非完整链式系统的输出跟踪控制——动态扩展线性化方法

针对非完整单链和多链系统,利用动态反馈线性化技术设计了输出跟踪控制器.证 明了当满足一定的条件时,通过选择适当的输出变量并利用动态反馈可使非完整链式系统实 现输入-输出完全线性化,从而可设计线性控制器跟踪期望的运动轨迹.最后以移动小车的跟 踪控制为例,通过仿真验证了文中方法的有效性.     

A general framework to design stabilizing nonlinear model predictive controllers

We propose a new model predictive control (MPC) framework to generate feedback controls for time-varying nonlinear systems with input constraints. We provide a set of conditions on the design parameters that permits to verify a priori the stabilizing properties of the control strategies considered. The supplied sufficient conditions for stability can also be used to analyse the stability of most previous MPC schemes. The class of nonlinear systems addressed is significantly enlarged by removing the traditional assumptions on the continuity of the optimal controls and on the stabilizability of the linearized system. Some important classes of nonlinear systems, including some nonholonomic systems, can now be stabilized by MPC. In addition, we can exploit increased flexibility in the choice of design parameters to reduce the constraints of the optimal control problem, and thereby reduce the computational effort in the optimization algorithms used to implement MPC.     

Bearing-based formation manoeuvre control of nonholonomic multi-agent systems

ABSTRACT

This paper concerns on the bearing-based leader–follower formation manoeuvre control problem for two- (2D) and three-dimensional (3D) multi-agent systems with nonholonomic constraint. The target formation is defined by relative-bearing measurements, which, for example, can be obtained from onboard cameras. The contributions of this paper are twofold. Firstly, a distributed formation manoeuvre control law is proposed for 2D nonholonomic agents according to the inter-bearing measurement. The multi-agent systems can achieve the desired formation which is defined by the bearings information. The formation manoeuvre can be achieved by steering at least two leaders. Secondly, the control law is nontrivially extended to 3D nonholonomic multi-agents systems. The leader–follower formation tracking problem can also be solved by the proposed proportional-integral control scheme. Simulation results for 2D and 3D nonholonomic multi-agents systems are presented. Experiments that used ground mobile robots verify the effectiveness of the proposed control laws.     

Control of high-order nonholonomic systems in power chained formusing discontinuous feedback

Addresses the problems of almost-asymptotic stabilization and global asymptotic regulation (GAR) for a class of high-order nonholonomic systems in power-chained form. This particular class of nonlinear systems is an extension of a nonholonomic system in chained form that has received considerable attention in the past few years. The nonholonomic system considered in this paper is not necessarily affine in the control variables and therefore cannot be handled by existing methods. Sufficient conditions are presented under which a discontinuous state-feedback control law (or a switching controller) can be recursively constructed, using the so-called "adding a power integrator" technique of C. Qian et al. (2001). We also illustrate how the results can be extend to multi-input systems in power-chained form. Simulation examples are provided to demonstrate the effectiveness of the proposed controllers     

Consensus of multiple nonholonomic chained form systems

Consensus problems of multiple nonholonomic systems are considered in this paper. This problem is simplified into consensus problems of two subsystems based on the cascaded structure of nonholonomic chained form systems. Continuous and hybrid distributed controllers have been constructed for these two subsystems respectively based on the theory of cascaded systems. Consensus of multiple nonholonomic chained form systems can be realized using the methodology proposed in this paper no matter whether the group reference signal is persistently exciting or not. Different to previous assumptions on group reference such as persistent excitation or converging to nonzero constant, the condition on the group reference signal have been further relaxed in this paper. Simulation results using Matlab have illustrated the effectiveness of the results presented in this paper.     

A neural gain scheduling network controller for nonholonomicsystems

We propose a neural gain scheduling network controller (NGSNC) to improve the gain scheduling controller for nonholonomic systems. We derive the neural networks that can approximate the gain scheduling controller arbitrarily well when the sampling frequency satisfies the sampling theorem. We also show that the NGSNC is independent of the sampling time. The proposed NGSNC has the following important properties: 1) same performance as the continuous-parameter gain scheduling controller; 2) less computing time than the continuous-parameter gain scheduling controller; 3) good robustness against the sampling intervals; and 4) straightforward stability analysis. We then show that some of nonholonomic systems can be converted to equivalent linear parameter-varying systems. As a result, the NGSNC can stabilize nonholonomic systems     

Fixed-time regulation control of uncertain nonholonomic systems and its applications

Stabilisation of nonholonomic systems is of great practical importance to the industry. Moreover, fixed-time control is more comfortable than finite-time control since the upper bound of the settling time is independent on the initial system states in a fixed-time control issue and therefore can be estimated in advance. Inspired by the aforementioned two points, we consider the fixed-time stabilisation for a kind of uncertain nonholonomic systems subject to perturbations in this paper. A globally fixed-time stabilisation strategy is proposed by taking advantage of adding one power integrator technique and switching ideal. Under the designed controllers, all states can be regulated to zero before a fixed time and kept zero afterwards. As an application, the fixed-time stabilisation for a class of dynamic nonholonomic systems is also addressed by the combined method of adding one power integrator and terminal sliding-mode control. Three mechanical and academic examples are provided to show the flexibility and effectiveness of the assumptions and control algorithms.     

Stabilization of Hamiltonian systems with nonholonomic constraints based on time-varying generalized canonical transformations

This paper is concerned with the stabilization of nonholonomic systems in port-controlled Hamiltonian formulae based on time-varying generalized canonical transformations. A special class of time-varying generalized canonical transformations are introduced which modify the kinetic energy of the original system without changing the generalized Hamiltonian structure with passivity. Utilizing these transformations, time-varying asymptotically stabilizing controllers for the nonholonomic Hamiltonian systems are derived. Since the proposed method is a natural generalization of passivity based control for conventional holonomic systems, it is expected that the tools developed for conventional systems will be applicable to nonholonomic systems based on the proposed method.     

Study of the internal dynamics of an autonomous mobile robot

The requirement of ideal rolling without sideways slipping for wheels imposes nonholonomic (non-integrable) constraints on the motion of the wheels and consequently on the motion of wheeled mobile robots. From the control point of view, the dynamics of nonholonomic systems can be divided in two parts: external and internal dynamics. The dimension of the external dynamics of nonholonomic systems depends on the number of inputs to the system and the dimension of the internal dynamics depends on the number of independent nonholonomic constraints. For different motion control problems of nonholonomic systems, a smooth (model based) state feedback control law only deals with the system external dynamics; therefore, the system internal dynamics must be examined separately and its stability has to be analyzed and proved.In this paper, the internal dynamics of a three-wheel mobile robot with front wheel steering and driving is investigated. In particular, its internal dynamics stability is analyzed for two different situations, when the mobile robot is moving and when it is stationary.     

Modeling for dynamics of rigid-body systems with friction by linear complementary problem (LCP)

The purpose of this paper is to study the modeling method for nonholonomic systems with friction by linear complementary problem (LCP). Firstly, the dynamic equation with multipliers for the nonholonomic system with friction is given. Secondly, a standard linear complementary model is established, which describes the normal and tangential characteristics for a nonholonomic system. Thirdly, by using LCP theory, a general criterion is obtained, which can identify the singularity induced by nonideal geometrical constraints in a nonholonomic system. By a typical example of a nonholonomic system with friction, it is revealed how the problem solving for the constraint reaction forces can be transformed into the standard linear complementary problem. The research work may provide reliable theoretical basis for the dynamical simulation of a nonholonomic system with non-smooth factors.