Quasi-optimal control of a solar thermal system via neural networks

Abstract

The optimal control of complex thermal energy systems is a challenge due to their dynamic behavior and constantly changing boundary conditions. To maximize the energy efficiency of such a dynamic system, optimal trajectories for the controlled variables are needed. Extensive system knowledge is required to model the system accurately enough to be able to compute optimal trajectories. The high computational cost of computing optimal control solutions with traditional approaches, especially with changing boundary conditions, often makes this approach unusable for applications with limited computational power, such as real-time applications on electronic control units (ECUs). This study investigates a possible solution to this challenge using a simplified example system. Optimal control solutions for different boundary and initial conditions are generated for the selected solar thermal system using a direct multiple shooting algorithm. Based on Bellman’s optimality principle, the generated solutions are transformed into a data set of optimal state–action pairs. On this basis, different types of neural networks are trained, specifically a feed-forward, a recurrent, and a radial basis function network. Thus, data generation and training can be performed offline, and the required online computations are significantly reduced since the evaluation of a trained neural network requires comparatively low central processing unit (CPU) power. The trained neural network controllers are tested for their ability to output near-optimal control actions based on the current system state. The feed-forward and recurrent neural networks show promising initial results in this regard. Open questions and the need for improvements are discussed.

Keywords

• Optimal control
• Neural networks
• Bellmann equation
• Thermal systems
• Optimization