Adaptive weight adjustment in multicriteria control of nonlinear systems based on a Lyapunov function

The paper develops an approach to the control of nonlinear dynamic systems within a multicriteria optimization framework in which criterion weights are adjusted during the control process. The method relies on a Lyapunov function that is included both in the performance functional and in trajectory constraints. A numerical algorithm is proposed for dynamic tuning of the criterion weights. The criteria are stability and control energy consumption, while their relative importance changes depending on the current system state and trajectory. Adaptation is performed based on the current value of the Lyapunov function and the system state, which enables automatic prioritization of objectives without operator intervention. A numerical analysis of the system behavior under different weight-adaptation schemes is carried out. For the considered models, the simulation results show that adaptive weight adjustment can provide faster decay of the Lyapunov function and lower control energy consumption compared with fixed scalarization. The method can be applied to control problems for nonlinear and multi-agent systems, including cyber-physical complexes, autonomous agents, and energy nodes.