Smart-Learning Enabled and Theory-supported Optimal Control

This work focuses on solving the general optimal control problems with smart-learning enabled and theory-supported optimal control (SET-OC) approaches. The proposed SETOC includes two main directions. Firstly, according to the basic idea of direct method, the smart-learning enabled iterative optimization algorithm (SEIOA) is proposed for solving discrete optimal control problems. Via discretization and reformulation, the optimal control problem is converted into general quadratically constrained quadratic programming (QCQP) problem. Then, the SEIOA is applied to solving QCQPs. To be specific, first, a structure-exploiting decomposition scheme is introduced to reduce the complexity of the original problem. Next, an iterative search, combined with an intersection cutting plane, is developed to achieve global convergence. Furthermore, considering the implicit relationship between the algorithmic parameters and convergence rate of the iterative search, deep learning is applied to design the algorithmic parameters from an appropriate amount of training data to improve convergence property. To demonstrate the effectiveness and improved computational performance of the proposed SEIOA, the developed algorithms have been implemented in extensive real-world application problems, including unmanned aerial vehicle path planning problem and general QCQP problems. According to the theoretical analysis of global convergence and the simulation results, the efficiency, robustness and improved convergence rate of the optimization framework compared to the state-of-the-art optimization methods for solving general QCQP problems are analyzed and verified. Secondly, the on-board learning-based optimal control method (L-OCM) is proposed to solve the optimal control problems. Supported by the optimal control theory, the necessary conditions of optimality for optimal control of the optimal control problem can be derived, which leads to two two-point-boundary-value-problems (TPBVPs). Then, critical parameters are identified to approximate the complete solutions of the TPBVPs. To find the implicit relationship between the initial states and these critical parameters, deep neural networks are constructed to learn the values of these critical parameters in real-time with training data obtained from the off-line solutions