Predictor-Feedback Stabilization of Multi-Input Nonlinear Systems

We develop a predictor-feedback control design for multi-input nonlinear systems with distinct input delays, of arbitrary length, in each individual input channel. Due to the fact that different input signals reach the plant at different time instants, the key design challenge, which we resolve, is the construction of the predictors of the plant's state over distinct prediction horizons such that the corresponding input delays are compensated. Global asymptotic stability of the closed-loop system is established by utilizing arguments based on Lyapunov functionals or estimates on solutions. We specialize our methodology to linear systems for which the predictor-feedback control laws are available explicitly and for which global exponential stability is achievable. A detailed example is provided dealing with the stabilization of the nonholonomic unicycle, subject to two different input delays affecting the speed and turning rate, for the illustration of our methodology.Comment: Submitted to IEEE Transactions on Automatic Control on May 19 201

Control of 2 × 2 Linear Hyperbolic Systems: Backstepping-Based Trajectory Generation and PI-Based Tracking

International audienceWe consider the problems of trajectory generation and tracking for general 2 × 2 systems of first-order linear hyperbolic PDEs with anti-collocated boundary input and output. We solve the trajectory generation problem via backstepping. The reference input, which generates the desired output, incorporates integral operators acting on advanced and delayed versions of the reference output with kernels which were derived by Vazquez, Krstic, and Coron for the backstepping stabilization of 2 × 2 linear hyperbolic systems. We apply our approach to a wave PDE with indefinite in-domain and boundary damping. For tracking the desired trajectory we employ a PI control law on the tracking error of the output. We prove exponential stability of the closed-loop system, under the proposed PI control law, when the parameters of the plant and the controller satisfy certain conditions, by constructing a novel " non-diagonal " Lyapunov functional. We demonstrate that the proposed PI control law compensates in the output the effect of in-domain and boundary disturbances. We illustrate our results with numerical examples