Necessary optimality conditions of fractional-order discrete uncertain optimal control problems

This paper is primarily dedicated to the necessary conditions of optimal control for uncertain discrete-time systems of fractional-order governed by left Riemann-Liouville-like fractional-order nabla difference equations. First, an existence result of solutions for backward right Riemann-Liouville-like fractional-order nabla difference equations is derived from the Banach contraction mapping theorem. Besides, necessary optimality conditions of these fractional-order uncertain optimal control problems are proposed by the variational method and Lagrange multiplier technique. Finally, a special LQ optimal control problem for uncertain discrete-time systems of fractional-order is solved by necessary conditions of optimality derived.