A Unified Approach of Controller Design and System Identification for Optimal Control of Single-Input Nonlinear Systems

This paper presents a novel unified approach of controller design and identification for unknown input affine nonlinear systems. An issue with obtaining the best performance of optimal control is that identification errors degrade control performance. One solution to overcome it is direct controller tuning without system identification, which is expected to give high quality control. However, many experiments with various control inputs are required in the design procedure. The proposed framework simultaneously implements system identification and controller design. This method adopts a weighted least squares method to cope with various identification criteria. An unknown plant system is identified with a weight selected appropriately for control. It is selected in a simple manner based on an analytical discussion of nonlinear optimal control theory, namely the Hamilton-Jacobi-Bellman equation. An iterative calculation procedure for a preliminarily given data set is derived. This iterative algorithm gives a (sub-)optimal pair of the weight and the model parameter that improves the control performance. Numerical results demonstrate that the proposed approach achieves better optimal control performance than the standard least squares method.