Design of nonlinear control systems by means of differential genetic programming

Based on the genetic programming (GP), a new design method of optimal and/or robust controllers of nonlinear systems is proposed. First we introduce a new type of genetic programming, which is called "differential GP". The differential GP combines the conventional GP with an automatic differentiation scheme, so that it can solve Hamilton-Jacobi-Bellman (HJB)/Hamilton-Jacobi-Isaacs (HJI)/Francis - Byrnes - Isidori (FBI) equations. Our design method is mainly based on the differential GP technique, and so it gives us a new possibility of the HJB/HJI/FBI based design techniques. Lastly, the effectiveness of the differential GP based design method is demonstrated through some design examples of nonlinear systems.