This paper is concerned with state and output feedback stabilization of a class of port-Hamiltonian systems with nonholonomic constraints. First we study canonical forms for port-Hamiltonian systems with nonholonomic constraints. Second, we give a new state feedback stabilization method by using non-smooth Hamiltonian functions via generalized canonical transformations. Third, we propose a dyna...

In this paper, the problem of finite-time stabilization is developed for nonholonomic chained form systems with communication delay in the input. The finite-time control laws are presented by utilizing the switching control strategy and the theory of finite-time stability, which can make the states of the nonholonomic chained form systems to converge from any non-equilibrium state to the equili...

This paper is devoted to a unified approach to trajectory tracking control of nonholonomic port-controlled Hamiltonian systems via generalized canonical transformations. The key idea is to construct an error system, which describes the dynamics of the tracking error, by a passive port-controlled Hamiltonian system. This strategy works for both holonomic and nonholonomic port-controlled Hamilton...

This note considers the tracking problem of nonholonomic dynamic systems with unknown inertia parameters. A new controller is proposed relying on newly defined tracking errors and the passivity property of the nonholonomic dynamic system. The proposed controller ensures that the entire state of the system asymptotically tracks the desired trajectory. Simulation results show effectiveness of the...

This paper addresses the concept of partial stabilization for driftless control systems called ”nonholonomic systems”. We introduce a class of feedback transformations that transforms our system in to a multi-chained triangular form. We show that we can bounded the first component; this can be done by using a smooth feedback control depending on the state. In addition the (n − 1) other componen...

This paper presents a geometric description on Lie algebroids of Lagrangian systems subject to nonholonomic constraints. The Lie algebroid framework provides a natural generalization of classical tangent bundle geometry. We define the notion of nonholonomically constrained system, and characterize regularity conditions that guarantee that the dynamics of the system can be obtained as a suitable...

In this paper, the trajectory tracking control problem of uncertain nonholonomic mechanical systems is investigated. By separately considering kinematic and dynamic models of a nonholonomic mechanical system, a new adaptive tracking control is proposed based on neural network approximation. The proposed design consists of two steps. First, the nonholonomic kinematic subsystem is transformed int...

Virtual constraints are relations imposed in a control system that become invariant via feedback instead of real physical acting on the system. Nonholonomic systems mechanical with non-integrable velocities. In this work, we introduce notion virtual nonholonomic geometric framework. More precisely, it is controlled distribution associated an affine connection We show existence and uniqueness la...

In this paper, we consider a hybrid control strategy for stabilization of nonholonomic systems. In particular, we deal with a typical nonholonomic system, namely a two-wheeled vehicle. We first rewrite the system in a chained form, and then transform it into a nonholonomic integrator (NHI) system. Finally, we apply and modify the hybrid control method for the NHI system, so that the entire syst...