Design of an MPC control policy for a non-linear system based on PWA model representation

Piecewise affine systems have emerged as focal points of study within the realm of control theory due to their ability to accurately model complex, non-linear dynamical systems. This thesis navigates the motivations behind the extensive investigation of piecewise affine systems and elucidates their practical utility. The inherent flexibility of piecewise affine models allows for a perfect representation of systems that exhibit distinct behaviors in different regions. This attribute makes them particularly well suited for applications in robotics, power systems, and process control, where the ability to capture nonlinearity is crucial. Examining the convenience of piecewise affine systems in control scenarios reveals their capacity to address challenging dynamics and facilitate the design of efficient control strategies. In the domain of optimal control solutions, Model Predictive Control (MPC) emerges as a compelling technique when applied to piecewise affine systems. Toward the conclusion of this exploration, this thesis delves into the MPC’s applicability in this context, highlighting the advantages it offers. By leveraging MPC’s predictive capabilities, these systems can achieve enhanced performance, increased robustness, and improved adaptability. The synergies between piecewise affine systems and MPC provide a promising avenue for advancing the state-of-the-art in control theory and its practical implementation. This thesis contributes to the ongoing discourse by explaining implications of studying piecewise affine systems, showcasing their versatility, and ultimately underscoring why MPC stands out as an optimal technique for harnessing the full potential of these intriguing dynamical models.