A finite horizon linear quadratic(LQ) optimal control problem is studied fora class of discrete-time linear fractional systems (LFSs) affected bymultiplicative, independent random perturbations. Based on the dynamicprogramming technique, two methods are proposed for solving this problem. Thefirst one seems to be new and uses a linear, expanded-state model of the LFS.The LQ optimal control problem reduces to a similar one for stochastic linearsystems and the solution is obtained by solving Riccati equations. The secondmethod appeals to the Principle of Optimality and provides an algorithm for thecomputation of the optimal control and cost by using directly the fractionalsystem. As expected, in both cases the optimal control is a linear function inthe state and can be computed by a computer program. Two numerical examplesproves the effectiveness of each method.
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