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

Practical stabilization of nonlinear systems with state-dependent sampling and retarded inputs

A solution to the problem of stabilizing nonlinear systems with input with a constant pointwise delay and state-dependent sampling is proposed. It relies on a recursive construction of the sampling instants and on a recent variant of the classical reduction model approach. State feedbacks without distributed terms are obtained. A lower bound on the maximal allowable delay is determined via a Lyapunov-Krasovskii analysis. © 2012 AACC American Automatic Control Council)

Practical stabilization of nonlinear systems with state-dependent sampling and retarded inputs.

International audienceA solution to the problem of stabilizing nonlinear systems with input with a constant pointwise delay and state- dependent sampling is proposed. It relies on a recursive construction of the sampling instants and on a recent variant of the classical reduction model approach. State feedbacks without distributed terms are obtained. A lower bound on the maximal allowable delay is determined via a Lyapunov- Krasovskii analysis

Stabilization of cascaded nonlinear systems under sampling and delays

Over the last decades, the methodologies of dynamical systems and control theory have been playing an increasingly relevant role in a lot of situations of practical interest. Though, a lot of theoretical problem still remain unsolved. Among all, the ones concerning stability and stabilization are of paramount importance. In order to stabilize a physical (or not) system, it is necessary to acquire and interpret heterogeneous information on its behavior in order to correctly intervene on it. In general, those information are not available through a continuous flow but are provided in a synchronous or asynchronous way. This issue has to be unavoidably taken into account for the design of the control action. In a very natural way, all those heterogeneities define an hybrid system characterized by both continuous and discrete dynamics. This thesis is contextualized in this framework and aimed at proposing new methodologies for the stabilization of sampled-data nonlinear systems with focus toward the stabilization of cascade dynamics. In doing so, we shall propose a small number of tools for constructing sampled-data feedback laws stabilizing the origin of sampled-data nonlinear systems admitting cascade interconnection representations. To this end, we shall investigate on the effect of sampling on the properties of the continuous-time system while enhancing design procedures requiring no extra assumptions over the sampled-data equivalent model. Finally, we shall show the way sampling positively affects nonlinear retarded dynamics affected by a fixed and known time-delay over the input signal by enforcing on the implicit cascade representation the sampling process induces onto the retarded system