At the child brain facility at the Erasmus Medical Centre, multiple tests are performed with children who have one of several disorders. Two of these tests are done with electroencephalogram measurements and are called mismatch negativity and acoustic change complex. After a signal processing pipeline, the EEG measurements from these tests are shown as waveforms called event-related potentials. The goal of these measurements is to see if there is any relation between the waveforms and the disorder, age and other information about the subjects.\newline

These waveforms are measured for each subject, EEG electrode, and in the case of MMN, for different stimuli, which naturally results in a tensor data structure. Algorithms for discriminant analysis and regression that are developed to be applied to tensors are described and altered to take into account the properties of the EEG data. Discriminant analysis can be used to improve classification algorithms that distinguish disorders, while regression can be used to predict variables such as test scores based on the measured data. The algorithms are first tested on simulated data, which shows they can have some merit. Classification rates improve in most simulated cases when the discriminant analysis is applied to the data. Regression can also reliably predict variables when strong correlations are present between the input tensor and output variable. Based on the data from the child brain facility, the discriminant analysis still improves classification rates in some cases, but not as significantly as on the simulated data. Regression using the algorithms described in this thesis is not useful in predicting test scores from other experiments done with the subjects. \newline

The algorithms are also dissected to discover which specific features in the data tensor are weighted heavier by the algorithms. This is done to gain new insights into the differences between the disorders. When comparing the weights that are used for the simulated data with the features that are of importance, there is some relation, but not a very strong one. When the input tensor is however segmented in the time mode, the times of interest can be identified. The regression algorithm also resulted in weights that can be analysed to look at when and where the measurements relate to the output, but this did not show any interesting results. For real data, the segmented tensor resulted in some interesting insights about the differences between the various disorders.\newline

For the current dataset, the discriminant analysis algorithms do improve classification rates, but not by much. The features weighted the most by this algorithm in combination with a segmented tensor might give some insight into the disorders. The tensor regression methods do not work to predict a test score and do not give new insights into the disorders.

Traditionally, Event-Triggered Control (ETC) methods are sample-and-hold control schemes that implement a triggering condition in order to reduce the number of control updates. Given a decay rate of the Lyapunov function, they focus on minimizing the (average) Inter-Sample Time (IST). In this thesis, we focused on the scheduling of Periodic Event-Triggered Control (PETC) controllers. By dynamically switching between triggering conditions, we
are maximizing the average rate of decay of the Common Lyapunov Function (CLF) given a minimum Average Inter Sample Time (AIST) or burst condition.

Given the physical system, we construct a switched system which captures all possible
scheduling behaviors. The l-complete abstraction of the switched system is constructed by solving a conjunction of quadratic equations. By setting a minimum AIST or burst condition, a set of states in the abstraction is marked and a safety game is played to construct the Maximal Permissive Controller (MPC).

On the safe behaviors inside the MPC, the guaranteed minimum control performance is maximized for the infinite horizon problem, i.e. by maximizing the minimum weighted time average of the primitive cycles in the MPC. First, several energy games are played to estimate
the maximum control performance. Thereafter, a mean-payoff game is played to generate the strategy securing this maximum control performance, which is used to construct the infinite horizon controller.

An end-to-end framework is developed to discover physical laws directly from videos, which can help facilitate the study on robust prediction, system stability analysis and gain the physical insight of a dynamic process. In this work, a video information extraction module is proposed to detect and collect the pixel position of moving objects, which would be further transformed into physical states we care about. A physical law discovery module is developed to learn closed-form expressions based on the extracted physical information. The video information extraction module takes advantage of contour detection and Hough transformation to extract position information. The physical law discovery module includes a deep neural network-like hierarchical structure Mathematical Operation Network (MathONet) which is consisted of basic mathematical operations. We develop a sparse Bayesian learning algorithm to learn both the topology and parameters of dynamic systems. Several simulated videos were generated to illustrate Newton’s law of motion, the state space of a Duffing oscillator, and the pendulum motion equation. By demonstrating on these examples, our method can discover the corresponding governing function without requiring much prior information.

Optical fibers form the backbone of our global data transmission infrastructure. As demands on global data transmission grow the capacity of these systems needs to be increased. The behaviour of light waves through these optical fibers is described by the Manakov Equation (ME), a system of nonlinear partial differential equations.

The ME is an integrable system, which can be solved analytically using Nonlinear Fourier Transforms. Recently, fiber-optic communication systems based on the Nonlinear Fourier Transform (NFT) of the ME have been proposed. Similar to the linear Fourier Transform, which decomposes a signal in linear frequency components, the NFT decomposes a signal in nonlinear frequency components. This nonlinear spectrum consists of a continuous and a discrete part. The continuous spectrum in general constitutes the whole real line. The discrete spectrum consists of distinct points in the complex plane which correspond to so-called solitons, which are stable wave forms. The evolution of the nonlinear spectrum along the fiber is trivial.

The nonlinear spectrum however cannot be computed analytically for most signals and therefore numerical methods are needed. The existing numerical methods have a high computational complexity of O(D^2) for computing the continuous spectrum, with D the number of time samples of the signal. For the Nonlinear Schrödinger Equation (NSE), a simplification of the ME, more efficient numerical methods exist with a computational complexity of O(D log^2(D)). In this thesis we present an extension of these so-called fast NFT methods to the ME. The resulting algorithms are second and fourth-order algorithms based on second and fourth order exponential integration methods respectively.

We developed open source software implementing the fast NFT algorithms for the ME and integrated them in the already existing Fast Nonlinear Fourier Transform (FNFT) software library. We provide detailed documentation and examples which allow other researchers to use the algorithms as tools or as a base for developing new algorithms. We furthermore test the accuracy of the developed algorithms against analytic examples. Of these examples, the rectangle signal and secant hyperbolic signal are new analytic examples for the ME to the best of our knowledge.

The use of artificial neural networks is becoming ever more ubiquitous as the computational power available to use grows. The widespread implementation of neural networks as controllers in the field of systems and control is however being hindered by the lack of verifiability of these controllers. One type of controller that does not lack verifiability is the correct-by-design controller. The main drawback of correct-by-design controllers is that they inherently produce large data structures in order to store their control rules. In this work, a novel methodology to synthesize correct-by-design neural network controllers is presented in order to alleviate these issues. This methodology combines reinforcement learning techniques and abstraction based correct-by-design control verification techniques in order to synthesize neural network controllers that are correct-by-design. The procedure does so by alternating between a controller training routine and a controller verification routine in a system abstraction framework. This framework ensures that numerical training and verification results in a controller with formal guarantees applicable to real systems. Using the proposed methodology, neural network controllers are synthesized and verified in order to prove that the methodology works. In addition to this, the resulting correct-by-design neural network controllers are compared to conventional correct-by-design controllers in order to judge their performance and data requirements. This comparison also includes alternative structures used to store these different controllers. Based on this comparison, a conclusion is drawn regarding when to use which type of controller. The proposed methodology is implemented into a correct-by-design neural network synthesis framework called COSYNNC. This framework is intended as a basis for further research into correct-by-design neural network control and is publicly available.

The world population is growing rapidly and the demand for healthy food grows with it. Greenhouse cultivation provides an efficient way to grow crops in a protected and controlled environment. In the past, many greenhouse control algorithms have been developed. How- ever, the majority of these algorithms rely on an explicit parametric model description of the greenhouse. These models are often based on physical laws such as conservation of mass and energy and contain many parameters which should be identified. Due to the complex and highly non-linear dynamics of greenhouses, these models might not be applicable to control greenhouses other than the one for which the model has been designed and identified. Hence, in current horticultural practice these control algorithms are scarcely used. Therefore, the need rises for a control algorithm which does not rely on a parametric system representa- tion but rather on input/output data of the greenhouse system, hereby establishing a way to control the system with unknown or unmodeled dynamics. A recently proposed algo- rithm, Data-Enabled Predictive Control (DeePC), is able to replace system identification, state estimation and future trajectory prediction by one single optimization framework. The algorithm exploits a non-parametric model constructed solely from input/output data of the system. This algorithm is employed in order to control the greenhouse climate. It is shown that in numerical simulation the DeePC algorithm is able to control the greenhouse climate. A comparison is made with the conventional Nonlinear Model Predictive Control (NMPC) algorithm in order to show the differences between a predictive control algorithm that has direct access to the non-linear greenhouse simulation model and a purely data-driven predic- tive control algorithm. Both algorithms are compared based on reference tracking accuracy and computational time. Furthermore, it is shown in numerical simulation that the DeePC algorithm is able to cope with changing dynamics within the greenhouse system throughout the crop cycle.

Dynamic model parameters (e.g. governor) are uncertain and hard to validate. A possible solution can be the usage of parameter identification techniques. So far parameter identification techniques have proved their potential in identifying model parameters on model scale, but this has never been applied on a full-scale propulsion system. During this thesis an attempt is made to estimate the dynamic model parameters of a Stan Tug 1205.

For large-scale system with tens of thousands of states and outputs the computation in the conventional Kalman filter becomes time-consuming such that Kalman filtering in large-scale real-time application is practically infeasible. A possible mathematical framework to lift the curse of dimensionality is to lift the problem in higher dimensions with the use of tensors and then decompose it. The tensor-train decomposition is chosen due to its computational advantages for systems with low tensor-train rank. Within this thesis two main limitations of the existing tensor Kalman filter are solved. First, a method is developed based on tensor-train rank truncation of the covariances to increase the computational speed for more general systems. Second, a MIMO tensor Kalman filter is developed for a specific class of systems. The power of the developed methods is shown on the example of adaptive optics which fits into the framework. A comparison with state-of-the-art large-scale estimation algorithms shows the computational advantage of the tensor Kalman filter at the cost of approximation errors.

In modern society cars are one of the most important means of transportation. Unfortunately, many people die in car accidents around the world. Research shows that the number of fatal casualties in car accidents has been increasing for the past decade and that the largest cause of these accidents is the human driver. For this reason, research on fully autonomous vehicles has gained a lot of attention. However, currently autonomous driving is only implemented to reduce the errors of human drivers. More research is necessary in order for fully autonomous vehicles to be implemented and to remove the human driver completely. A robust navigation algorithm which is able to run in real time is one of the challenges in development of fully autonomous vehicles. Important topics in navigation of autonomous vehicles include the path planner and the motion controller. The path planner finds a path for the vehicle from its current location to the target location. At the same time the path planner avoids obstacles and fulfills the non-holonomic constraints of the autonomous vehicle. The motion controller tries to follow the path the path planner made as close as possible by controlling the vehicle. These two topics influence each other and are therefore dependent. In literature little research is done on integrated algorithms that combine path planning and motion control. Therefore, this thesis will research navigation of autonomous vehicles by using an integrated algorithm that includes both path planning and motion control. The objective of this thesis is to develop a Lyapunov stable control algorithm that is capable of planning a path for all possible vehicle maneuvers. Besides path planning the proposed algorithm must be capable of controlling the vehicle along this path. Furthermore, the algorithm needs to include obstacles and the non-holonomic dynamics of an autonomous vehicle. The main contribution of this thesis is an integrated path planner and motion controller for navigation of autonomous vehicles. The stability of the proposed algorithm is proven by using the Lyapunov method. Simulation results prove that the algorithm is capable of planning the path and the motion of the autonomous vehicle with non-holonomic constraints and with the presence of obstacles.

The extraordinary capability of swarming ant species in route finding and foraging efficiency through trail trail development has been studied for many years. Scientists have been able to capture the behavior of individual ants in control algorithms and used the resulting artificial swarm of ants to solve difficult problems. These problems include function optimization, sorting, clustering and route finding. So far, the route finding capabilities, where agents solely rely on local available information, have only been demonstrated in virtual discrete domains. The aim of this thesis is the development of an agent based control method that allows a swarm of robots to establish a trail between a source and target, placed in an unknown domain. The method solely relies on information locally available to the agent. No direct communication among the agents is necessary as agents mark the environment to relay information. Simulations are performed in a Python and C-based computer program, developed in tandem with this study. A versatile controller is presented that, in conjunction with suggestions for the swarm size and pheromone characteristics, can be implemented on real robots to explore unknown environments in a multitude of scenarios.

System identification for switched linear systems from input output data has received substantial attention in recent years. There is a growing interest for techniques that pose the identification problem as a sparse optimisation problem. At the same time a vast amount of research is dedicated to improving SAT solvers which as a result become faster every year. In this work a novel identification method for Switched AutoRegressive eXogenous (SARX) systems
and PieceWise AutoRegressive eXogenous (PWARX) systems is proposed that combines sparse optimisation with a SAT solver. The presented method aims to minimise the number of submodels needed to fit the data, while facilitating a prescribed minimum dwell time between switches. The procedure for the identification of switched ARX models is composed of two steps. The First phase determines the switching times in an iterative process aided by a SAT solver. Second, the model parameters and the switching sequence are estimated by
optimising the sparsity of a sequence. The identification procedure for PWARX models operates similarly although it incorporates the knowledge that switches depend on the regressor. An extension to these methods that makes the identification of large datasets tractable is also put forward. The proposed algorithm is evaluated on synthetic systems from the literature and shows promising results. Finally, the proposed algorithm is applied to an experimental benchmark dataset for a nonlinear system. All the algorithms proposed in this thesis project are implemented in the form of a toolbox that is made publicly available.