Simulation of optimal linear control for stabilizing chaotic behavior in a chemical reaction model

Abstract

Complex dynamical systems, such as multicomponent chemical reactions, can exhibit chaotic behaviour, posing challenges for process control and optimisation. The pursuit of effective control methodologies to stabilise chaotic reaction systems constitutes a broad field of research and application. This study proposes the application of optimal linear control to mitigate chaotic behaviour in a model of four-component chemical reactions within a continuous stirred-tank reactor (CSTR). The methodology involves representing the reaction system through differential equations and minimising the Hamilton–Jacobi-Bellman functional equation via a linear feedback controller based on a Lyapunov function. Numerical simulations validate the methodology’s efficacy, demonstrating the controller’s capacity to transition the system of equations from a chaotic state to a stable periodic regime. The results highlight the potential of optimal linear control for optimising the model of complex chemical processes, thereby opening possibilities for technological applications in specific scenarios. Optimal linear control has proven effective in stabilising the model of the reaction system, presenting itself as a promising tool for the design of industrial processes involving continuous flow reactors. In these reactors, precise control of concentrations is crucial to ensure process quality and safety.