Approximate noninteracting control with stability for nonlinearsystems

A notion of approximate noninteracting control with stability for nonlinear systems is introduced, and the design of both static and dynamic state-feedback control laws that achieve this property for a given plant is considered. This approach to the problem is based on the notion of extended linearization, and begins with an extension of the linearization approach pointwise to all constant operating points in an open neighborhood of the nominal. Under natural assumptions it is shown that obstructions to extract noninteracting control with internal stability, or input-state/output stability, can be circumvented in the context of approximate noninteraction     

Fixed modes and nonlinear noninteracting control with stability

The existence of a fixed internal dynamics, inherent to the noninteraction requirement, is identified. When unstable, this represents an obstruction to the achievement of noninteracting control with stability, by means of static state-feedback. Remarkably, whenever one leaves the class of linear systems, this obstruction cannot, in general, be removed by dynamic state-feedback     

A sufficient condition for nonlinear noninteracting control withstability via dynamic state feedback

A sufficient condition is given to solve the problem of achieving local noninteracting control with asymptotic stability via dynamic state feedback for a nonlinear affine system. The condition, which is automatically satisfied in the case of linear systems, although only sufficient, is helpful in overcoming some of the geometric obstructions pointed out in the literature. An example, in which the author' assumptions are satisfied, is given, clearly showing how to construct a decoupling and stabilizing dynamic state feedback and how the condition can weaken the requirement that the P* dynamics be locally asymptotically stable     

Robust computationally efficient control of cooperative closed-chain manipulators with uncertain dynamics

This article presents a decentralized control scheme for the complex problem of simultaneous position and internal force control in cooperative multiple manipulator systems. The proposed controller is composed of a sliding mode control term and a force robustifying term to simultaneously control the payload's position/orientation as well as the internal forces induced in the system. This is accomplished independently of the manipulators dynamics. Unlike most controllers that do not require prior knowledge of the manipulators dynamics, the suggested controller does not use fuzzy logic inferencing and is computationally inexpensive. Using a Lyapunov stability approach, the controller is proven to be robust in the face of varying system's dynamics. The payload's position/orientation and the internal force errors are also shown to asymptotically converge to zero under such conditions.     

Parameterization of decoupling control laws for affine nonlinearsystems

The problem of parameterizing all the decoupling feedbacks is investigated and applied to the design of a stable noninteracting control for affine nonlinear systems. An algebraic study of controlled invariance is presented. It covers a new criterion for controlled invariance, parameterization and novel properties of the friend set, and computational aspects of the maximal controlled invariant distribution. This analysis is used to derive Falb-Wolovich-like conditions for general decoupling (including disturbance decoupling and noninteracting control) problems. It is shown that to determine all the decoupling feedbacks one usually needs infinitely many (sets of) controlled invariant or controllability distributions that can arise as solutions to the problems. It is also shown that under certain conditions, stable noninteracting design based on first parameterizing the decoupling feedbacks is still a feasible approach in the sense that a feedback can be chosen from the friend set of the maximal solution for the exponentially stable and noninteracting design problem     

Noninteracting control with stability for a class of nonlinear systems

In this paper we address the problem of noninteracting control with stability for the class of nonlinear square systems for which noninteraction can be achieved (without stability) by means of invertible static state-feedback. The use of both static state-feedback and dynamic state-feedback is investigated. We prove that in both cases the asymptotic stabilizability of certain subsystems is necessary to achieve noninteraction and stability. We use this and some recent results to state a complete set of necessary and sufficient conditions in order to solve the problem.     

Output-feedback Dynamic Surface Control for a Class of Nonlinear Non-minimum Phase Systems

In this paper, an output-feedback tracking controller is proposed for a class of nonlinear non-minimum phase systems. To keep the unstable internal dynamics bounded, the method of output redefinition is applied to let the stability of the internal dynamics depend on that of redefined output, thus we only need to consider the new external dynamics rather than internal dynamics in the process of designing control law. To overcome the explosion of complexity problem in traditional backstepping design, the dynamic surface control (DSC) method is firstly used to deal with the problem of tracking control for the nonlinear non-minimum phase systems. The proposed outputfeedback DSC controller not only forces the system output to asymptotically track the desired trajectory, but also drives the unstable internal dynamics to follow its corresponding bounded and causal ideal internal dynamics, which is solved via stable system center method. Simulation results illustrate the validity of the proposed output-feedback DSC controller.      

A new design approach for the anti-swing trajectory control of overhead cranes with high-speed hoisting

This paper proposes a new approach for the design of anti-swing control of overhead cranes. An anti-swing trajectory control scheme is designed based on the trolley and load-hoisting dynamics, and then extended to an adaptive scheme. The load-swing dynamics is controlled by employing a sliding surface that couples the load-swing dynamics with trolley motion. The number of degrees of freedom of the trolley and load-hoisting dynamics is the same as that of the control inputs; therefore, the control problem is reduced to finding a coupled sliding surface that stabilizes the crane control system, based on the load-swing dynamics. In this study, the Lyapunov stability theorem is used as a mathematical design tool. The proposed control guarantees asymptotic stability of the anti-swing trajectory control while keeping all internal signals bounded. The coupled sliding surface allows a direct control of the damping of load swing. In addition, the proposed control provides clear gain-tuning criteria for easy application. Finally, the proposed control realizes an anti-swing control along a typical anti-swing trajectory in practice, with high-speed load hoisting. The validity of the theoretical results is shown by computer simulation.     

Stability analysis of the internal dynamics of a wheeled mobile robot

The stability of the internal dynamics of a wheeled mobile robot is analyzed. It is shown that the wheeled mobile robot exhibits unstable internal dynamics when moving backwards. Most control methods of wheeled mobile robots are designed based on input-output relations. Since the internal dynamics are not represented in input-output relations, stability properties of the internal dynamics are generally neglected. Nevertheless, the internal dynamics do affect the behavior of mobile robots. Taking the look-ahead control method as an example, it is shown that, by using a novel Liapunov function, the internal dynamics of a two-wheel differential-drive mobile robot are unstable when it is commanded to move backwards. Both simulation and experimental results are provided to verify the analysis. ©1997 John Wiley & Sons, Inc.     

一类欠驱动机械系统的非线性控制

针对一类欠驱动机械系统．分析了其数学模型,提出了一种基于部分反馈线性化的非线性控制方案．该方案利用精确线性化的方法将欠驱动系统直接激励部分线性化,将被动部分作为系统的内部动态考虑;并选择直接激励的自由度作为系统输出．进行系统的轨迹跟踪控制;通过分析系统的内部动态,证明了零动态的稳定性能保证控制系统的稳定性．最后通过对吊车的负载防摆控制的研究．验证了该方案的可行性．     

A dynamic feedback control strategy for control loops with time-varying delay

Dynamic systems of nth order with time-varying delay in the control loop are examined in this paper. The infinite-dimensional pure delay problem is approximated using a jth-order Padé approximation. Although the approximation provides a well-matched finite-dimensional configuration, it poses a new challenge in terms of unstable internal dynamics for the resulted non-minimum phase system. Such a non-minimum phase characteristic limits the closed-loop system bandwidth and leads to an imperfect tracking performance. To circumvent this problem, the unstable internal dynamics of the system is captured and a new dynamic compensator is proposed to stabilise it in a systematic framework. A dynamic controller is developed, which provides the overall system stability against unmatched perturbation and meets the desired tracking error dynamics. The proposed approach is then applied to fuelling control in gasoline engines addressing the varying transport delay of the oxygen-sensor measurement in the exhaust. The developed methodology is finally validated on a Ford F-150 SI lean-burn engine model with large time-varying delay in the control loop.     

含未知信息的轮式移动机器人编队确定学习控制

本文研究含未知信息的轮式移动机器人(wheeled mobile robots,WMR)的编队控制问题.首先,基于领航–跟随法和虚拟结构法,将WMR编队控制问题转化为跟随机器人对参考虚拟机器人的跟踪控制问题.然后,利用径向基函数神经网络(radial basis function neural networks,RBF NN)对WMR的未知系统动态进行学习,以及根据李雅普诺夫稳定性理论设计了稳定的自适应RBF NN控制器和RBF NN权值估计的学习率.依据确定学习理论,闭环系统内部信号在对回归轨迹实现跟踪控制的过程中满足部分持续激励(persistent excitation,PE)条件.随着PE条件的满足,RBF NN权值估计收敛到其理想权值,实现了对未知闭环系统动态的准确学习.最后,利用学习结果设计了RBF NN学习控制器,保证了控制系统的稳定与收敛,实现了闭环稳定性和改进了控制性能,并通过仿真验证了所提控制方法的正确性和有效性.     

Time-Varying Asymmetrical BLFs Based Adaptive Finite-Time Neural Control of Nonlinear Systems With Full State Constraints

This paper concentrates on asymmetric barrier Lyapunov functions (ABLFs) based on finite-time adaptive neural network (NN) control methods for a class of nonlinear strict feedback systems with time-varying full state constraints. During the process of backstepping recursion, the approximation properties of NNs are exploited to address the problem of unknown internal dynamics. The ABLFs are constructed to make sure that the time-varying asymmetrical full state constraints are always satisfied. According to the Lyapunov stability and finite-time stability theory, it is proven that all the signals in the closed-loop systems are uniformly ultimately bounded (UUB) and the system output is driven to track the desired signal as quickly as possible near the origin. In the meantime, in the scope of finite-time, all states are guaranteed to stay in the pre-given range. Finally, a simulation example is proposed to verify the feasibility of the developed finite time control algorithm.      

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.     

Neural network adaptive control for a class of nonlinear uncertain dynamical systems with asymptotic stability guarantees.

In this paper, a neuroadaptive control framework for continuous- and discrete-time nonlinear uncertain dynamical systems with input-to-state stable internal dynamics is developed. The proposed framework is Lyapunov based and unlike standard neural network (NN) controllers guaranteeing ultimate boundedness, the framework guarantees partial asymptotic stability of the closed-loop system, that is, asymptotic stability with respect to part of the closed-loop system states associated with the system plant states. The neuroadaptive controllers are constructed without requiring explicit knowledge of the system dynamics other than the assumption that the plant dynamics are continuously differentiable and that the approximation error of uncertain system nonlinearities lie in a small gain-type norm bounded conic sector. This allows us to merge robust control synthesis tools with NN adaptive control tools to guarantee system stability. Finally, two illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach.     

非线性稳定无交互控制的例题及反例研究

本文首先给出非线性控制系统的一般稳定无交互控制问题可解的一个一般结论,进而研 究两个例题,其中之一揭示所涉及问题中典型的非线性现象,另一个表明以往一个结论的错 误.     

Dynamic inversion for multivariable non-affine-in-control systems via time-scale separation

This paper presents a tracking design methodology applicable to multivariable non-affine-in-control systems. The main focus is on solving the tracking problem for non-linear systems whose dynamics depend non-linearly on the control input. The latter is designed to be faster than the main system dynamics. Using singular perturbation theory along with the Lyapunov stability theorems, it is shown that the proposed controller approximates an unknown dynamic inversion based solution with bounded errors, provides closed-loop stability, and solves the tracking problem with bounded errors. Simulations illustrate the theoretical results.     

Dynamic control of free-floating coordinated space robots

The position and force control of coordinated robots mounted on spacecraft, manipulating objects with closed kinematic chain constraints, represents an important class of control problem. In this article, the kinematics and dynamics of free-floating coordinated space robotic system with closed kinematic constraints are developed. An approach to position and force control of free-floating coordinated space robots with closed kinematic constraints is proposed for the first time. Unlike previous coordinated space robot control methods which are for open kinematic chains, the method presented here addresses the main difficult problem of control of closed kinematic chains. The controller consists of two parts, position controller and internal force controller, which regulate, respectively, the object position and internal forces between the object and end-effectors. The stability of the closed-loop coordinated robotic system is analyzed using the error models of the object position and internal forces. It is proved that the errors in the object position and internal forces asymptotically converge to zero under the assumption of exact kinematic and dynamic models. © 1998 John Wiley & Sons, Inc.     

Robust fuzzy 3D path following for autonomous underwater vehicle subject to uncertainties

This paper addresses a three-dimensional (3D) path following control problem for underactuated autonomous underwater vehicle (AUV) subject to both internal and external uncertainties. A two-layered framework synthesizing the 3D guidance law and heuristic fuzzy control is proposed to achieve robust adaptive following along a predefined path. In the first layer, a 3D guidance controller for underactuated AUV is presented to guarantee the stability of path following in the kinematics stage. In the second layer, a heuristic adaptive fuzzy algorithm based on the guidance command and feedback linearization Proportional-Integral-Derivative (PID) controller is developed in the dynamics stage to account for the nonlinear dynamics and system uncertainties, including inaccuracy modelling parameters and time-varying environmental disturbances. Furthermore, the sensitivity analysis of the heuristic fuzzy controller is presented. Against most existing methods for 3D path following, the proposed robust fuzzy control scheme reduces the design and implementation costs of complicated dynamics controller, and relaxes the knowledge of the accuracy dynamics modelling and environmental disturbances. Finally, numerical simulation results validate the effectiveness of the proposed control framework and illustrate the outperformance of the proposed controller as well.     

A solution for the cooperative formation-tracking problem in a network of completely unknown nonlinear dynamic systems without relative position information

In this paper, a solution of the formation-tracking problem is provided for a network that contains nonlinear agents with completely unknown dynamics and working under unknown disturbances. By the combination of a cooperative observer and an adaptive model-free controller, the requirement of inter-agent relative position information in the network is eliminated. Here, a cooperative observer is designed to estimate the time-varying reference trajectory and the time-varying parameters of the desired formation topology at each agent in the network. The stability of the proposed cooperative observer is analysed using Lyapunov analysis. Utilising the cooperative observer, the formation-tracking problem in the network of dynamic agents is transformed to a tracking problem in a single agent system. Moreover, an adaptive model-free control policy is applied to each agent for providing the tracking objective. Utilising the algebraic connectivity originating from graph theory, this model-free control algorithm is formulated to scale-up for a network of multi-agents. The proposed decentralised controller includes two model-free adaptive laws for online estimating of the completely unknown dynamics at each agent in the network. The application of the proposed solution is simulated for a network of four quadrotors with unknown internal dynamics and unknown external disturbances.