorithm have been employed to solve the analysis and design problem for Markovian jump systems. However, it should be pointed out that most of the algorithms proposed in the existing literature are applicable to time-invariant systems only. In fact, the majority of real-world engineering systems exhibit the time-varying nature and the desired control performance index is set over a finite horizon to reflect the transient system behavior. Nevertheless, the finite-horizon control problem for general time-varying nonlinear Markovian jump systems in the presence of positivistic sensor failures has yet not been investigated, due probably to the mathematical complexity.

Motivated by the above discussion, in this chapter it is our objective to deal with the mixed H₂/H_∞ control problem over a finite horizon ...