The reliably stable neural network controllers' synthesis with the transient process parameters optimization

Abstract

The subject of this paper is to develop a method for synthesizing stable neural network controllers with optimization of transient process parameters. The goal is to develop a method for synthesizing a neural network controller for control systems that guarantees the closed-loop system stability through automated selection of Lyapunov function with the involvement of an additional neural network trained on the data obtained in the solving process the integer linear programming problem. The tasks to be solved are: study the stability of a closed-loop control system with a neural network controller, train the neurocontroller and Lyapunov neural network function, create an optimization model for the loss function minimization, and conduct a computational experiment as an example of the neural network stabilizing controller synthesis. The methods used are: a neural network-based control object simulator training method described by an equations system taking into account the SmoothReLU activation function, a direct Lyapunov method to the closed-loop system stability guarantee, and a mixed integer programming method that allows minimizing losses and ensuring stability and minimum time regulation for solving the optimization problem. The following results were obtained: the neural network used made it possible to obtain results related to the transient process time reduction to 3.0 s and a 2.33-fold reduction in overregulation compared to the traditional controller (on the example of the TV3-117 turboshaft engine fuel consumption model). The results demonstrate the proposed approach's advantages, remarkably increasing the dynamic stability and parameter maintenance accuracy, and reducing fuel consumption fluctuations. Conclusions. This study is the first to develop a method for synthesizing a stabilizing neural network controller for helicopter turboshaft engines with guaranteed system stability based on Lyapunov theory. The proposed method's novelty lies in its linear approximation of the SmoothReLU activation function using binary variables, which allowed us to reduce the stability problem to an optimization problem using the mixed integer programming method. A system of constraints was developed that considers the control signal and stability conditions to minimize the system stabilization time. The results confirmed the proposed approach's effectiveness in increasing engine adaptability and energy efficiency in various operating modes.

Keywords

• optimization
• controller
• neural network
• lyapunov function
• mixed integer programming