Towards Provable Guarantees for Learning-based Control Paradigms

 Within recent years, there has been a renewed interest in developing data-driven learning based algorithms for solving longstanding challenging control problems. This interest is primarily motivated by the availability of ubiquitous data and an increase in computational resources of modern machines.  However, there is a prevailing concern on the lack of provable performance guarantees on data-driven/model-free learning based control algorithms. This dissertation focuses the following key aspects: i) with what facility can state-of-the-art learning-based control methods eke out successful performance for challenging flight control applications such as aerobatic maneuvering?; and ii) can we leverage well-established tools and techniques in control theory to provide some provable guarantees for different types of learning-based algorithms?  

To these ends, a deep RL-based controller is implemented, via high-fidelity simulations, for Fixed-Wing aerobatic maneuvering. which shows the facility with which learning-control methods can eke out successful performances and further encourages the development of learning-based control algorithms with an eye towards providing provable guarantees.

Two learning-based algorithms are also developed: i) a model-free algorithm which learns a stabilizing optimal control policy for the bilinear biquadratic regulator (BBR) which solves the regulator problem with a biquadratic performance index given an unknown bilinear system; and ii) a model-free inverse reinforcement learning algorithm, called the Model-Free Stochastic inverse LQR (iLQR) algorithm, which solves a well-posed semidefinite programming optimization problem to obtain unique solutions on the linear control gain and the parameters of the quadratic performance index given zero-mean noisy optimal trajectories generated by a linear time-invariant dynamical system. Theoretical analysis and numerical results are provided to validate the effectiveness of all proposed algorithms.