Stable neural controllers for nonlinear dynamic systems
It is known that nonlinear dynamic systems can behave in a very complicated manner. Therefore, stabilizing controllers for nonlinear systems are hard to determine. Here, a stability based approach for designing neural controllers is proposed. It is assumed that the linearized system can be stabilized using static output feedback. By training the neural controller appropriately it is shown that the closed-loop system can be made stable. The framework of such an off-line training procedure permits to develop more efficient algorithms based on nonlinear programming. Such a stable neural controller is illustrated through a simulation example. Results are compared with the linear controller and show a larger stability region than in the linear controller case. For stabilization one needs a scalar positive definite function with a negative definite derivative at all points in the state space. The authors choose a Lyapunov function in quadratic form. For the linearized system supposed here it seems that the method works. But in the general case, e.g., for chaotic systems, it cannot be used. So, in this sense, the problem of stable (neural) controllers is still open.
scientific article; zbMATH DE number 1325784