Barrier Lyapunov function-based fixed-time FTC for high-order nonlinear systems with predefined tracking accuracy

Nonlinear Dynamics - This article proposes a fixed-time adaptive fault-tolerant control methodology for a larger class of high-order (powers are positive odd integers) nonlinear systems subject to...     

Robust adaptive control of nonholonomic systems with uncertainties

Robust adaptive control of nonholonomic systems in chained form with linearly parameterized and strongly nonlinear disturbance and drift terms is dicussed. The novelty of the proposed method is a combined use of the state-scaling and the back-stepping procedure.     

Energy integrals for mechanical systems with nonlinear nonholonomic constraints

The work analyzes energy relations for nonholonomic systems, whose motion is restricted by nonlinear nonholonomic constraints. For the mechanical systems with linear constraints, the analysis of energy relations was carried out in [1], [2], [3], [4], [5], [6] …. On the basis of corresponding Lagrange’s equations, a general law of the change in energy dε/dt is formulated for mentioned systems by the help of which it is shown that there are two types of the laws of conservation of energy, depending on the structure of elementary work of the forces of constraint reactions. Also, the condition for existing the second type of the law of conservation of energy is formulated in the form of the system of partial differential equations. The obtained results are illustrated by a model of nonholonomic mechanical system.     

Finite-/fixed-time robust stabilization of switched discontinuous systems with disturbances

Nonlinear Dynamics - This paper investigates the finite-time and fixed-time stabilization (FFTS) of switched systems with discontinuous dynamics, external disturbances and delays. Firstly, a new...     

Equations of motion for nonholonomic mechanical systems with unilateral constraints

IntroductionThemotionofamechanicalsystemwithunilateralconstraintsismoregeneralthanwithbilateralconstraints1andyetitsinvestigationismoredifficult[1,2].Thesystemswithunilateralconstraintsinvolvetheholonomicmechanicalsystemswithunilateralholonomicconstraints[3～6]andthenonholonondcmeChanicalsystemswithunilateralholonondcconstraintS[7]andthenonholonondcmechanicalsystemswithunilateralnonholonondcconstraintS[2]andsoon.ThispaperstUdiesatypeofmoregeneralsystemswithunilateralconstfaints:nonholonondcs…     

On the stability of equilibria of nonholonomic systems with nonlinear constraints

Lyapunov＇s first method, extended by V. V. Kozlov to nonlinear mechani- cal systems, is applied to the study of the instability of the position of equilibrium of a mechanical system moving in the field of conservative and dissipative forces. The mo- tion of the system is limited by ideal nonlinear nonholonomic constraints. Five cases determined by the relationship between the degree of the first nontrivial polynomials in Maclaurin＇s series for the potential energy and the functions that can be generated from the equations of nonlinear nonholonomic constraints are analyzed. In the three eases, the theorem on the instability of the position of equilibrium of nonholonomic systems with linear homogeneous constraints （V. V. Kozlov （1986）） is generalized to the case of nonlin- ear nonhomogeneous constraints. In the other two cases, new theorems are set extending the result from V. V. Kozlov （1994） to nonholonomic systems with nonlinear constraints.     

Distributed optimal control for nonholonomic systems with input constraints and uncertain interconnections

Nonlinear Dynamics - This paper studies a distributed optimal tracking control method for nonholonomic mobile mechanical multi-agent systems under complex conditions such as input constraints, the...     

A novel method for modeling skidding for systems with nonholonomic constraints

In this paper, the effect of wheel skidding on the steering motion of a simple vertical rolling disk is investigated. By modifying the nonholonomic constraints, two novel dynamic models are proposed. The first model rotates the constraints and enforces them along a plane correlated to the skid angle. It then relates the skidding in a wheel to the Lagrange multipliers associated with the kinematic constraints of that wheel. The second model relaxes the no-skidding constraint, allowing its transgression and relates the skidding to the generalized velocities of the actuated degrees of freedom of the system. To validate our model, we compare it to one in the literature and we analyze the motion of the disk on icy and snowy road conditions, where skidding can be significant.     

On the invariant theory of nonholonomic systems with constraints of non-Chetaev type

This paper deals with the theory of the differential invariant and integral invariant for a nonholonomic system with constraints of non-Chetaev type. It gives the restricted conditions of virtual displacement in velocity space for nonholonomic constraints of non-Chetaev type and extends the Jourdain principle and the canonical equation for the system. It presents and proves generalized Noether theorem, and gives generalized energy integral and cyclic integral for the system. Finally, the basic integral variants for the system are extended and the integral invariant of Poincaré-Cartan and the universal integral invariant of Poincaré for the system are obtained.     

Decentralized stabilization of large-scale linear interconnected systems with time-varying delays

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｒｅｃｅｎｔｙｅａｒｓ,ｄｅｃｅｎｔｒａｌｉｚｅｄｓｔａｂｉｌｉｚａｔｉｏｎｏｆｌａｒｇｅ＿ｓｃａｌｅｉｎｔｅｒｃｏｎｎｅｃｔｅｄｓｙｓｔｅｍｓｈａｓｂｅｅｎｗｉｄｅｌｙｓｔｕｄｉｅｄ .ＬｅｅａｎｄＲａｄｏｖｉｃ[1,2 ]ｅｓｔａｂｌｉｓｈｅｄｓｏｍｅｄｅｃｅｎｔｒａｌｉｚｅｄｓｔａｂｉｌｉｚａｔｉｏｎｃｏｎｄｉｔｉｏｎｓｆｏｒｌａｒｇｅ＿ｓｃａｌｅｌｉｎｅａｒｃｏｎｔｉｎｕｏｕｓａｎｄｄｉｓｃｒｅｔｅｔｉｍｅ＿ｄｅｌａｙ .Ｉｎｔｈｉｓｍｅｔｈｏｄ ,ｍｏｒｅｓｔｒｕｃｔｕ…     

Modeling and analysis of nonholonomic dynamic systems with a class of rheonomous affine constraints

This paper is devoted to modeling and theoretical analysis of dynamic control systems subject to a class of rheonomous affine constraints, which are called $A$ -rheonomous affine constraints. We first define $A$ -rheonomous affine constraints and explain their geometric representation. Next, a necessary and sufficient condition for complete nonholonomicity of $A$ -rheonomous affine constraints is shown. Then, we derive nonholonomic dynamic systems with $A$ -rheonomous affine constraints (NDSARAC), which are included in the class of nonlinear control systems. We also analyze linear approximated systems and accessibility for the NDSARAC. Finally, the results are applied to some physical examples in order to check the application potentiality.     

A METHOD FOR SOLVING THE DYNAMICS OF MULTIBODY SYSTEMS WITH RHEONOMIC AND NONHOLONOMIC CONSTRAINTS

ＡＭＥＴＨＯＤＦＯＲＳＯＬＶＩＮＧＴＨＥＤＹＮＡＭＩＣＳＯＦＭＵＬＴＩＢＯＤＹＳＹＳＴＥＭＳＷＩＴＨＲＨＥＯＮＯＭＩＣＡＮＤＮＯＮＨＯＬＯＮＯＭＩＣＣＯＮＳＴＲＡＩＮＴＳ￥ＳｈｕｉＸｉａｏｐｉｎｇ（水小平）ＺｈａｎｇＹｏｎｇｆａ（张永发）（Ｄｅｐａｒ...     

Recursive identification of discrete-time nonlinear cascade systems with time-varying output hysteresis

Nonlinear Dynamics - A recursive identification method for discrete-time nonlinear cascade systems with a linear dynamic system followed by a time-varying output hysteresis is presented. The...     

Numerical method for dynamics of multi-body systems with two-dimensional Coulomb dry friction and nonholonomic constraints

Based on the dynamical theory of multi-body systems with nonholonomic constraints and an algorithm for complementarity problems, a numerical method for the multi-body systems with two-dimensional Coulomb dry friction and nonholonomic constraints is presented. In particular, a wheeled multi-body system is considered. Here,the state transition of stick-slip between wheel and ground is transformed into a nonlinear complementarity problem(NCP). An iterative algorithm for solving the NCP is then presented using an event-driven method. Dynamical equations of the multi-body system with holonomic and nonholonomic constraints are given using Routh equations and a constraint stabilization method. Finally, an example is used to test the proposed numerical method. The results show some dynamical behaviors of the wheeled multi-body system and its constraint stabilization effects.     

Noether's theorem for nonholonomic systems of non-Chetaev's type with unilateral constraints in event space

Ｔｈｅｓｔｕｄｙｏｆｃｏｎｓｅｒｖａｔｉｏｎｌａｗｓｏｆｄｙｎａｍｉｃａｌｓｙｓｔｅｍｉｓａｓｉｇｎｉｆｉｃａｎｔａｓｐｅｃｔｏｆｍｏｄｅｒｎａｎａｌｙｔｉｃａｌｍｅｃｈａｎｉｃｓ.Ｉｎ1918,ｕｓｉｎｇｔｈｅｉｎｖａｒｉａｎｃｅｏｆＨａｍｉｌｔｏｎａｃｔｉｏｎｕｎｄｅｒｔｈｅｉｎｆｉｎｉｔｅｓｉｍａｌｔｒａｎｓｆｏｒｍａｔｉｏｎｓ,Ｎｏｅｔｈｅｒ[1]ｓｔｕｄｉｅｄｃｏｎｓｅｒｖａｔｉｏｎｌａｗｓｏｆｍｅｃｈａｎｉｃａｌｓｙｓｔｅｍａｎｄｐｒｅｓｅｎｔｅｄｔｈｅｆａｍｏｕｓＮｏｅｔｈｅｒ’ｓｔｈｅｏｒ…