OPTIMAL CONTROL FOR DISCRETE-TIME, LINEAR FRACTIONAL-ORDER SYSTEMS WITH MARKOVIAN JUMPS

This paper considers a finite-horizon linear quadratic (LQ) optimal control problem for a class of stochastic discrete-time, linear systems of fractional order which are generated by the operator involved in the definition of the fractional-order derivative of Grunwald-Letnikov type. This subject is new for discrete-time, linear, fractional-order systems (DTLFSs) with infinite Markovian jumps. We use an equivalent linear expanded-state model of the DTLFS with jumps and an equivalent quadratic cost functional to reduce the original optimal control problem to a similar one for discrete-time, linear, integer-order systems with Markovian jumps. The obtained optimal control problem is then solved by applying a dynamic programming technique.