Neural Networks-Based Computational Modeling of Bilinear Control Systems for Conservation Laws: Application to the Control of Cogeneration

This paper considers the computational modeling of the class of bilinear control systems for hyperbolic conservation laws with nonstandard boundary conditions. These systems arise from (control) engineering applications of systems displaying propagation phenomena, i.e., integrating steam, water, and gas pipes. The aim of this paper is achieved by means of a systematic computational procedure previously introduced and adapted here for the class of systems under consideration. The procedure, based on a convergent Method of Lines ensures the convergence of the approximate numerical solution and also the preservation of the basic properties of the “true” solution as well as its Lyapunov stability. Thus, the approximate computational model allows numerical quantitative and qualitative analysis relevant to a specific problem. The computational efficiency of the procedure is ensured by its implementation based on some, possibly massively, parallel-structured devices belonging to the Artificial Intelligence field-the cell-based recurrent neural networks. As a case study, we consider a control system occurring in the cogeneration process (combined heat and electricity generation). A comparison between the results of the qualitative analysis and those of the numerical simulations demonstrates the correctness and effectiveness of the computational procedure for the dynamics and transients analysis. The paper ends with some conclusions and a list of open problems.