Collocation Methods for the Investigation of Periodic Motions of Constrained Multibody Systems

The investigation of periodic motions of constrained multibodysystems requires the numerical solution of differential-algebraicboundary value problems. After briefly surveying the basics of periodicmotion analysis the paper presents an extension of projected collocationmethods [6] to a special class of boundary value problems for multibodysystem equations with position and velocity constraints. These methodscan be applied for computing stable as well as unstable periodicmotions. Furthermore they provide stability information, which can beused to detect bifurcations on periodic branches. The special class ofequations stemming from contact problems like in railroad systems [22]can be handled as well. Numerical experiments with a wheelset modeldemonstrate the performance of the algorithms.     

An Improved Formulation for Constrained Mechanical Systems

This paper presents an investigation of the advantages of a new formulation in the study of mechanical systems with holonomic and nonholonomic constraints. The formulation, originally proposed for systems of constrained particles, provides an efficient and robust means of simulating general multibody systems in the presence of redundant, degenerate and intermittent constraints. The structure of the formulation also allows the use of a dynamics code for pure kinematics analysis with a simple substitution. In addition, the formulation separates applied and constraint forces explicitly allowing recovery of constraint forces by straightforward means. Several examples are given to demonstrate the effectiveness of the formulation in special circumstances.     

Advanced Programmed Motion Tracking Control of Nonholonomic Mechanical Systems

Trajectory tracking control of nonholonomic systems has been extended to tracking a desired motion. The desired motion is specified by equations of constraints, referred to as programmed, which may be differential equations of high order and may be nonholonomic. The strategy enables motion tracking control under the assumption that the system dynamics are accurately known. It is referred to as a model reference tracking control strategy for programmed motion. In this paper, adaptive and repetitive extensions of the strategy are proposed. Two selected advanced tracking control algorithms, i.e., the desired compensation adaptation law and the repetitive control law, which were originally dedicated to holonomic systems, are adapted to motion tracking control of nonholonomic systems. Simulation studies that illustrate programmed motion tracking control of systems with unknown parameters and the performance of repetitive motions are provided. A new performance measure to evaluate a programmed motion tracking performance is introduced.      

Scalable Variational Integrators for Constrained Mechanical Systems in Generalized Coordinates

We present a technique to implement scalable variational integrators for generic mechanical systems in generalized coordinates. Systems are represented by a tree-based structure that provides efficient means to algorithmically calculate values (position, velocities, and derivatives) needed for variational integration without the need to resort to explicit equations of motion. The variational integrator handles closed kinematic chains, holonomic constraints, dissipation, and external forcing without modification. To avoid the full equations of motion, this method uses recursive equations, and caches calculated values, to scale to large systems by the use of generalized coordinates. An example of a closed-kinematic-chain system is included along with a comparison with the open-dynamics engine (ODE) to illustrate the scalability and desirable energetic properties of the technique. A second example demonstrates an application to an actuated mechanical system.      

On the Equations of Kinematics and Dynamics of Constrained Mechanical Systems

The method of constructing of kinematical and dynamicalequations of mechanical systems, applied to numerical realization, isproposed in this paper. The corresponding difference equations, whichare obtained, give a guarantee of computations with given precision. Theequations of programmed constraints and those of constraintperturbations are defined. The stability of the programmed manifold fornumerical solutions of the kinematical and dynamical equations isobtained by means of corresponding construction of the constraintperturbation equations. The dynamical equations of system withprogrammed constraints are set up in the form of Lagrange equations ingeneralized coordinates. Certain inverse problems of rigid body dynamicsare considered.     

Two-Dimensional Compact Third-Order Polynomial Reconstructions. Solving Nonconservative Hyperbolic Systems Using GPUs

We present a new kind of high-order reconstruction operator of polynomial type, which is used in combination with the scheme presented in Castro et al. (J. Sci. Comput. 39:67?C114, 2009) for solving nonconservative hyperbolic systems. The implementation of the scheme is carried out on Graphics Processing Units (GPUs), thus achieving a substantial improvement of the speedup with respect to normal CPUs. As an application, the two-dimensional shallow water equations with geometrical source term due to the bottom slope is considered.     

基于非线性映射的约束系统自适应反推控制

针对基于障碍Lyapunov函数的非线性约束系统反推控制中, 控制器结构复杂、约束量初值选取区间小、会引入额外参数等问题, 提出了一种新的基于非线性映射的自适应反推控制方案. 该方法扩大约束量的初值选取区间为整个约束区间, 增加了系统初值选取和控制器设计的便易性. 约束量被映射至实数空间中, 因此映射后的新系统可以直接应用反推法设计控制器, 简化了控制器结构且不会引入额外参数. 证明了映射前后系统具有一致的收敛性, 保证闭环系统所有信号一致有界, 并且跟踪误差渐近收敛于零. 仿真结果进一步验证了本文方法的有效性.     

Stability Analysis of Time-Delay Systems With Incommensurate Delays Using Positive Polynomials

We present a new stability condition for linear time-delay systems (TDS) with multiple incommensurate delays based on the Rekasius substitution and positive polynomials. The condition is checked by testing the positivity of multivariate polynomials in certain domains. For this purpose, we propose two alternative algorithms based on linear programming and sum of squares methods, respectively. The efficiency and accuracy of the algorithms is compared in an example to alternative stability conditions taken from the literature.      

Robust Stability of LTI Systems Over Semialgebraic Sets Using Sum-of-Squares Matrix Polynomials

This paper deals with the robust stability of discrete-time linear time-invariant systems with parametric uncertainties belonging to a semialgebraic set. It is asserted that the robust stability of any system over any semialgebraic set (satisfying a mild condition) is equivalent to solvability of a semidefinite programming (SDP) problem, which can be handled using the available software tools. The particular case of a semialgebraic set associated with a polytope is then investigated, and a computationally appealing method is proposed to attain the SDP problem by means of a sampling technique, introduced recently in the literature. Furthermore, it is shown that the current result encompasses the ones presented in some of the recent works. The efficacy of the proposed method is demonstrated through some illustrative examples, and the results are compared to some of the existing methods.      

A Systematic Approach for Designing Analytical Dynamics and Servo Control of Constrained Mechanical Systems

A systematic approach for designing analytical dynamics and servo control of constrained mechanical systems is proposed. Fundamental equation of constrained mechanical systems is first obtained according to Udwadia-Kalaba approach which is applicable to holonomic and nonholonomic constrained systems no matter whether they satisfy the D'Alember's principle. The performance specifications are modeled as servo constraints. Constraint-following servo control is used to realize the servo constraints. For this inverse dynamics control problem, the determination of control inputs is based on the Moore-Penrose generalized inverse to complete the specified motion. Secondorder constraints are used in the dynamics and servo control. Constraint violation suppression methods can be adopted to eliminate constraint drift in the numerical simulation. Furthermore, this proposed approach is applicable to not only fully actuated but also underactuated and redundantly actuated mechanical systems. Two-mass spring system and coordinated robot system are presented as examples for illustration.      

Dynamic Resource Management in Energy Constrained Heterogeneous Computing Systems Using Voltage Scaling

An ad hoc grid is a wireless heterogeneous computing environment without a fixed infrastructure. This study considers wireless devices that have different capabilities, have limited battery capacity, support dynamic voltage scaling, and are expected to be used for eight hours at a time and then recharged. To maximize the performance of the system, it is essential to assign resources to tasks (match) and order the execution of tasks on each resource (schedule) in a manner that exploits the heterogeneity of the resources and tasks while considering the energy constraints of the devices. In the single-hop ad hoc grid heterogeneous environment considered in this study, tasks arrive unpredictably, are independent (i.e., no precedent constraints for tasks), and have priorities and deadlines. The problem is to map (match and schedule) tasks onto devices such that the number of highest priority tasks completed by their deadlines during eight hours is maximized while efficiently utilizing the overall system energy. A model for dynamically mapping tasks onto wireless devices is introduced. Seven dynamic mapping heuristics for this environment are designed and compared to each other and to a mathematical bound.     

受限正控制系统的可控性

本文提出当控制不仅只能取正值且在幅值上还要受限时线性多变量离散时间系统的零可控性、可达性及完全可控性的一些结果。     

Equivalent Control of Constrained Multibody Systems

This paper investigates the title problem from the perspective ofdetermining which forcesystems, although different, will have the same dynamic effectwhen applied to a mechanical system.A procedure is presented for determining how differences incontrol force/moment input are nullifiedby constraints on the system. This in turn provides a basis foroptimal control. The theoreticaldevelopment is illustrated by a series of examples with a model ofa redundant manipulator – a constrained/controlled triple pendulum.     

Computer-Aided Integration of Motions of the Discontinuous Mechanical System

Consideration was given to computer-aided modeling of the dynamics of multiple-link manipulators and other mechanical systems. Various perturbing factors that can affect this process were examined. Conditions for correct modeling that provides motions close to those of the physical system were established. Motion of the mechanical system is often described by differential equations whose computer-aided integration is usually defined as difference schemes that occur, for example, if finiteness of the integration step is taken into account. For the differential equations with smooth right-hand sides, sufficiently efficient methods of constructing an adequate scheme of integration were developed. The present paper focused on the mechanical systems where the generalized forces may be discontinuous. Construction of an adequate integration scheme for them is a challenge. Established were the conditions for motions of the difference scheme to converge to those of the system of discontinuous differential equations of the mechanical system.     

Control of a Class of Underactuated Mechanical Systems Using Sliding Modes

In this paper, we present a sliding mode control algorithm to robustly stabilize a class of underactuated mechanical systems that are not linearly controllable and violate Brockett's necessary condition for smooth asymptotic stabilization of the equilibrium, with parametric uncertainties. In defining the class of systems, a few simplifying assumptions are made on the structure of the dynamics; in particular, the damping forces are assumed to be linear in velocities. We first propose a switching surface design for this class of systems, and subsequently, a switched algorithm to reach this surface in finite time using conventional and higher order sliding mode controllers. The stability of the closed-loop system is investigated with an undefined relative degree of the sliding functions. The controller gains are designed such that the controller stabilizes the actual system with parametric uncertainty. The proposed control algorithm is applied to two benchmark problems: a mobile robot and an underactuated underwater vehicle. Simulation results are presented to validate the proposed scheme.     

Optimal Energy-Efficient Programmed Control of Distributed Parameter Systems

Journal of Computer and Systems Sciences International - A constructive solution of the optimal energy-efficient programmed control problem for distributed parameter systems with a given-precision...     

Constrained Control of Positive Systems with Delays

This technical note addresses controller design for continuous-time delayed linear systems. The control is under positivity constraint, which means that the resulting closed-loop systems are not only stable, but also positive. Bounded control is also considered, further requiring that the trajectory of the closed-loop system is bounded by a prescribed boundary, if the initial condition is bounded by the same boundary. The contribution lies in three aspects. First, some necessary and sufficient conditions are presented for the existence of controllers satisfying the positivity constraint. Second, a necessary and sufficient condition is established, determining whether the trajectory of a positive system can be bounded by a prescribed boundary, provided that the initial condition is bounded by the same boundary. Third, a sufficient condition is presented for bounded control, and it is shown to be also necessary if asymptotic stability is not required.      

Constrained Learning in Neural Networks: Application to Stable Factorization of 2-D Polynomials

Adaptive artificial neural network techniques are introduced and applied to the factorization of 2-D second order polynomials. The proposed neural network is trained using a constrained learning algorithm that achieves minimization of the usual mean square error criterion along with simultaneous satisfaction of multiple equality and inequality constraints between the polynomial coefficients. Using this method, we are able to obtain good approximate solutions for non-factorable polynomials. By incorporating stability constraints into the formalism, our method can be successfully used for the realization of stable 2-D second order IIR filters in cascade form.     

Simulation of Unilateral Constrained Systems with Many Bodies

Nowadays the theory of multi-body systems including unilateral constraints is quite well established. However, the tendency towards more and more detailed and complex models may not be compensated with increasing computer power. In fact the growing computational effort demands for improved numerical methods in order to solve large systems. In this paper a time-stepping method is proposed for the computation of multi-body systems with many unilateral constraints. Stability and accuracy are discussed with respect to the given discretisation. In order to handle many contacts an iterative algorithm is applied based on a Gauss-Seidel relaxation scheme. A numerical example shows the efficiency of the relaxation scheme in comparison with Lemke's method and an Augmented Lagrangian approach.