Stability, safety and optimality are often sought-after properties in the field of controller synthesis. In the last century, linear control theory has matured to a level where scalable algorithms are widely available that are able to synthesize controllers with stability and optimality guarantee. However, the synthesis of safe controllers largely remains an open question. Furthermore, when nonlinear systems are considered, these methods often result in sub-optimal performance, or fail to provide a stabilizing solution at all. Current nonlinear controller synthesis methods typically lack stability, safety and/or optimality guarantee, or require computationally expensive online optimization. This thesis presents a novel method that is able to overcome these limitations. The presented controller synthesis method combines techniques from Approximate Dynamic Programming, Lyapunov theory and barrier theory, to synthesize an optimal controller in the form of a Neural Network. Alongside the controller a second Neural Network is deployed, which is trained to serve as a certificate function to provide stability and/or safety guarantee. To assure the correctness of the procedure, Satisfiability Modulo Theory and Counterexample-Guided Inductive Synthesis are utilized. We subject the method to a number of case studies, through which the versatility of the method is demonstrated. We show the method is able to work with linear and nonlinear systems, as well as systems with input and state constraints. Furthermore, we show the method yields controllers that are able to outperform linear controllers in terms of cost minimization.

A wet clutch is a device that transfers torque between two shafts via a hydraulic mechanism. Wet clutch control is key to achieve smooth and fast clutch engagements. Optimal control of a wet clutch is not trivial because of the complexity of the system due to nonlinearities, hybrid dynamics and changing dynamics over time due to changing temperatures and wear. Nowadays simple parametrized feedforward controllers are used in industry. The parameters of the control signal are tuned by hand and updated over time by an operator to account for the changing dynamics. Several solutions to the wet clutch control problem exist in the literature, however the structure of the solutions is fixed beforehand and they rely on expert knowledge of the system. Another challenging aspect of wet clutch control is model uncertainty, currently robustness of performance is considered by running a finite number of experiments, but no hard guarantees can be given. In this thesis a method is developed to automatically synthesize controllers for a wet clutch which are robust to model uncertainties. The method uses Genetic Programming (GP) to automatically synthesize controllers. Using GP controllers for a wet clutch can synthesize without fixing the structure beforehand and in a multi-objective way. Robustness is considered by optimizing the worst case performance. To be able to give a guarantee on the worst case performance of a controller a method, that is able to formally guarantee a lower bound on the worst case performance using reachability analysis, is developed. This method is to costly to incorporate into GP and instead a use cheap estimation of the worst performance in practice.
This method was able to find robust controllers which outperformed a hand tuned baseline controller, but in order to compare this method to other methods in literature, real life experiments are needed.

A repetitive motion system supporting nano meter precision is positioned at high accelerations, which produces a force that disturbs the demanded accuracy requirements. Iterative learning control is used to learn optimal feedforward control signals for the attenuation this disturbance force. The iterative method comes with a limitation, as it has to learn the compensation signals one by one. In this study, a data-driven approach is taken to design a feedforward controller that generalizes the control action, by finding a model that fits the learned optimal compensation signals. The multi-objective evolutionary algorithm genetic programming is used for its unique ability to search directly in the
program space, therefore returning compact analytic equations as feedforward controller. Feedforward artificial neural networks with the ReLU and tanh activation function are used, due to their excellent approximation qualities. sherlock is a tool that efficiently computes the maximum and minimum output off a ReLU network for a compact input set. The tool is used to find a guaranteed output range for the feedforward controller constructed from ReLU networks, which is desirable from a safety perspective. Finally, the designed controller are compared based on their attenuation of the disturbance force
and their model size. The designed feedforward controllers are capable of reducing the disturbance force by at least 40.01%. The analytic controllers found with genetic programming provide the user with insights in the control problem, cost less memory storage and come with a faster computation time.