Stabilization of nonlinear dynamical systems using neural networks

The problem of stabilization of a dynamical system around an equilibrium point is considered. The main objective is to indicate how, based on theoretical results in nonlinear control theory, practically viable controllers can be designed using neural networks. Simulation results are included to complement the theoretical discussions. The controllability and stabilization of an unknown system have been considered. Though it is initiated using local rank conditions, the range of validity of the result is significantly larger. Controllability is a generic property of linear systems and hence it is a very reasonable assumption to make. The rank condition, which is invariant under feedback or coordinate transformation, can easily be checked. The system need not be brought to any special form to check whether it holds. This combination of simplicity and large range of validity should prove it to be a most useful and practical method for the purpose of stabilizing nonlinear systems