Reachability problems for PAMs

Piecewise affine maps (PAMs) are frequently used as a reference model to show the openness of the reachability questions in other systems. The reachability problem for one-dimentional PAM is still open even if we define it with only two intervals. As the main contribution of this paper we introduce new techniques for solving reachability problems based on p-adic norms and weights as well as showing decidability for two classes of maps. Then we show the connections between topological properties for PAM's orbits, reachability problems and representation of numbers in a rational base system. Finally we show a particular instance where the uniform distribution of the original orbit may not remain uniform or even dense after making regular shifts and taking a fractional part in that sequence.Comment: 16 page

Holistic Vehicle Control Using Learning MPC

In recent years, learning MPC schemes have been introduced to address these challenges of traditional MPC. They typically leverage different machine learning techniques to learn the system dynamics directly from data, allowing it to handle model uncertainty more effectively. Besides, they can adapt to changes by continuously updating the learned model using real-time data, ensuring that the controller remains effective even as the system evolves. However, there are some challenges for the existing learning MPC techniques. Firstly, learning-based control approaches often lack interpretability. Understanding and interpreting the learned models and their learning and prediction processes are crucial for safety critical systems such as vehicle stability systems. Secondly, existing learning MPC techniques rely solely on learned models, which might result in poor performance or instability if the model encounters scenarios that differ significantly from the training data. Thirdly, existing learning MPC techniques typically require large amounts of high-quality data for training accurate models, which can be expensive or impractical in the vehicle stability control domain. To address these challenges, this thesis proposes a novel hybrid learning MPC approach for HVC. The main objective is to leverage the capabilities of machine learning algorithms to learn accurate and adaptive models of vehicle dynamics from data, enabling enhanced control strategies for improved stability and maneuverability. The hybrid learning MPC scheme maintains a traditional physics-based vehicle model and a data-based learning model. In the learned model, a variety of machine-learning techniques can be used to predict vehicle dynamics based on learning from collected vehicle data. The performance of the developed hybrid learning MPC controller using torque vectoring (TV) as the actuator is evaluated through the Matlab/Simulink and CarSim co-simulation with a high-fidelity Chevy Equinox vehicle model under a series of harsh maneuvers. Extensive real-world experiments using a Chevy Equinox electric testing vehicle are conducted. Both simulation results and experimental results show that the developed hybrid learning MPC approach consistently outperforms existing MPC methods with better yaw rate tracking performance and smaller vehicle sideslip under various driving conditions

Statistical Learning and Stochastic Process for Robust Predictive Control of Vehicle Suspension Systems

Predictive controllers play an important role in today's industry because of their capability of verifying optimum control signals for nonlinear systems in a real-time fashion. Due to their mathematical properties, such controllers are best suited for control problems with constraints. Also, these interesting controllers can be equipped with different types of optimization and learning modules. The main goal of this thesis is to explore the potential of predictive controllers for a challenging automotive problem, known as active vehicle suspension control. In this context, it is intended to explore both modeling and optimization modules using different statistical methodologies ranging from statistical learning to random process control. Among the variants of predictive controllers, learning-based model predictive controller (LBMPC) is becoming more and more interesting to the researchers of control society due to its structural flexibility and optimal performance. The current investigation will contribute to the improvement of LBMPC by adopting different statistical learning strategies and forecasting methods to improve the efficiency and robustness of learning performed in LBMPC. Also, advanced probabilistic tools such as reinforcement learning, absorbing state stochastic process, graphical modelling, and bootstrapping are used to quantify different sources of uncertainty which can affect the performance of the LBMPC when it is used for vehicle suspension control. Moreover, a comparative study is conducted using gradient-based as well as deterministic and stochastic direct search optimization algorithms for calculating the optimal control commands. By combining the well-established control and statistical theories, a novel variant of LBMPC is developed which not only affords stability and robustness, but also surpasses a wide range of conventional controllers for the vehicle suspension control problem. The findings of the current investigation can be interesting to the researchers of automotive industry (in particular those interested in automotive control), as several open issues regarding the potential of statistical tools for improving the performance of controllers for vehicle suspension problem are addressed