Optimal control in environmental systems and stability analysis

This paper aims at optimizing control in an environmental system with pollution dynamics, economic activity and climatic parameters. The optimal control is calculated using the Pontryagin’s Maximum Principle. The stability of the system is investigated by two methods: Lyapunov’s second method and eigenvalue analysis of the Jacobian matrix. The Lyapunov method can give a conclusion about the system’s asymptotic stability, while the eigenvalue analysis can give information about the stability in the neighbourhood of the equilibrium points. We present a numerical solution of the model and discuss the conditions for stability and the possibility of adjusting the system’s parameters to reach environmental equilibrium.