A Nonlinear Control Concept for Rolling Mills

This contribution is concerned with the nonlinear control of a temper rolling mill based on the exact input/output linearization method. The considered subsystem of the temper rolling plant consists of a four‐high mill stand with a hydraulic adjustment system, and bridle rolls in the entry and the exit section. The demand on the temper rolling process is to establish a certain elongation of the steel strip under the action of the roll force and certain predefined backward and forward strip tensions in order to achieve the desired material characteristics and surface properties of the rolled product. The nonlinear control concept to be presented is characterized by the fact that the torques of the bridle rolls are intended as control inputs for the elongation and master speed control, whereas the hydraulic adjustment system and the main mill drive are used to take effect on the strip tensions. After a brief review of the mathematical model of the mill we will focus on the multi‐input nonlinear tension control.     

混沌记忆系统的自适应反馈控制和轨迹跟踪控制

研究了混沌记忆系统的自适应反馈控制和基于反馈线性化的轨迹跟踪控制问题.首先,通过绘制系统的时域波形图和混沌吸引子图验证系统的复杂的动力学行为;然后,分别应用自适应反馈控制方法和基于反馈线性化的轨迹跟踪控制方法设计控制器,对系统施加控制;最后,通过数值仿真验证控制器的有效性.     

The explicit synthesis of stabilizing (time optimal) feedback controls for the attitude control of a rotating satelite

The attitude stabilization problem for a spinning satellite controlled by two small jets may be modelled as a four-dimensional, nonlinear control system, linear in the controls. The recent feedback linearization theorem of Hunt and Su may be applied to transform this system, via state feedback and a local coordinate change, to a pair of uncoupled, two-dimensional, linear systems. Feedback controls for the problem of time optimal transfer to the origin for these linear systems are explicitly calculated and then transformed to give explicit feedback controls for time optimal stabilization in the original nonlinear problem. The theory is illustrated by sample calculations.     

Mathematical modeling and control of population systems: Applications in biological pest control

The aim of this paper is to apply methods from optimal control theory, and from the theory of dynamic systems to the mathematical modeling of biological pest control. The linear feedback control problem for nonlinear systems has been formulated in order to obtain the optimal pest control strategy only through the introduction of natural enemies. Asymptotic stability of the closed-loop nonlinear Kolmogorov system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton–Jacobi–Bellman equation, thus guaranteeing both stability and optimality. Numerical simulations for three possible scenarios of biological pest control based on the Lotka–Volterra models are provided to show the effectiveness of this method.     

Adaptive fuzzy backstepping control for a class of MIMO switched nonlinear systems with unknown control directions

In this article, an adaptive fuzzy output tracking control approach is proposed for a class of multiple‐input and multiple‐output uncertain switched nonlinear systems with unknown control directions and under arbitrary switchings. In the control design, fuzzy logic systems are used to identify the unknown switched nonlinear systems. A Nussbaum gain function is introduced into the control design and the unknown control direction problem is solved. Under the framework of the backstepping control design, fuzzy adaptive control and common Lyapunov function stability theory, a new adaptive fuzzy output tracking control method is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed‐loop system are bounded and the tracking error remains an adjustable neighborhood of the origin. A numerical example is provided to illustrate the effectiveness of the proposed approach. © 2015 Wiley Periodicals, Inc. Complexity 21: 155–166, 2016     

Multivariable RBF-ARX model-based robust MPC approach and application to thermal power plant

For a class of smooth nonlinear multivariable systems whose working-points vary with time and the future working-points knowledge are unknown, a combination of a local linearization and a polytopic uncertain linear parameter-varying (LPV) state-space model is built to approximate the present and the future system’s nonlinear behavior, respectively. The combination models are constructed on the basis of a matrix polynomial multi-input multi-output (MIMO) RBF-ARX model identified offline for representing the underlying nonlinear system. A min–max robust MPC strategy is designed to achieve the systems’ output-tracking control based on the approximate models proposed. The closed loop stability of the MPC algorithm is guaranteed by the use of time-varying parameter-dependent Lyapunov function and the feasibility of the linear matrix inequalities (LMIs). The effectiveness of the modeling and control methods proposed in this paper is illustrated by a case study of a thermal power plant simulator.     

粘弹性板混沌振动的输出变量反馈线性化控制

研究了粘弹性板混沌振动的控制问题·　应用非线性系统精确线性化控制理论导出了一类非仿射控制系统的非线性反馈控制律·　建立了描述材料非线性的粘弹性板运动的数学模型并利用Ｃａｌｅｒｋｉｎ 方法进行简化·　采用相空间曲线和频率谱密度函数说明了在特定参数条件下系统将出现混沌振动,并以位移为输出变量将混沌振动控制为给定的周期运动·     

A global geometrical input-output linearization theory

Input-Output linearization is a method that uses nonlinear statefeedback control to obtain linear equations between the inputand output of a nonlinear control system. Its success dependscrucially on the ability of the control to steer across thelevel sets of the output function. This is essentially a globalcontrollability problem. In this work, we present a linearizationtheory that is geomentrical. This mean that the relation ofthe control vector fields to the output function is consideredfrom a global geometrical perspective. Our argument involvesgeneric vector fields and output functions and linearizationfor typical trajectories. We prove that the relative degreeis generically one. This approach also succeeds in resolving the problems of controlpast the singular set, and thus goes further than the existingliterature. The unavoidable cost is that linearization may bepiecewise, since the concept of strong relative degree cannot(in general) be defined globally. A simple example is includedwith a common type of output function, and linearization isworked out in some detail as an illustration of some of thenovel approach.     

Stabilization of nonlinear networked systems with sensor random packet dropout and time-varying delay

In this paper, a nonlinear stochastic system model is proposed to describe the networked control systems (NCSs) with both random packet dropout and network-induced time-varying delay. Based on this more general nonlinear NCSs model, by choosing appropriate Lyapunov functional and employing new discrete Jensen type inequality, a sufficient condition is derived to establish the quantitative relation of maximum allowable delay upper bound, packet dropout rate and the nonlinear level to the exponential stability of the nonlinear NCSs. Design procedures for output feedback controller are also presented in terms of utilizing cone complementarities linearization algorithm or solving corresponding linear matrix inequalities (LMIs). Illustrative examples are provided to demonstrate the effectiveness of the proposed method.     

State feedback linearization of nonlinear control systems on homogeneous time scales

The paper addresses the state feedback linearization problem for nonlinear systems, defined on homogeneous time scale. Necessary and sufficient solvability conditions are given within the algebraic framework of differential one-forms. The conditions concerning the exact dynamic state feedback linearization are equivalent to the property of differential flatness of the system. An output function which defines a right invertible system without zero-dynamics is shown to exist if and only if the basis of some space of one-forms can be transformed, via polynomial matrix operator over the field of meromorphic functions, into a system of exact one-forms. The results extend the corresponding results for the continuous-time case.     

Decoupling problems around a trajectory: from linearity to nonlinearity

Given a nonlinear control system for which an admissible statetrajectory is specified, we solve approximately the input outputdecoupling problem around this nominal trajectory. An approximatesolution for this problem is obtained by dealing with the linearizedsystem along this trajectory. An exact solution to the inputoutput decoupling problem for the linearization is shown tobe an approximate solution to the input output decoupling problemaround the nominal trajectory for the original nonlinear system.In a similar way, we provide an approximate solution to thedisturbance decoupling problem around a specified trajectoryof the nonlinear system. The nonlinear model of a two link robotmanipulator is used to illustrate the results on input outputdecoupling.     

An experiment in chaotic scattering using repulsive magnetic forces

We consider the scattering of a particle injected into a system of three coplanar potentials that give rise to inverse square law repulsive forces. Most of the parameter space defined by the combination of injection energy and impact parameter is found to be associated with geometrically simple input–output trajectories. These regions in parameter space are separated by narrow ridges which correspond to chaotic scattering. Experimental data are also reported for the scattering of a magnetic puck propelled into the domain of three fixed magnets.     

Static output feedback and guaranteed cost control of a class of discrete-time nonlinear systems with partial state measurements

In this paper both the static output feedback issue and the observer-based control of a class of discrete-time nonlinear systems are considered. Thanks to a newly developed linearization lemma, it is shown that the solution of the discrete-time output feedback problem is conditioned by a set of simple convex optimization conditions that are numerically tractable and free from any equality constraint. An illustrative example is provided to show the usefulness of the proposed control designs.     

Boundary output feedback stabilization for a class of coupled parabolic systems

In this paper, the boundary output feedback stabilization problem is addressed for a class of coupled nonlinear parabolic systems. An output feedback controller is presented by introducing a Luenberger‐type observer based on the measured outputs. To determine observer gains, a backstepping transform is introduced by choosing a suitable target system with nonlinearity. Furthermore, based on the state observer, a backstepping boundary control scheme is presented. With rigorous analysis, it is proved that the states of nonlinear closed‐loop system including state estimation and estimation error of plant system are locally exponentially stable in the L²norm. Finally, a numerical example is proposed to illustrate the effectiveness of the presented scheme.     

Rate of afferent stimulus dependent synchronization and coding in coupled neurons system

Sequences of intervals between firing times (interspike interval (ISI)) from a pair of locus ceruleus (LC) neurons coupled by axon–dendrite synapse with stimulus of constant and chaos are investigated in this paper. We analyze how the dynamical properties of chaotic input determine those of the output ISI sequences, and assess how various strength of stimulus and coupling affects the input–output relationship. The attractors constructed from delay embeddings of ISIs and of chaotic input are compared from the points of view of geometry and nonlinear dynamics characteristics, i.e., Lyapunov exponent spectrum (LES), Kaplan–York fractal dimension (KY_D) and unstable periodic orbit (UPO). For the coupled LC neurons system investigated, with the moderate strength of stimulus and coupling, the synchronous oscillation of the two neurons is well preserved even if the external stimulus is chaotic; the similarity between these attractors is high only when the afferent stimulus strength is smaller and rate is lower. When these conditions are satisfied, the output two ISI sequences are reciprocally related to input signals, and their oscillation wave shape in time course can be derived from that of the input signals variation, furthermore, the similar input sequence of order of UPOs, distribution of LES and value of KY_D remain in attractors reconstructed from ISI sequences. But these phenomena will disappear in higher rate of stimulus activity or in changing of the strength of stimulus and coupling, for this situation, the ISIs shows bifurcate behavior. These results may be of vital importance for any kind of information processing based on the neurons and temporal coding.     

Viscosity Solutions of HJB Equations with Unbounded Data and Characteristic Points

We study a class of infinite horizon and exit-time control problems for nonlinear systems with unbounded data using the dynamic programming approach. We prove local optimality principles for viscosity super- and subsolutions of degenerate Hamilton–Jacobi equations in a very general setting. We apply these results to characterize the (possibly multiple) discontinuous solutions of Dirichlet and free boundary value problems as suitable value functions for the above-mentioned control problems.     

飞艇姿态跟踪系统的研究

研究了具有参数不确定和外部干扰的飞艇姿态跟踪控制问题．飞艇姿态运动的数学模型为一个多输入/多输出不确定非线性系统,根据该系统的特点,采用了一个基于不确定项上界的鲁棒输出跟踪控制器设计方法,应用输入/输出反馈线性化法和李雅普诺夫方法,设计了飞艇姿态鲁棒控制律,它可确保系统输出按指数规律跟踪期望输出．该控制器设计简单,易于实现．仿真结果表明:即使系统存在不确定性和外界干扰,仍可在闭环系统中实现精确的姿态控制．     

Identification of switched linear systems using subspace and integer programming techniques

We consider the identification of a switched linear system which consists of linear sub-models, with a rule that orchestrates the switching mechanism between the sub-models. Taking a set of switched linear systems and using a state space framework, we show that it is possible to combine subspace methods with mixed integer programming for system identification. The states of the system are first extracted from input–output data using sub-space methods. Once the state variables are known, the switched system is re-written as a mixed logical dynamical (MLD) system and the model parameters are calculated for via mixed integer programming. We report an example at the end of this paper together with simulation results in the presence of noise.     

A NARMAX model-based state-space self-tuning control for nonlinear stochastic hybrid systems

A novel state-space self-tuning control methodology for a nonlinear stochastic hybrid system with stochastic noise/disturbances is proposed in this paper. via the optimal linearization approach, an adjustable NARMAX-based noise model with estimated states can be constructed for the state-space self-tuning control in nonlinear continuous-time stochastic systems. Then, a corresponding adaptive digital control scheme is proposed for continuous-time multivariable nonlinear stochastic systems, which have unknown system parameters, measurement noise/external disturbances, and inaccessible system states. The proposed method enables the development of a digitally implementable advanced control algorithm for nonlinear stochastic hybrid systems.