Control of Nonlinear Dynamical Systems Using. . .

41 kx 0 k < 0:4, it becomes unstable for larger initial conditions. The response of the of the system for the initial condition x 0 = (0:15; 00:25;0:35), shown in Figure 8, indicates that the trajectory becomes very large after 10 units of time. Simulation 2 reveals how the method proposed using a nonlinear controller may increase the region of attraction substantially. 5 Conclusion A general approach to the design of neural network based controllers for nonlinear dynamical systems is discussed in the paper. The state vector of the nonlinear plant to be controlled is assumed to be accessible and the main objective is to stabilize the plant around an equilibrium state. The theoretical and practical questions that arise are examined and the prior information needed to design the controllers are specied. The most important aspect of the methods proposed is that they are practically viable. This is demonstrated through simulation studies on the stabilization of nonlinear systems for which other methods are not currently available. The problem of control becomes substantially more complex (as is well known in linear theory) when the state of the system is not accessible and control has to be achieved using input-output data. The use of observers (or identiers) and the problem of output regulation will be treated in two following reports [10, 11].