Subsystems on Nonlinear Control Dynamical Systems

The subsystems on nonlinear control dynamical systems are presented. A control dynamical system is a very complex object because it essentially is a union set of ordinary differential equations. The concept of subsystem can facilitate the solution of control problems by reducing them to simpler ones. The reduction is based on the fact that subsystems are simpler than the original system because they only deal with a part of solutions of the original system. The concept of subsystem in the theory of control systems is similar to the concept of subspace in the theory of linear spaces or to a subgroup in group theory. Affine control systems are nonlinear systems that are linear in controls. The problem of finding all the P-manifolds and the corresponding subsystems is generally very difficult. The dual Pfaffian system generating the associated codistribution of system can be formally obtained by eliminating the variables.