Explicit Model Predictive Control Design based on Constrained Zonotope Propagation

Zonotopes have become a widely used tool in control design, demonstrating their effectiveness in various applications ranging from state estimation to explicit model predictive control. However, the traditional use of zonotopes is limited by a set certain geometric shapes that restrict the range of state sets that can be considered. This paper proposes a novel approach to control design using constrained zonotopes that can encode arbitrary polytopes. We present a propagation scheme and an affine approximation of the exact control law for this representation, and discuss issues related to center identification for constrained zonotopes. A fast method for detecting set membership is also proposed based on lifting the constrained zonotopes into a higher dimensional space. The proposed method extends the range of shapes that can be considered in control design and offers a promising alternative to the limitations of regular zonotopes. It has the potential for wide-ranging impact in various areas of control, providing a valuable tool for solving complex control problems.