The Optimal Power Flow (OPF) problem, a cornerstone of power system operations, has gained increased attention since its inception by Carpentier in 1962. OPF is fundamentally an optimization challenge aimed at enhancing electric power system operations within the bounds of physical and operational constraints. Over the decades, various methodologies have been explored to address the OPF problem, adapting to evolving grid complexities and the integration of distributed energy resources. These advancements have brought to the fore issues related to system randomness, fluctuation, and the need for rapid control mechanisms. This thesis introduces a comprehensive solution incorporating an online optimization algorithm tailored for real-time OPF applications. This approach, characterized by minimal computation times, integrates a feedback strategy that obviates the necessity for instantaneous power demand information and employs a Shape-constrained Gaussian Process for the estimation of unknown cost functions. The proposed control algorithm demonstrates robust tracking performance and satisfactory computation efficiency, marking a significant improvement towards optimizing future power networks fraught with increasing size and complexity. Moreover, this work delves into the investigation of various system design parameters, offering insights into potential avenues for enhancing system performance. Through a meticulous examination of these parameters, the thesis sheds light on strategies to refine the integrated system’s efficacy, paving the way for more resilient and efficient power networks.

Navigation systems in an Autonomous Vehicles (AV) can be divided into two parts: a path planning block which takes in the environmental data and rules to design a collision-free obstacle and a vehicle control and tracking block which generates actuator inputs for the AV to follow the reference path generated by the path planning block. Each task is fulfilled by a different algorithm with its own performance indices. These algorithms are not usually designed to get the best overall vehicle performance but the best performance of their respective blocks. A planned path that the vehicle cannot follow can therefore be generated and can lead to high tracking error and in some cases collision with obstacles. This can be solved by integrating path planning and vehicle control blocks with the dynamics of the AV.

The goal of this graduation project is therefore to develop an integrated planning and vehicle control algorithm for an Autonomous Vehicles (AV). This is done by integrating a novel-Artificial Potential Fields (APF) with Model Predictive Control (MPC) to solve both path planning and vehicle control using a single optimization problem. The addition of the AV and the Obstacle Vehicle (OV) dynamics to the optimization problem as prediction models along with recursive computation can determine accurate inputs to be given to the AV.

Unlike traditional APF-based path planning where the minimum potential path is generated as the result of a gradient descent method applied on the available map data and obstacle information, the APF is added as a cost to the objective function of the MPC based optimization problem to find the minimum potential path. By using a receding horizon approach for solving the final optimization problem, the potential field can be updated at each time step to avoid moving obstacles. The dynamics of the vehicle added to the optimization problem include both lateral and longitudinal dynamics and are linearized at each time step at the current state of the AV.

This however generates a path which does not travel in the centre of the lane and makes risky manoeuvres. Therefore, a Mixed-Integer Model Predictive Control (MIMPC) algorithm with logical constraints is used to generate an optimal lane to travel in. This optimal lane is used to generate a road potential which can guide the vehicle to the centre of the optimal lane. The MIMPC and the APF-MPC algorithms are run successively to generate a collision-free path.

The logical constraints, also called MLD constraints are converted into a set of linear inequalities with the introduction of logical variables. These logical variables are used to represent individual logical constraints based on the states of the system and on a combination of logical and state constraints. A novel-APF inspired by the Yukawa Potential [?] is designed to represent each obstacle. A convex representation of this non-convex obstacle potential is formulated to simplify the optimization problem. The convex representation of the obstacle APF is obtained by approximating it using a region-based APF where the region is defined by the position of the AV around the obstacle. This is further simplified by approximation using a quadratic Taylor-series expansion.

The simulation was performed on MATLAB on a two-lane road with multiple obstacles. The thesis report ends with a discussion on future work to be taken to further enhance the performance of the controller and to make it road-ready.