Solving nonlinear optimal control problems is a challenging task, particularly for high-dimensional problems. We propose algorithms for model-based policy iterations to solve nonlinear optimal control problems with convergence guarantees. The main component of our approach is an iterative procedure that utilizes neural approximations to solve linear partial differential equations (PDEs), ensuring convergence. We present two variants of the algorithms. The first variant formulates the optimization problem as a linear least square problem, drawing inspiration from extreme learning machine (ELM) for solving PDEs. This variant efficiently handles low-dimensional problems with high accuracy. The second variant is based on a physics-informed neural network (PINN) for solving PDEs and has the potential to address high-dimensional problems. We demonstrate that both algorithms outperform traditional approaches, such as Galerkin methods, by a significant margin. We provide a theoretical analysis of both algorithms in terms of convergence of neural approximations towards the true optimal solutions in a general setting. Furthermore, we employ formal verification techniques to demonstrate the verifiable stability of the resulting controllers.

Abstract Unmanned aerial vehicle based precision agriculture is a predominant research area. The modern flying ad‐hoc network leverages the advanced low latency vehicular communication and intelligent computing paradigms that help the ecosystem to grow up to the next level. In this work, we propose an ecosystem for precision agriculture that leverages the use of the opportunistic MQTT protocol in an edge‐enabled intelligent drone network for sensing and performing crop prediction using an intelligent ensemble machine learning model. The proposed approach leverages the edge computing system that requires low energy devices and also exploits the ultra‐low latency opportunistic message transfer methodology. The experimental results show the maximum of 0.9 message delivery ratio and a minimum of 600 ms latency is achieved by opportunistic MQTT protocol in an ultra‐low latency sparse network scenario. A weighted ensemble model is deployed onto the edge enabled devices or the drones. An accuracy of 96.5% is achieved in predicting the type of crops that can be grown in the soil about the selected area of interest.