ISS of predictor feedback for multi-input affine nonlinear systems with distinct input delays

Abstract

We develop a predictor feedback control scheme for multi-input affine nonlinear systems with distinct input delays in each individual input channel and additive disturbances. The input-to-state stable control Lyapunov function (ISS-CLF) is used to design control laws for the delay-free affine nonlinear systems. Then, a predictor-feedback controller is constructed for this class of nonlinear systems with input delays. We establish input-to-state stability with respect to additive plant disturbances, as well as we show that the control law derives gain margin guarantees. Our proofs are based on the infinite-dimensional backstepping transformation and the construction of a Lyapunov functional. The developed method is applied to the control of vehicular traffic flow at distant bottlenecks.