Abbas Karami

Fractional-order control (FOC) represents memory-dependent, hereditary, and nonlocal dynamics by incorporating non-integer integration and differentiation operators into conventional control laws. However, the numerical realization of these operators increases the effective controller order and imposes additional computational and hardware requirements. This systematic literature review synthesizes 136 peer-reviewed studies published between 2010 and 2025 and identified through six scholarly databases and search platforms. Five focal strategy families—Fractional-Order Proportional–Integral–Derivative Control (FOPID), Fractional-Order Sliding Mode Control (FOSMC), Fractional-Order Adaptive Control (FOAC), Fractional-Order Impedance Control (FOIC), and Fractional-Order Optimal Control (FOOC)—are compared across nonlinear mechanical, biological/physiological, and aerospace/vehicle systems. The comparative analysis reveals distinct operational trade-offs. FOPID extends the conventional PID structure from three to five tunable parameters and provides the highest real-time feasibility, but its enlarged tuning space increases design complexity. FOSMC offers strong robustness and disturbance rejection but requires demanding fractional-order stability analysis and does not fully eliminate switching-induced chattering. FOAC accommodates unknown and time-varying dynamics through online adaptation but increases computational load and validation complexity. FOIC effectively captures compliant and viscoelastic force–motion interactions but involves numerous coupled impedance parameters and interaction-stability constraints. FOOC provides a powerful framework for memory-dependent multi-objective optimization but imposes the highest numerical and theoretical burden, often making direct real-time deployment impractical. Across the five strategies, increasing the order of numerical approximations improves the representation of fractional dynamics over the selected frequency range but adds internal filter states, memory requirements, arithmetic operations, and execution latency. Therefore, performance scalability is fundamentally constrained by growth in the effective state dimension and the available embedded-hardware resources. Future research should prioritize reduced-order fractional approximations, standardized benchmarks and software libraries, stability-certified adaptive architectures, and experimentally validated real-time implementations.

In this paper, two new approaches for handling multiple tasks in redundant manipulators based on predefined allocated priorities are proposed. The first approach is an integrated scheme which employs null-space base vector for handling prioritized tasks. Clear task and null-space representation, better execution of the lower priority tasks, and intuitive formulation are its basic features. The second approach aims to improve the performance of all the prioritized tasks, especially during algorithmic singularities beside clear null-space dynamics representation. This approach can be considered as a modification and extension of the Reverse Priority (RP) algorithm in acceleration level. The commands related to each tasks are added to each other following reverse order of priorities and by suitable projectors. The projector definition is given using minimal representation of the null-space. Clear null-space dynamics in the proposed methods facilitate the stability analysis. A detailed evaluation by means of computer simulation in various cases is reported. Tasks accomplishment using the proposed approaches is compared with the classic method. The results, in general, show higher performance and accuracy of the tasks by the proposed approaches.