Analysis and Control of Water Pollution Models

Water pollution poses a considerable threat to public health, and it is important to understand water pollution transmission dynamics. This paper presents a mathematical framework involving bifurcation analysis and multiobjective nonlinear model predictive control (MNLMPC) for two models involving water pollution. Bifurcation analysis is a powerful mathematical tool used to address the nonlinear dynamics of any process. The MATLAB program MATCONT was utilized to conduct the bifurcation analysis of the water pollution models. Several factors must be taken into account, and multiple objectives must be achieved simultaneously. The MNLMPC calculations for the water pollution models were performed using the optimization language PYOMO in conjunction with the advanced global optimization solvers IPOPT and BARON. The bifurcation analysis revealed the presence of branch points in the two models. These branch points are advantageous as they allow the multiobjective nonlinear model predictive control calculations to converge to the Utopia point, which represents the most beneficial solution. The combination of bifurcation analysis and multiobjective nonlinear model predictive control for models involving water pollution is the main contribution of this paper.