Optimization comprises the maximization or minimization of a function by systematically choosing input values from a valid input set and computing the function value. Thus, optimization techniques are oriented toward retrieving the best possible solution and element within constraints in a set with respect to a given criterion, which is pivotal in terms of performance maximization and resource allocation in control systems. Control theory, as the domain of applied mathematics, employs feedback to affect the behavior of a system for the purpose of achieving an objective. Control theory draws on the means to design systems which are capable of maintaining desired outputs in spite of the emerging disturbances. At these junctures, optimization has been among the most extensively used tools to compute control law, adjust tuning, or controller parameters, conduct model-fitting and find appropriate conditions to fulfill a given closed-loop property. Real-world control systems need to comply with certain conditions and constraints to be considered in the formulation of problems, which represent some of the relevant challenges in the application of the optimization algorithms.

Mathematical methods and numerical analyses constitute a foundational structure to understand and manipulate dynamic and complex systems within optimization, control and dynamic systems. While mathematical methods offer the theoretical framework, benefiting from calculus, fractional calculus, fractional derivatives, linear algebra and differential / integral equations to model system behavior, numerical analyses convert these theoretical models into computational algorithms that enable feasible solutions to real-world phenomena with applications spanning diverse fields, including mathematics, physics, biology, mathematical biology, epidemiology, chemistry, computer science, applied sciences, engineering, robotics, economics, finance, among others.

Based on these concepts, theories and application aspects, our special session is to discuss the current needs and challenges in mathematical methods, numerical analyses and computer simulations alongside their corresponding applicable solutions, predictive means as well as optimization and control techniques in dynamic and transient systems.

The topics include but are not limited to: