Linearizable Feedforward Systems: A Special Class

We address the problem of linearizability of systems in feedforward form. In a recent paper [22] we completely solved the linearizability for strict feedforward systems. We extend here those results to a special class of feedforward systems. We provide an algorithm, along with explicit transformations, that linearizes the system by change of coordinates when some easily checkable conditions are met. We also re-analyze type II class of linearizable strict feedforward systems provided by Krstic in [9] and we show that this class is the unique linearizable among the class of quasi-linear strict feedforward systems (see Definition III.1). Our results allow an easy computation of the linearizing coordinates and thus provide a stabilizing feedback controller for the original system. They can also be implemented via software like mathematica/matlab/maple using simple integrations, derivations of functions

Explicit Feedback Linearization of Control Systems

This paper addresses the problem of feedback linearization of nonlinear control systems via state and feedback transformations. Necessary and sufficient geometric conditions were provided in the early eighties but finding the feedback linearizing coordinates is subject to solving a system of partial differential equations and had remained open since then. We will provide in this paper a complete solution to the problem (see the companion paper where the state linearization has been addressed) by defining an algorithm that allows to compute explicitly the linearizing state coordinates and feedback for any nonlinear control system that is truly feedback linearizable. Each algorithm is performed using a maximum of n - 1 steps (n being the dimension of the system) and they are made possible by explicitly solving the Flow-box or straightening theorem. A possible implementation via software like mathematica/ matlab/maple using simple integrations, derivations of functions might be considered

Forwarding design with prescribed local behavior

International audienceAmong the non-linear control techniques, some Lyapunov design methods (Forwarding / Backstepping) take advantage of the structure of the system (Feedforward-form / Feedback-form) to formulate a continuous control law which stabilizes globally and asymptotically the equilibrium. In addition to stabilization, we focus on the local behaviour of the closed loop system, providing conditions under which we can predetermine the behaviour around the origin for Feedforward systems

State Linearization of Control Systems: An Explicit Algorithm

In this paper we address the problem of linearization of nonlinear control systems using coordinate transformations. Although necessary and sufficient geometric conditions have been provided in the early eighties, the problem of finding the linearizing coordinates is subject to solving a system of partial differential equations and remained open 30 years later. We will provide here a complete solution to the problem by defining an algorithm allowing to compute explicitly the linearizing state coordinates for any nonlinear control system that is indeed linearizable. Each algorithm is performed using a maximum of n - 1 steps (n being the dimension of the system) and they are made possible by explicitly solving the Flow-box or straightening theorem. The problem of feedback linearization is addressed in a companion paper. A possible implementation via software like mathematica/matlab/maple using simple integrations, derivations of functions might be considered

Feedback Linearizability of Strict Feedforward Systems

For any strict feedforward system that is feedback linearizable we provide (following our earlier results) an algorithm, along with explicit transformations, that linearizes the system by change of coordinates and feedback in two steps: first, we bring the system to a newly introduced Nonlinear Brunovský canonical form (NBr) and then we go from (NBr) to a linear system. The whole linearization procedure includes diffeo-quadratures (differentiating, integrating, and composing functions) but not solving PDE’s. Application to feedback stabilization of strict feedforward systems is given

Dynamic vs static scaling: an existence result

International audienceThe relation between static and dynamic control Lyapunov functions scaling is discussed. It is shown that, under some technical assumptions, stabilizability by means of static scaling implies stabilizability by means of dynamic scaling. A motivating example and a worked out design example complement the theoretical part