Optimized fractional-order control for finite-time stabilization of energy-saving and emission-reduction process

This paper presents a novel finite-time stabilization method for an energy-saving and emission-reduction hyperchaotic system (F-oESERHS), modeled by fractional-order (Fr-o) differential equations. The proposed modified fractional-order prediction-based controller (MFoP-bC), which is characterized by the difference between the fractional form of the predicted future state error vector of the uncontrolled fractional-order chaotic system (Fo-CS) and the current state error vector, is developed to stabilize the unstable equilibrium points (EPs) of the F-oESERHS in finite time. The two components of the control law are scaled by matrices consisting of elementary gain coefficients, which are subject to optimization. The design process is formulated as a multiobjective optimization problem to meet finite-time stabilization performance criteria. Finite-time stability (FT-Stab) is rigorously established via the Lyapunov direct method, incorporating recent theoretical stability results for Fr-o systems. Furthermore, the proposed enhanced artificial gorilla troops algorithm (E-AGTA) is employed as the optimization tool. A barrier function is used to handle the convex optimization interaction between the E-AGTA and the system under consideration. Finally, numerical simulations and a comparative analysis of four control strategies are performed to validate the effectiveness of the proposed control approach.