Safe Adaptive Control Using Differential Inclusions and Nonlinear Model Predictive Control

Sammanfattning

Controlling nonlinear systems with unknown dynamics is a major challenge, especially when safety and re liability are important. This thesis presents a robust Model Predictive Control (MPC) approach that uses differential inclusions to handle uncertainty in system behavior. The unknown dynamics are approximated using interval bounds based on finite-length trajectory data, allowing the controller to make safe decisions without requiring a complete model. The MPC is designed to work with these bounds, formulated with CasADi and solved using IPOPT framework to ensure constraint satisfaction and stability despite model uncertainties. The method is validated through simulations on three systems: a unicycle model for trajec tory tracking, an unmanned aerial vehicle (UAV) performing obstacle avoidance, and a two-link manipulator required to reach a reference point. The results demonstrate that the approximation algorithm provides con servative but reliable bounds, even with small data sets being stored, enabling the robust MPC to navigate uncertain environments safely and achieve tracking objectives. However, a key limitation of the proposed approach is the computational cost of solving the robust MPC problem online, particularly as the complex ity of the system increases. Moreover, stability guarantees cannot be provided in general for systems with unknown or highly uncertain dynamics, especially when only limited data are available for model learning or uncertainty quantification. Formal stability guarantees are difficult to establish in these settings. As such, the method should be viewed as a safety-oriented control strategy with adaptive capabilities, rather than a universally stabilizing solution. However, the framework demonstrates potential to achieve safe control in constrained scenarios and lays the foundation for future improvements in computational efficiency and theoretical guarantees.