Rebecka Winqvist

In the context of control systems, the integration of machine learning mechanisms has emerged as a key approach for improving performance and adaptability. Notable progress has been made across several aspects of the control loop, including learning-based techniques for system identification and estimation, filtering and denoising, and controller design. This thesis delves into the rapidly expanding domain of learning in control, with a particular focus placed on learning-based controllers and learning-based identification methods. The first part of this thesis is devoted to the investigation of Neural Network approximations of Model Predictive Control (MPC). Model-agnostic neural network structures are compared to networks employing MPC-specific information, and evaluated in terms of two performance metrics. The main novel aspect lies in the incorporation of gradient data in the training process, which is shown to enhance the accuracy of the network generated control inputs. Furthermore, experimental results reveal that MPC-informed networks outperform the agnostic counterparts in scenarios when training data is limited. In acknowledgement of the crucial role accurate system models play in in the control loop, the second part of this thesis lends its focus to learning-based identification methods. This line of work addresses the important task of characterizing and modeling dynamical systems, by introducing cooperative system identification techniques to enhance estimation performance. Specifically, it presents a novel and generalized formulation of the Correctional Learning framework, leveraging tools from Optimal Transport. The correctional learning framework centers around a teacher-student model, where an expert agent (teacher) modifies the sampled data used by the learner agent (student), to improve the student’s estimation process. By formulating correctional learning as an optimal transport problem, a more adaptable framework is achieved, better suited for estimating complex system characteristics and accommodating alternative intervention strategies.

The contribution of this paper is a generalized formulation of correctional learning using optimal transport, which is about how to optimally transport one mass distribution to another. Correctional learning is a framework developed to enhance the accuracy of parameter estimation processes by means of a teacher-student approach. In this framework, an expert agent, referred to as the teacher, modifies the data used by a learning agent, known as the student, to improve its estimation process. The objective of the teacher is to alter the data such that the student’s estimation error is minimized, subject to a fixed intervention budget. Compared to existing formulations of correctional learning, our novel optimal transport approach provides several benefits. It allows for the estimation of more complex characteristics as well as the consideration of multiple intervention policies for the teacher. We evaluate our approach on two theoretical examples, and on a human-robot interaction application in which the teacher’s role is to improve the robots performance in an inverse reinforcement learning setting.

This paper investigates the problem of controller identification given the data from a linear quadratic Model Predictive Controller (MPC) with constraints. We propose an approach for learning MPC that explicitly uses the gradient information in the training process. This is motivated by the observation that recent differentiable convex optimization MPC solvers can provide both the optimal feedback law from the state to control input as well as the corresponding gradient. As a proof of concept, we apply this approach to explicit MPC (eMPC), for which the feedback law is a piece-wise affine function of the state, but the number of pieces grows rapidly with the state dimension. Controller identification can here be used to find an approximate low complexity functional approximation of the controller. The eMPC is modelled using a Neural Network (NN) with Rectified Linear Units (ReLUs), since such NNs can represent any piece-wise affine function. A key motivation is to replace on-line solvers with neural networks to implement MPC and to simplify the evaluation of the function in larger input dimensions. We also study experimental design and model evaluation in this framework, and propose a hit-and-run sampling algorithm for input design. The proposed algorithms are illustrated and numerically evaluated on a second order MPC problem.