Adaptive fine-tuning of non-linear control systems with application to the urban traffic control strategy TUC

Practical large-scale nonlinear control systems require an intensive and time-consuming effort for the fine-tuning of their control parameters in order to achieve a satisfactory performance. In most cases, the fine-tuning process may take years and is performed by experienced personnel. The purpose of this paper is to introduce and analyze a systematic approach for the automatic fine-tuning of the control parameters of practical large-scale nonlinear control systems and investigate its efficiency when applied to the recently developed urban traffic control strategy TUC (Traffic-responsive Urban Control). The proposed approach is based on a concept similar to the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm. The difference between the SPSA algorithm and the proposed approach is that, SPSA employs an approximation of the gradient of an appropriate objective function using only the most recent fine-tuning experiments, while in the proposed approach the approximation of the gradient is performed by using a linear-in-the-parameters approximator that incorporates information of a user-specified time-window of the past experiments. Mathematical analysis of the proposed approach establishes its convergence properties and that SPSA can be regarded as a special case of the proposed approach. Simulation results using the traffic network of the city of Chania, Greece - a typical urban traffic network containing all possible varieties of complex junction staging - demonstrate the efficiency of the proposed approach.