We study the problem of approximating one-dimensional nonintegrable codistributions by integrable ones and apply the resulting approximations to approximate feedback linearization of single-input systems. The approach derived in this paper allows one to nd a linearizable nonlinear system that is close to the given system in a least squares (L 2) sense. A linearly controllable single input aane ...

In this short paper it is theoretically shown that Kaizer's low-frequency model for nonlinear distortion in electrodynamic loudspeakers is feedback linearizable in current drive as well as voltage drive. This means there exists some nonlinear feedback mechanism such that the given system can be transformed into an exact linear system, provided one has full state information and there would be n...

This paper presents applications of polytopic approximation methods for reachable set computation using dynamic optimization. The problem of computing exact reachable sets can be formulated in terms of a Hamilton-Jacobi partial differential equation (PDE). Numerical solutions which provide convergent approximations of this PDE have computational complexity which is exponential in the continuous...

Abstract—This study proposes the transformation of nonlinear Magnetic Levitation System into linear one, via state and feedback transformations using explicit algorithm. This algorithm allows computing explicitly the linearizing state coordinates and feedback for any nonlinear control system, which is feedback linearizable, without solving the Partial Differential Equations. The algorithm is pe...

A wheeled mobile robot is subject to both holonomic and nonholonomic constraints. Representing the motion and constraint equations in the state space, this paper studies the feedback linearization of the dynamic system of a wheeled mobile robot. The main results of the paper are: (1) It is shown that the system is not input-state linearizable. (2) If the coordinates of a point on the wheel axis...

Control laws for continuous-time dynamical systems are most often implemented via digital controllers using a sample-and-hold technique. Numerical discretization of the continuous system is an integral part subsequent analysis. Feedback linearizability such sampled dependent upon choice map or In this article, feedback linearizable systems, we utilize idea retraction maps to construct discretiz...

We present a new method for motion planning and feedback control of three-link planar robot arms with a passive rotational third joint. These underactuated mechanical systems are shown to be fully linearizable and input-output decoupable by means of a nonlinear dynamic feedback, provided a physical singularity is avoided. The linearizing output is the position of the so-called center of percuss...

We deal with nonlinear dynamical systems, consisting of a linear nominal part perturbed by model uncertainties, nonlinearities and both additive and multiplicative random noise, modeled as a Wiener process. In particular, we study the problem of finding suitable measurement feedback control laws such that the resulting closed-loop system is stable in some probabilistic sense. To this aim, we in...

In this paper we discuss the nonlinear control of a novel biped robot with three-degrees-of-freedom and two control inputs, whose dynamics are linear apart from the gravitational torque and the impact equations. We show that the equations of motion are locally feedback linearizable by nonlinear change of coordinates and nonlinear feedback in a region that includes all walking gates of interest....

We investigate the effect of sampling on linearization for continuous time systems. It is shown that the discretized system is linearizable by state coordinate change for an open set of sampling times if and only if the continuous time system is linearizable by state coordinate change. Also, it is shown that linearizability via digital feedback imposes highly nongeneric constraints on the struc...