Multi-criteria control of large-scale nonlinear dynamical systems without linearization, based on Lyapunov functions

This paper proposes a numerical control method for large-scale nonlinear dynamical systems, focused on maintaining stability without using linearization. The approach under study is based on the principles of multi-criteria optimization, where the stability of the system is directly included in the vector of target criteria through Lyapunov functions. This allows us not only to minimize deviations from the target states and energy consumption for control, but also to guarantee the asymptotic stability of the system under arbitrary initial conditions. A mathematical formulation of the problem is presented, a discrete numerical control scheme is developed, and a scalarization strategy is proposed that provides an approximation to Pareto-optimal solutions. A series of numerical experiments implemented in Python has been conducted, confirming the effectiveness of the method using examples of both single- and multi-agent systems. The results demonstrate the stable behavior of the trajectories, a decrease in the Lyapunov function over time and correct operation even with strong nonlinearity of the model.