Fractional Optimal Control And Microbial Batch Culture

This paper considers a class of fractional optimal control problems(FOCPs)with canonical equality and inequality constraints.The definition of fractional derivative in the dynamic system is described in the Caputo sense.By the control parameterization method,we approximate the FOCPs by a sequence of finite-dimensional optimization problems.We then present the gradient formulas by introducing some auxiliary fractional systems.On this basis,a gradientbased optimization is developed to solve the FOCPs.To illustrative this method a numerical example is presented.Further,this paper considers the microbial batch culture for producing 1,3-propanediol(1,3-pd)via glycerol disproportionation.Due to the nature of the fractional order operations,a novel fractional order model,which is based upon original ordinary differential dynamic system,is introduced to describe the complex bioprocess in a more accurate manner.Existence and uniqueness of solutions to the novel fractional order system and the continuity of solutions with respect to the parameters are discussed respectively.In addition,a parameter identification problem of the system is presented and a particle swarm optimization algorithm is constructed to solve it.