State-Space Self-Tuning Control for Stochastic Fractional-Order Chaotic Systems

Based on the modified state-space self-tuning control (STC), a novel low-order tuner via the modified observer/Kalman filter identification (OKID) is proposed for stochastic fractional-order chaotic systems. The OKID method is a time-domain technique that identifies a discrete input-output map by using known input-output sampled data in the general coordinate form, through an extension of the eigensystem realization algorithm (ERA). First, the estimated system in the general coordinate based on the conventional OKID method is transformed to the one in an observer form to fit the state-space innovation form for the STC. Then, in stead of the conventional recursive least squares (RLS) identification algorithm used for STC, the Kalman filter as a parameter estimator with the state-space innovation form is presented for effectively estimating the time-varying parameters. Besides, taking the advantage of the digital redesign approach, the derivation of the current-output-based observer is proposed for the modified STC. As a result, the low-order state-space self-tuner with the high-gain controller property is then proposed for stochastic fractional-order chaotic systems, which the fractional operators are well approximated using the standard high integer-order operators. Finally, the fractional-order Chen and Roumlssler systems with stochastic system process and measurement noises are used as illustrative examples to demonstrate the effectiveness of the proposed methodology