Decomposition and suboptimal control in dynamic systems

Constructive methods of control for dynamical systems subject to bounded controls are proposed. Lagrangian systems governed by nonlinear ordinary differential equations and linear systems governed by partial differential equations are considered. The approach is based on the decomposition of the original system with a finite or infinite number of degrees of freedom into simple subsystems with one degree of freedom each. Methods of optimal control and differential games are applied to the subsystems. Explicit feedback control laws are obtained which bring the original dynamical systems to the prescribed terminal states in finite time. Upper estimates on the control time are obtained. Control­ lability of systems subject to bounded controls is discussed. The proposed methods are applicable to robots and elastic systems.