An Algorithm for Optimizing a Nonlinear System, Based on the Behavior of the Hamiltonian on the Optimal Trajectory

摘要

The article deals with the problem of control synthesis for nonlinear dynamical systems represented by mathematical models with a linear structure and state-dependent parameters (SDC-model). The value that the Hamiltonian takes for suboptimal control synthesized using the SDC-model for an unlimited control time interval is established. A new parametric control algorithm is developed that uses the behavior of the Hamiltonian under the appropriate control and state of the system. In general, a condition is obtained under which this algorithm provides asymptotic stability of the original control system. The effectiveness of the proposed algorithm was tested using mathematical modeling methods.