Memory identification of fractional order systems: Background and theory

This paper presents a novel work that how to determine the memory (initialization function) of fractional order systems by using the recent sampled input-output data. The background and basic theories of initialized fractional order systems are introduced. A practical algorithm is proposed to estimate the initial value of initialization function, which is adaptive to all system parameters. A P-type learning law is applied so that the initialization function can be computed accordingly. The whole process is optimized by using finite system information. The above strategy is available for both Caputo and Riemann-Liouville fractional order systems, where the initial values are applied instead of the initial conditions.