A novel state feedback control based on SVR

Abstract

The SVM is one of the methods which can introduce the statistical learning theory for solving the pattern recognition problem with small samples and learning problems such as function estimation. The relationships between the states with desirable responses can be expressed by some functions and these functions are estimated by using SVM. There are classification problems and regression problems in support vector machines. Only the support vector regression problem is used in this paper. This paper proposes a very novel method which makes it possible that state feedback controller can be designed for unknown dynamic system with measurable states. The SVR algorithm is used for the identification of inputoutput relationship. A virtual state space representation is derived from the relationship and the SVM makes the relationship between actual states and virtual states. For unknown dynamic systems, a state feedback controller can be designed based on the virtual system and the SVM makes the controller being with actual states. The results of this paper can give many opportunities that the state feedback control can be applied for unknown dynamic systems. The first step of this design method is to identify the input-output relationship of the unknown system as a transfer function by using SVR. Next step is to design a virtual system based on the transfer function. Final step is to derive the relationship between the actual states and virtual states by using SVM. The linear kernel function is used in SVR. A state feedback controller is designed based on the virtual system and the virtual system can be replaced by actual states by using the above relationship and it gives the actual states feedback controller. And simulation results are provided to show the performance of the proposed control method. Finally, the results of this paper make it is possible to the state feedback control theory to be used for unknown dynamic systems. This result can be expected to be applied to unknown nonlinear systems.