Sampled-Data Indirect Adaptive Control of Bioreactor Using Affine Radial Basis Function Network Architecture

Abstract

This paper considers a problem of bioreactor control, which is formulated in Anderson and Miller (1990) and Ungar (1990) as a benchmark problem for application of neural network-based adaptive control algorithms. A completely adaptive control of this strongly nonlinear system is achieved with no a priori knowledge of its dynamics. This becomes possible thanks to a novel architecture of the controller, which is based on an affine Radial Basis Function network approximation of the sampled-data system mapping. Approximation with such net-work could be considered as a generalization of a standard practice to linearize a nonlinear system about the working regime. As the network is affine in the control components, it can be inverted with respect to the control vector by using fast matrix computations. The considered approach includes several features, recently introduced in some advanced process control algorithms. These features—multirate sampling, on-line adaptation, and Radial Basis Function approximation of the system nonlinearity—are crucial for the achieved high performance of the controller.