Quasi-Optimal Regulators for Nonholonomic Systems Driven by Rough Paths∗

Nonholonomic systems such as port-Hamiltonian systems are well known to be difficult to control. To reduce the difficulty, in this paper, we derive quasi-optimal regulators for nonholonomic systems such as a typical chained system with some restriction to the form of control inputs. To achieve the solution, we employ a notion of stability in roughness, which is Lyapunov stability theory for dynamical systems driven by rough paths. The rough paths are capable of transforming some nonholonomic systems into holonomic systems with “hidden control inputs”. Thus, the control problems are simplified in exchange for the degradation of some control performances.