Adaptive Feedback Control of Fractional Order Discrete State-Space Systems

The paper is devoted to the application of Fractional Calculus concepts to modeling, identification and control of discrete-time systems. Fractional Difference Equations (FÄE) models are presented and their use in identification, state estimation and control context is discussed. The Fractional Difference state-space model is proposed for that purpose. For such a model stability conditions are given. A Fractional Kalman Filter (FKF) for this model is recalled. The proposed state-space model and Fractional Order Difference Equation are used in an identification procedure which produces very accurate results. Finally, the statespace model is used in closed-loop state feedback control form together with FKF as a state estimator. The latter is also given in an adaptive form together with FKF and a modification of Recursive Least Squares (RLS) algorithm as a parameters identification procedure. All the algorithms presented were tested in simulations and the example results are given in the paper.