Quasi-Optimal Control Law for Lagrangian Systems with a Deficit of Control Influences

Mechanical systems with a deficit of control influences are essentially nonlinear dynamic systems of high order, which are characterized by the presence of significant dynamic interaction between the elements. Therefore, the task of control synthesis should be considered in the initial nonlinear formulation, since the use of linear synthesis methods can lead to a loss of stability or significantly worsen the quality of the control process. When solving the problem of synthesis with a deficit of control influences, it is advisable to analyze such a mechanical system as a non-stationary one and use the principle of decomposition in conjunction with the maximum condition of generalized power, which makes it possible to find the structure of a universal two-level control system. The resulting quasi-optimal control provides an increase in the stability area and the quality of the transient process in terms of a quadratic criterion in comparison with known linear algorithms.