Controlled contractive sets for low-complexity constrained control

The design of explicit constrained control is relatively simple when a controlled contractive set is available. However, the complexity of the explicit controller will depend on the complexity of the controlled contractive set. The ability to design a low complexity controlled contractive set is therefore desirable. Most methods for finding controlled contractive sets either assume the use of a constant linear state feedback, or exploit reachable set computations. In the first case, the assumption of a constant linear state feedback is restrictive (as controllers for constrained linear systems, such as MPC, are typically piecewise affine), while in the second case the complexity of the controlled contractive set may be very high. Initial results on the construction of low complexity controlled contractive sets without assuming linear state feedback were reported in the recent literature. The present paper extends these results, including the ability to handle more general classes of system dynamics. The paper develops a method for finding a controlled contractive set of a specified complexity, allowing for a trade-off between the complexity of the set and its volume.