Support Vector Machines Based Generalized Predictive Control of Chaotic Systems

This work presents an application of the previously proposed Support Vector Machines Based Generalized Predictive Control (SVM-Based GPC) method [1] to the problem of controlling chaotic dynamics with small parameter perturbations. The Generalized Predictive Control (GPC) method, which is included in the class of Model Predictive Control, necessitates an accurate model of the plant that plays very crucial role in the control loop. On the other hand, chaotic systems exhibit very complex behavior peculiar to them and thus it is considerably difficult task to get their accurate model in the whole phase space. In this work, the Support Vector Machines (SVMs) regression algorithm is used to obtain an acceptable model of a chaotic system to be controlled. SVM-Based GPC exploits some advantages of the SVM approach and utilizes the obtained model in the GPC structure. Simulation results on several chaotic systems indicate that the SVM-Based GPC scheme provides an excellent performance with respect to local stabilization of the target (an originally unstable equilibrium point). Furthermore, it somewhat performs targeting, the task of steering the chaotic system towards the target by applying relatively small parameter perturbations. It considerably reduces the waiting time until the system, starting from random initial conditions, enters the local control region, a small neighborhood of the chosen target. Moreover, SVM-Based GPC maintains its performance in the case that the measured output is corrupted by an additive Gaussian noise.