Ellipsoidal techniques for dynamic systems: The problem of control synthesis

This article gives an early account of the application of ellipsoidal techniques to various problems in modeling dynamical systems. The problem of control synthesis for a linear system under bounded controls was selected as the first simple application of these techniques. In forthcoming papers, these results will be extended to the case where unknown but bounded disturbances are present. Guaranteed state estimation—also to be interpreted as a tracking problem—again under unknown but bounded disturbances will also be discussed.Although the problem is treated here for linear systems only, the synthesized system is driven by a nonlinear control strategy and is therefore generically nonlinear. Taking a scheme based on the notion of extremal aiming strategies of N. N. Krasovski, the present article concentrates on constructive solutions generated through ellipsoidal-valued calculus and related approximation techniques for set-valued maps. The primary problem, which originally required an application of set-valued analysis, is substituted for here by one based on ellipsoidal-valued functions. This yields constructive schemes applicable to algorithmic procedures and simulation with computer graphics. Editor: G. Leitmann     

High-pain adaptive stabilization of multivariable linear systems — revisited

We consider the class of multi-input multi-output, finite dimensional, state space systems of the form , where the state dimension is unknown, the system is minumum phase, and it is known that det(CB) ≠ 0. For this class a universal adaptive high gain controller — not based on identification or estimation algorithms — is presented which ensures exponential decay of the motion of the closed-loop system. It is shown that the controller is robust with respect to certain nonlinear perturbations.     

Robust IDA‐PBC for underactuated mechanical systems subject to matched disturbances

The problem of robustification of interconnection and damping assignment passivity‐based control for underactuated mechanical system vis‐à‐vis matched, constant, and unknown disturbances is addressed in the paper. This is achieved adding an outer‐loop controller to the interconnection and damping assignment passivity‐based control. Three designs are proposed, with the first one being a simple nonlinear PI, while the second and the third ones are nonlinear PIDs. While all controllers ensure stability of the desired equilibrium in spite of the presence of the disturbances, the inclusion of the derivative term allows us to inject further damping enlarging the class of systems for which asymptotic stability is ensured. Numerical simulations of the Acrobot system and experimental results on the disk‐on‐disk system illustrate the performance of the proposed controller. Copyright © 2016 John Wiley & Sons, Ltd.     

ADAPTIVE ROBUST CONTROL OF UNCERTAIN SYSTEMS WITH TIME‐VARYING STATE DELAY

In this paper, a new adaptive robust control scheme is developed for a class of uncertain dynamical systems with time‐varying state delay, unknown parameters and disturbances. By incorporating adaptive techniques into the robust control method, we propose a continuous adaptive robust controller which guarantees the uniform boundedness of the system and at the same time, the regulating error enters an arbitrarily designated zone in a finite time. The proposed controller is independent of the time‐delay, hence it is applicable to a class of dynamical systems with uncertain time delays. The paper includes simulation studies demonstrating the performance of the proposed control scheme.     

Adaptive output feedback tracking control of a nonholonomic mobile robot

An adaptive output feedback tracking controller for nonholonomic mobile robots is proposed to guarantee that the tracking errors are confined to an arbitrarily small ball. The major difficulties are caused by simultaneous existence of nonholonomic constraints, unknown system parameters and a quadratic term of unmeasurable states in the mobile robot dynamic system as well as their couplings. To overcome these difficulties, we propose a new adaptive control scheme including designing a new adaptive state feedback controller and two high-gain observers to estimate the unknown linear and angular velocities respectively. It is shown that the closed loop adaptive system is stable and the tracking errors are guaranteed to be within the pre-specified bounds which can be arbitrarily small. Simulation results also verify the effectiveness of the proposed scheme.     

不确定非线性系统的鲁棒自适应输出反馈控制

基于自适应非线性阻尼,提出一种鲁棒自适应输出反馈控制方法。该方法适用于带有未建模动态、未知非线性、有界扰动、未知非线性参数和不确定控制系数的多输入多输出非线性系统。理论证明,在一定的假设条件下,该方法能保证闭环系统所有动态信号有界;不论有多少不确定非线性参数、多高阶的非线性系统,只需要一个自适应控制参数和观察参数;而且通过选择适当的控制器和观测器参数,能使控制误差和估计误差达到任意小。仿真结果表明了所提出方法的有效性。     

Non-linear inferential control of packed-bed reactors

Two distinct types of inferential control strategies for the single-input/single-output (SISO) system of a packed-bed reactor are investigated, i.e. non-linear inferential control (NLIC)—the state feedback control (SFC) scheme—and linear inferential control (LIC)—the internal model control (IMC) scheme—to deal with non-linear and unmeasured output process control problems, and the effects of modelling errors and measurement noise on control system performance. The basic structure of an inferential control system is coupled with a state estimator and a controller consisting of the process model and a filter with adjustable parameter, A non-linear estimator is used to estimate the state variables of the process from the temperature measurements. Simulation results have shown that the performances of the SFC scheme are much better than those of the IMC scheme, in spite of modelling errors and measurement noise. The results also indicate that a substantial improvement in control is possible using NLIC.     

模糊免疫PID控制在矿用设备座椅减振系统中的应用

针对现有矿用设备座椅减振系统因弹簧无法控制而导致减振效果不佳的问题,介绍了一种矿用设备座椅减振系统的组成及工作原理,重点阐述了模糊免疫PID控制在该系统中的应用方案。该系统以PLC为主控制器,通过气缸组件工作状态的变化调整气体弹簧的刚度,从而实现座椅减振;针对系统非线性、时变性、滞后性等特点,采用模糊免疫PID控制策略进行减振控制。仿真和应用结果表明,采用模糊免疫PID控制的矿用设备座椅减振系统鲁棒性高,驾驶员乘坐舒适性好,满足实际使用要求。     

Decentralized stabilization of Markovian jump interconnected systems with unknown interconnections and measurement errors

This paper investigates the decentralized output feedback control problem for Markovian jump interconnected systems with unknown interconnections and measurement errors. Different from some existing results, the global operation modes of all subsystems are not required to be completely accessible for the decentralized control system. A decentralized dynamic output feedback controller is constructed using neighboring mode information and local outputs, where the measurement errors between actual and measured outputs are considered. Subsequently, a new design method is developed such that the resultant closed‐loop system is stochastically stable and satisfying an L_∞‐norm constraint. Sufficient conditions are formulated by linear matrix inequalities, and the controller gains are characterized in terms of the solution of a convex optimization problem. Finally, an example is given to illustrate the effectiveness of the proposed theoretical results.     

Adaptive output feedback control for nonholonomic systems with uncertain chained form

The output feedback adaptive control problem is investigated for nonholonomic systems with strongly nonlinear uncertainties and unknown virtual control directions. A nonlinear output feedback switching controller based on the output measurement of the first subsystem is employed in order to make the state scaling effective and ensure the convergence of the system states. The novel observer/estimator is introduced for state and unknown parameter estimates. The integrator backstepping technique by the use of a constructive recursive is applied to the design of the adaptive controller and to overcome the unknown virtual control directions. The simulation result validates the effectiveness of the proposed scheme.     

Controller design for natural and robotic systems with transmission delays

Robust stability and two‐dimensional trajectory following problems are considered for n‐link robotic systems with transmission delays. Such problems appear in telerobotics, where the controller is physically far from the robot, and in neural control of musculo‐skeletal (biological) systems, where muscle actuation and neural sensing are subject to time delays. A typical second‐order nonlinear dynamical model is taken with input and output time delays. In a prior work by the authors, a control strategy was developed for stable movement of the planar linkage system, using the standard Q‐parameterization and solving an H^∞ control problem to determine the free parameter. In this article, a new control scheme is proposed to eliminate the steady‐state errors seen in the tracking performance of the controller derived in the earlier work. Simulation examples are shown to demonstrate the effectiveness of the proposed control methodology. © 2002 Wiley Periodicals, Inc.     

Control of bilateral teleoperators with time delays using only position measurements

A major drawback in the control of bilateral teleoperators is time delays. The nature of the communication channel that interconnects the local and the remote manipulators imposes these delays, which can be time‐varying. Several commercially available robots do not incorporate velocity sensors, and velocities are usually estimated using dirty derivatives. In this paper, we are interested in the control of bilateral teleoperators with variable time delays and without requiring velocity measurements. The proposal makes use of a second‐order dynamical controller that backpropagates damping to the local and the remote manipulators. If sufficient damping is injected in the controller and under the common passivity assumption of the human operator and the environment, it is proved that position errors and velocities are bounded. Invoking Barbalat's lemma, when the human and the environment do not inject forces in the system, it is shown that position error and velocities globally asymptotically converge to zero. A simulation comparison with other two control techniques shows the performance of the novel proposal. Experimental results evidence the robustness of the proposed scheme to interconnecting time delays.     

一类离散时间切换线性系统的无差拍控制

研究一类带多控制器和多传感器离散时间线性系统的无差拍控制.对能控系统,通过适当的状态坐标变换获得系统矩阵的块三角结构,再设计状态反馈和周期切换策略使得状态反馈矩阵在有限周期内为零,从而保证闭环系统的无差拍稳定.进一步,对能观系统,设计具有有限时间精确估计的动态输出反馈,通过适当的周期切换策略实现闭环系统的无差拍稳定.最后,给出一个例子以验证所提设计方法的有效性.     

Decentralized Nonlinear Robust Coordinated Control of UPFC and Generators in Multi‐ Machine Power System Via Pseudo‐Generalized Hamiltonian Theory

In this paper, based on a structure preserving power system with a unified power flow controller (UPFC), using pseudo‐generalized Hamiltonian function method and boundary‐function method, a nonlinear robust coordinated control law is constructed for multi‐machine power system oscillation damping. The 4‐machine 2‐area power system is used to demonstrate the performance of the proposed controller. Simulation results indicate that the proposed coordinated control scheme can effectively improve both transient stability and voltage regulation performance of the power system. ©2014 Chinese Automatic Control Society and Wiley Publishing Asia Pty Ltd     

Decentralized receding horizon control for large scale dynamically decoupled systems

We present a detailed study on the design of decentralized receding horizon control (RHC) schemes for decoupled systems. We formulate an optimal control problem for a set of dynamically decoupled systems where the cost function and constraints couple the dynamical behavior of the systems. The coupling is described through a graph where each system is a node, and cost and constraints of the optimization problem associated with each node are only function of its state and the states of its neighbors. The complexity of the problem is addressed by breaking a centralized RHC controller into distinct RHC controllers of smaller sizes. Each RHC controller is associated with a different node and computes the local control inputs based only on the states of the node and of its neighbors. We analyze the properties of the proposed scheme and introduce sufficient stability conditions based on prediction errors. Finally, we focus on linear systems and show how to recast the stability conditions into a set of matrix semi-definiteness tests.     

A Novel Robust Attitude Control for Quadrotor Aircraft Subject to Actuator Faults and Wind Gusts

A novel robust fault tolerant controller is developed for the problem of attitude control of a quadrotor aircraft in the presence of actuator faults and wind gusts in this paper. Firstly, a dynamical system of the quadrotor taking into account aerodynamical effects induced by lateral wind and actuator faults is considered using the Newton-Euler approach. Then, based on active disturbance rejection control (ADRC), the fault tolerant controller is proposed to recover faulty system and reject perturbations. The developed controller takes wind gusts, actuator faults and measurement noises as total perturbations which are estimated by improved extended state observer (ESO) and compensated by nonlinear feedback control law. So, the developed robust fault tolerant controller can successfully accomplish the tracking of the desired output values. Finally, some simulation studies are given to illustrate the effectiveness of fault recovery of the proposed scheme and also its ability to attenuate external disturbances that are introduced from environmental causes such as wind gusts and measurement noises.      

Nonlinear multivariable adaptive control using multiple models and neural networks

In this paper, a multivariable adaptive control approach is proposed for a class of unknown nonlinear multivariable discrete-time dynamical systems. By introducing a k-difference operator, the nonlinear terms of the system are not required to be globally bounded. The proposed adaptive control scheme is composed of a linear adaptive controller, a neural-network-based nonlinear adaptive controller and a switching mechanism. The linear controller can assure boundedness of the input and output signals, and the neural network nonlinear controller can improve performance of the system. By using the switching scheme between the linear and nonlinear controllers, it is demonstrated that improved performance and stability can be achieved simultaneously. Theory analysis and simulation results are presented to show the effectiveness of the proposed method.     

A modified Elman neural network-based power controller in mobile communications systems

It has been well recognized that power control is an important technique to combat with the harmful near-far effect as well as increase the maximum user capacity of direct sequence code division multiple access (DS/CDMA) cellular systems. In this paper, we propose a modified Elman neural network (MENN)-based power control scheme, which can regulate the received power level at the base station. Unlike the conventional “bang–bang” and fuzzy logic power control, our MENN-based controller first identifies the inverse dynamical characteristics of mobile channel by adaptive on-line learning. The inverse channel model is then employed for power regulation to reduce large overshoots and shorten long rise time. Simulations show that the fluctuation of controlled received power levels can be smoothed with small channel tracking errors. Acknowledgments The authors would like to thank the anonymous reviewers for their insightful comments and constructive suggestions that have improved this paper.     

Stabilization in spite of matched unmodeled dynamics and an equivalent definition of input-to-state stability

We consider nonlinear systems with input-to-output stable (IOS) unmodeled dynamics which are in the range of the input. Assuming the nominal system is globally asymptotically stabilizable and a nonlinear small-gain condition is satisfied, we propose a first control law such that all solutions of the perturbed system are bounded and the state of the nominal system is captured by an arbitrarily small neighborhood of the origin. The design of this controller is based on a gain assignment result which allows us to prove our statement via a Small-Gain Theorem [JTP, Theorem 2.1]. However, this control law exhibits a high-gain feature for all values. Since this may be undesirable, in a second stage we propose another controller with different characteristics in this respect. This controller requires morea priori knowledge on the unmodeled dynamics, as it is dynamic and incorporates a signal bounding the unmodeled effects. However, this is only possible by restraining the IOS property into the exp-IOS property. Nevertheless, we show that, in the case of input-to-state stability (ISS)—the output is the state itself-ISS and exp—ISS are in fact equivalent properties.Yuan Wang was supported in part by NSF Grant DMS-9403924 and by a scholarship from Université Lyon I, France.     

一个五维受控混沌系统的动力学行为

用状态反馈的方法对L櫣系统的混沌运动进行控制,在L櫣系统中增加两个新的状态变量,获得了一个五维的受控混沌系统,该系统有复杂的动力学行为.计算了系统的Lyapunov指数、功率谱和相轨迹.数值模拟表明：通过改变控制参数,可以将系统的周期运动改变为混沌运动、混沌运动改变为周期运动.