As a result of the exhaustion of fossil energy sources and the corresponding increase of their negative environmental impact, recent research has intensively focused on regions of alternative energy resources and, especially, on solar energy. Slow tracking of the maximum power point (MPP) and fluctuations around the MPP reduce the efficiency of photovoltaic power generation systems (PV). This study offers a novel design for the MPPT controller, which we refer to as the “hybrid IC-LQI approach”, which combines the incremental conductance (IC) technique and the linear quadratic integral (LQI) controller based on the boost converter’s small signal model. We conduct a comparative study of the proposed hybrid IC-LQI, and the classical one-stage IC technique in order to show the effectiveness of our proposal under three different scenarios of weather conditions and load. According to simulation findings, the proposed hybrid IC-LQI approach has a high tracking efficiency of up to 98.92%, owing to faster tracking of MPP with very large reduction of oscillations. On the other hand, the IC technique provides less efficiency, up to 96.1%, showing very slow tracking and high oscillations. The presented analysis of the results confirms the superior performance of the developed hybrid IC-LQI technique to the classical IC technique.

This paper deals with the tuning of conventional PID and fractional-order PID (FOPID) controllers by using a particle swarm optimization (PSO) algorithm, for a class of fractional-order MIMO systems. This algorithm is motivated from the organism behavior of fish schooling and bird flocking, and involves the social psychology principles in socio-cognition human agents and evolutionary computations. It has a good numerical convergence for solving optimization problem. To illustrate the validity of the PSO-based FOPID and PID controllers, some simulation results are given. In addition, a comparative study between those optimized controllers is carried out.

Chaotic systems appear in a wide range of natural and engineering contexts, making the design of reliable and flexible control strategies a crucial challenge. This work proposes a robust control scheme based on the Fractional-Order Backstepping Control (FOBC) method for the stabilization of non-commensurate fractional-order chaotic systems subject to bounded uncertainties and external disturbances. The method is developed through a rigorous stability analysis grounded in the Mittag–Leffler function, enabling the step-by-step stabilization of each subsystem. By incorporating fractional-order derivatives into carefully selected Lyapunov candidate functions, the proposed controller ensures global system stability. The performance of the FOBC approach is validated on fractional-order versions of the Duffing–Holmes system and the Rayleigh oscillator, with the results compared against those of a fractional-order PID (FOPID) controller. Numerical evaluations demonstrate the superior performance of the proposed strategy: the error dynamics converge rapidly to zero, the system exhibits strong robustness by restoring state variables to equilibrium quickly after disturbances, and the method achieves low energy dissipation with a high error convergence speed. These quantitative indices confirm the efficiency of FOBC over existing methods. The integration of fractional-order dynamics within the backstepping framework offers a powerful, robust, and resilient approach to stabilizing complex chaotic systems in the presence of uncertainties and external perturbations.