LQ optimal control of fractional-order discrete-time uncertain systems

•Expected value model of LQ optimal control problem for fractional-order discrete time uncertain systems is proposed.•The proposed expected value model is indirectly solved by dynamic programming method.•A new expected value model of LQ optimal control problem for macroeconomic systems is established and solved. This paper primarily focuses on LQ optimal control problem of fractional-order discrete-time systems based on uncertainty theory that is a significant tool to model belief degree. First, an equivalent LQ problem, which is integer-order one, is presented by expanding the state variables with the unchanging control variables. This equivalent problem is then solved by dynamic programming approach. Accordingly, the solution of the proposed LQ optimal control problem reduces to solve a system of backward matrix difference equations. Finally, a numerical example is provided to show how to solve the proposed LQ optimal control problem. As an application, an LQ optimal control problem of macroeconomic system is discussed by the achieved results.