Data- and Model-Driven Predictive Control: With Applications to Connected Autonomous Vehicles

Traditional techniques for analyzing and developing control laws in safety-critical applications usually require a precise mathematical model of the system. However, there are many control applications where such precise, analytical models can not be derived or are not readily available. Increasingly, data-driven approaches from machine learning are used in conjunction with sensor or simulation data in order to address these cases. Such approaches can be used to identify unmodeled dynamics with high accuracy. However, an objective that is increasingly prevalent in the literature involves merging or complementing the analytical approaches from control theory with techniques from machine learning.

Autonomous systems such as self-driving vehicles, distributed sensor networks, aerial drones, and agile robots, need to interact with their environments that are ever-changing and difficult to model. These and many other applications motivate the use of data-driven decision-making and control together. However, if data-driven systems are to be applied in these new settings, it is critical that they be accompanied by guarantees of safety and reliability, as failures could be catastrophic.

This dissertation addresses the problems in which there are interactions between model-based and data-driven systems and develops learning-based control strategies for the entire system that guarantees safety and optimality. Applications of these systems can be sough in autonomous networked mobile systems that are quickly making their way into the marketplace and are soon expected to serve a wide range of new tasks including package delivery, cooperatively fighting wildfires, and search and rescue after a natural disaster. As the number of these systems increases, their performance and capabilities can be greatly enhanced through wireless coordination. Wireless channel extremely contributes to the optimality and safety of the whole system, but it is a data-driven factor and there is no explicit mathematical model for it to be involved in the model-based part, that is mostly model predictive controller.

This dissertation presents two approaches to address the above-mentioned problem. The first proposed approach is the Gaussian  Process-based  Model  Predictive  Controller (GP-MPC) that leverages Gaussian Processes (GPs) to learn the variations of the data-driven variable in a defined time horizon. To avoid a large number of interactions with the environment in the learning process, the algorithm iterates in the reachable set from the current state to decrease the size of the kernel matrix and converge to the optimal trajectory faster. To reduce the computational cost further, an efficient recursive approach is developed to calculate the inverse of kernel matrix while MPC updates at each time step.

The second approach is Data-and Model-Driven Predictive Control (DMPC) which is a data-efficient learning controller that provides an approach to merge both the model-based (MPC) and data-based systems. DMPC is developed to solve an MPC problem that deals with an unknown function operating interdependently with the model. It is assumed that the value of the unknown function is predicted or measured for a given trajectory by an exogenous data-driven system that works separately from the controller. This algorithm can cope with very little data and builds its solutions based on the recently generated solution and improves its cost in each iteration until converging to an optimal solution, which typically needs only a few trials. Theoretical analysis for recursive feasibility of the algorithm is presented and it is proved that the quality of the trajectory does not get worse with each new iteration.

In the end, the developed algorithms are applied to the motion planning of two connected autonomous vehicles with linear and nonlinear dynamics. The results illustrate that the controller can create a safe trajectory that not only is optimal in terms of control effort and highway capacity usage but also results in a more stable wireless channel with maximum packet delivery rate (PDR).