Abstract
Abstract The optimal control of discrete-time jump systems that would be linear but for randomly jumping parameters are considered. These parameter jumps, which are indexed by a finite state form process, can be used to model systems subject to component failures or structural changes. The control of such systems when the jump probabilities can be controlled by choice of a finite-valued input is considered. This input (form control) can be thought of as corresponding to a maintenance or repair policy. The optimal control problem with quadratic costs (whose weighting matrices depend on the jumping parameters and form control) is formulated for such systems. The optimal solution for finite and infinite time horizon problems is developed. In addition, sufficient conditions for the existence of a steady-state, stabilizing solution to the infinite time problem are given in terms of appropriately defined controllability and observability properties.
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