Optimal Control Based on Neuro Estimator for Fractional Order Uncertain Non-linear Continuous-Time Systems

In this paper, a novel method is presented for optimal control of fractional order systems in the presence of an unknown term in system dynamic where fractional order derivative is considered to be between zero and one. In this method, neural network is used to estimate the unknown term in system dynamic. Neural network coefficients are updated adaptively and online. Updating laws are presented considering system requirements to achieve a homogeneous fractional order system. Another problem is formulating optimal control laws for fractional order system which is solved through fractional differential calculus. Since optimal fractional order control is non-causal and does not have a online solution, step-by-step progression and predictive control idea are used to obtain control signal and combine optimal controller and estimator. This method results in an optimal run-time control and resolves unknown terms in system dynamic. In addition, the closed loop system being uniform ultimate bounded is proved through direct Lyapunov method. Finally, simulation results are given to show efficiency of the proposed method.