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- Malmström, Magnus, 1994-
(författare)
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Approximative Uncertainty in Neural Network Predictions
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Suppose data-driven black-box models, e.g., neural networks, should be used as components in safety-critical systems such as autonomous vehicles. In that case, knowing how uncertain they are in their predictions is crucial. However, this needs to be provided for standard formulations of neural networks. Hence, this thesis aims to develop a method that can, out-of-the-box, extend the standard formulations to include uncertainty in the prediction. The proposed method in the thesis is based on a local linear approximation, using a two-step linearization to quantify the uncertainty in the prediction from the neural network. First, the posterior distribution of the neural network parameters is approximated using a Gaussian distribution. The mean of the distribution is at the maximum a posteriori estimate of the parameters, and the covariance is estimated using the shape of the likelihood function in the vicinity of the estimated parameters. The second linearization is used to propagate the uncertainty in the parameters to uncertainty in the model’s output. Hence, to create a linear approximation of the nonlinear model that a neural network is. The first part of the thesis considers regression problems with examples of road-friction experiments using simulated and experimentally collected data. For the model-order selection problem, it is shown that the method does not under-estimate the uncertainty in the prediction of overparametrized models. The second part of the thesis considers classification problems. The concept of calibration of the uncertainty, i.e., how reliable the uncertainty is and how close it resembles the true uncertainty, is considered. The proposed method is shown to create calibrated estimates of the uncertainty, evaluated on classical image data sets. From a computational perspective, the thesis proposes a recursive update of the parameter covariance, enhancing the method’s viability. Furthermore, it shows how quantified uncertainty can improve the robustness of a decision process by formulating an information fusion scheme that includes both temporal correlational and correlation between classifiers. Moreover, having access to a measure of uncertainty in the prediction is essential when detecting outliers in the data, i.e., examples that the neural network has yet to see during the training. On this task, the proposed method shows promising results. Finally, the thesis proposes an extension that enables a multimodal representation of the uncertainty. The third part of the thesis considers the tracking of objects in image sequences, where the object is detected using standard neural network-based object detection algorithms. It formulates the problem as a filtering problem with the prediction of the class and the position of the object viewed as the measurements. The filtering formulation improves robustness towards false classifications when evaluating the method on examples from animal conservation in the Swedish forests.
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| 2. |
- Shoja, Shamisa, 1991-
(författare)
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On Complexity Certification of Branch-and-Bound Methods for MILP and MIQP with Applications to Hybrid MPC
- 2023
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In model predictive control (MPC), an optimization problem is solved at each time step, in which the system dynamics and constraints can directly be taken into account. The MPC concept can be further extended to the control of hybrid systems, where a part of the state and control variables has a discrete set of values. When applying MPC to linear hybrid systems with performance measures based on the 1-norm or the∞-norm, the resulting optimal control problem can be formulated as a mixed-integer linear program (MILP), while the optimal control problem with a quadratic performance measure can be cast as a mixed-integer quadratic program (MIQP). An efficient method to solve these non-convex MILP and MIQP problems is branch and bound (B&B) which relies on solving convex relaxations of the problem ordered in a binary search tree. For the safe and reliable real-time operation of hybrid MPC, it is desirable to have a priori guarantees on the worst-case complexity such that the computational requirements of the problem do not exceed the time and hardware capabilities.Motivated by this need, this thesis aims to certify the computational complexity of standard B&B methods for solving MILPs and MIQPs in terms of, e.g., the size of the search tree or the number of linear systems of equations (iterations) that are needed to be solved online to compute optimal solution. In particular, this knowledge enables us to compute relevant worst-case complexity bounds for the B&B-based MILP and MIQP solvers, which has significant importance in, e.g., real-time hybrid MPC where hard real-time requirements have to be fulfilled. The applicability of the proposed certification method is further extended to suboptimal B&B methods for solving MILPs, where the computational effort is reduced by relaxing the requirement to find a globally optimal solution to instead finding a suboptimal solution, considering three different suboptimal strategies. Finally, the proposed framework is extended to the cases where the performance of B&B is enhanced by considering three common start heuristic methods that can help to find good feasible solutions early in the B&B search process.
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| 3. |
- Ljungqvist, Oskar, 1990-
(författare)
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Motion planning and feedback control techniques with applications to long tractor-trailer vehicles
- 2020
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- During the last decades, improved sensor and hardware technologies as well as new methods and algorithms have made self-driving vehicles a realistic possibility in the near future. At the same time, there has been a growing demand within the transportation sector to increase efficiency and to reduce the environmental impact related to transportation of people and goods. Therefore, many leading automotive and technology companies have turned their attention towards developing advanced driver assistance systems and self-driving vehicles.Autonomous vehicles are expected to have their first big impact in closed environments, such as mines, harbors, loading and offloading sites. In such areas, the legal requirements are less restrictive and the surrounding environment is more controlled and predictable compared to urban areas. Expected positive outcomes include increased productivity and safety, reduced emissions and the possibility to relieve the human from performing complex or dangerous tasks. Within these sites, tractor-trailer vehicles are frequently used for transportation. These vehicles are composed of several interconnected vehicle segments, and are therefore large, complex and unstable while reversing. This thesis addresses the problem of designing efficient motion planning and feedback control techniques for such systems.The contributions of this thesis are within the area of motion planning and feedback control for long tractor-trailer combinations operating at low-speeds in closed and unstructured environments. It includes development of motion planning and feedback control frameworks, structured design tools for guaranteeing closed-loop stability and experimental validation of the proposed solutions through simulations, lab and field experiments. Even though the primary application in this work is tractor-trailer vehicles, many of the proposed approaches can with some adjustments also be used for other systems, such as drones and ships.The developed sampling-based motion planning algorithms are based upon the probabilistic closed-loop rapidly exploring random tree (CL-RRT) algorithm and the deterministic lattice-based motion planning algorithm. It is also proposed to use numerical optimal control offline for precomputing libraries of optimized maneuvers as well as during online planning in the form of a warm-started optimization step.To follow the motion plan, several predictive path-following control approaches are proposed with different computational complexity and performance. Common for these approaches are that they use a path-following error model of the vehicle for future predictions and are tailored to operate in series with a motion planner that computes feasible paths. The design strategies for the path-following approaches include linear quadratic (LQ) control and several advanced model predictive control (MPC) techniques to account for physical and sensing limitations. To strengthen the practical value of the developed techniques, several of the proposed approaches have been implemented and successfully demonstrated in field experiments on a full-scale test platform. To estimate the vehicle states needed for control, a novel nonlinear observer is evaluated on the full-scale test vehicle. It is designed to only utilize information from sensors that are mounted on the tractor, making the system independent of any sensor mounted on the trailer.
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