Nonlinear H ∞ Control of Uncertain Nonholonomic Systems in Chained Forms

Abstract—Nonlinear H ∞ control is considered for uncertain nonholonomic systems with external disturbances in their chained form kinematic models. State feedback controllers are explicitly constructed to guarantee an L2 gain performance from the disturbance to the system output. Without the presence of the disturbance, the system states are regulated to the origin. Recent results in robust and adaptive control of uncertain nonholonomic systems are extended to include external disturbance inputs. A simulation example shows the effectiveness of the proposed control schemes. Index Terms—Nonlinear control, nonholonomic systems, back-stepping, disturbance attenuation, L2 gain. 1