Metaheuristic-Optimized Direct Parameter Control: A Flexible Framework for Chaos Control and Target-Oriented Chaos Shaping

Abstract

Many dynamical systems exhibit chaotic behavior, making it difficult to steer their dynamics toward predefined dynamical behaviors, particularly when system-specific analytical analysis becomes complex. Metaheuristic-Optimized Direct Parameter Control (MODPC) is proposed as a flexible framework that uses metaheuristic optimization to determine control variables that modify a prescribed system parameter through a transformation function. The framework separates target selection from control operation: global dynamical information obtained from a bifurcation diagram is used in the offline design stage to identify a desired dynamical behavior, while metaheuristic optimization is performed in the online control stage to drive the system toward the corresponding target trajectory. This formulation enables different algebraic and nonlinear transformation functions, including multidimensional control variables, to be incorporated into the control process. Numerical experiments on discrete and continuous dynamical systems demonstrate the feasibility of the proposed framework under the tested conditions, including the steering of chaotic dynamics toward stable fixed points and periodic regimes. The theoretical analysis clarifies that target reachability depends on the reachable set induced by the transformation function and the prescribed control domain. A Mackey–Glass case study further illustrates the ability of the framework to steer chaotic dynamics toward a selected period-3 regime. These results indicate that MODPC provides a flexible approach for chaos control and targeted dynamical behavior, while its convergence and general applicability remain dependent on the transformation function, search domain, and system conditions.