Optimal regulation problem with fractional order performance index

摘要

This paper addresses a new view to the optimal control problems in a more realistic perspective. It is clear for control engineers that one of the most serious adversities in defining the performance index is to decide what characteristics of the system response are important to be considered and how they have to be weighted if they are not treated totally equal. In this manuscript, using fractional order integration, a time-weighted performance index is introduced for evaluating the performance of optimal regulation problems which extends the quadratic cost functional in the classical process control systems. Such formulations are gained in the light of intrinsic kernel in the definition of the Riemann-Liouville fractional order integral which weighs the Lagrangian of the performance index upon the time progresses. Moreover, a constraint on the fractional order derivative of the control signal is included in the generalized performance index to overcome the saturation problem occurred in the real control systems. The proposed techniques are supported by some discussions and several numerical simulations.