Some problems of linear differential equations on abstract spaces and unbounded perturbations of linear operator semigroup

This paper is a survey for development of linear distributed parameter system. At first we point out some questions existing in current study of control theory for the L^p linear system with an unbounded control operator and an unbounded observation operator, such as stabilization problem and observer theory that are closely relevant to state feedback operator. After then we survey briefly some results on relevant problems that are related to solvability of linear differential equations in general Banach space and semigroup perturbations. As a principle, we propose a concept of admissible state feedback operator for system (A, B). Finally we give an existence result of admissible state feedback operators, including semigroup generation and the equivalent conditions of admissibility of state feedback operators, for an L^p well-posed system.     

Adaptive output feedback stabilization for nonholonomic systems with strong nonlinear drifts

This paper investigates the design of an output feedback adaptive stabilization controller for a nonholonomic chained system with strong nonlinear drifts, including modeled nonlinear dynamics, unmodeled dynamics, and dynamics modeled with unknown parameters. Also the virtual control directions of the system are unknown. The purpose is to design a nonlinear output feedback switching controller such that the closed loop system is globally asymptotically stable. A novel observer and estimator are introduced for states and parameter estimates, respectively. A constructive procedure of design for an output feedback adaptive controller is given, by using the integrator backstepping approach and based on the proposed observer and parameter estimator. An example is given to show the effectiveness of the proposed scheme.     

Stabilization of a one‐dimensional wave equation with variable coefficient under non‐collocated control and delayed observation

In this paper, we consider stabilization of a 1‐dimensional wave equation with variable coefficient where non‐collocated boundary observation suffers from an arbitrary time delay. Since input and output are non‐collocated with each other, it is more complex to design the observer system. After showing well‐posedness of the open‐loop system, the observer and predictor systems are constructed to give the estimated state feedback controller. Different from the partial differential equation with constant coefficients, the variable coefficient causes mathematical difficulties of the stabilization problem. By the approach of Riesz basis property, it is shown that the closed‐loop system is stable exponentially. Numerical simulations demonstrate the effect of the stable controller. This paper is devoted to the wave equation with variable coefficients generalized of that with constant coefficients for delayed observation and non‐collocated control.     

Observability and observers in a food web

The problem of the possibility of recovering the time-dependent state of a whole population system from the observation of certain components has been studied in earlier publications, in terms of the observability concept of mathematical systems theory. In the present note a method is proposed for effectively calculating the state process. For an illustration an observer system for a simple food web is numerically constructed.     

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.     

Finite-time converging jump observer for switched linear systems with unknown inputs

This work addresses the state observation problem for a class of switched linear systems with unknown inputs. The proposed high-order sliding-mode observer provides a finite-time converging estimate of the continuous system’s state vector in spite of the presence of unknown inputs. The design procedure, which assumes knowledge of the discrete state of the switched system, is based on the principles of disturbance decoupling and hierarchical observer output injection. In order to cope with the switching nature of the plant under observation, jumps in the observer state space are enforced intentionally. The implementation of an additional observer allows for the reconstruction of the unknown inputs, which may be important in the framework of fault detection. Numerical examples illustrate the effectiveness of the suggested technique.     

Lyapunov reducibility and stabilization of nonstationary systems with an observer

For a linear nonstationary control system with an observer, we assume that the coefficients are locally Lebesgue integrable and integrally bounded on ℝ and construct a linear feedback such that the closed-loop plant-controller system is Lyapunov reducible to the special triangular form corresponding to an independent shift of the diagonal coefficients in the original system and in the system of asymptotic estimation of the state by an arbitrary pregiven quantity. For a periodic system, we prove that the constructed controls and Lyapunov transformation are periodic. We obtain corollaries on the uniform stabilization and global controllability of the central and singular exponents of the system.     

Direct Method of Constructing H 2-Suboptimal Controllers: Continuous-Time Systems

An H ₂-suboptimal control problem is defined and analyzed. Then, an algorithm called H ₂-suboptimal state feedback gain sequence algorithm (Algorithm A1) is developed. Rather than utilizing a perturbation method, which is numerically stiff and computationally prohibitive, Algorithm A1 utilizes a direct eigenvalue assignment method to come up with a sequence of H ₂-suboptimal state feedback gains. Also, although the sequence of H ₂-suboptimal state feedback gains constructed by Algorithm A1 depends on a parameter , the construction procedure itself does not require explicitly the value of the parameter . Next, attention is focused on constructing a sequence of H ₂-suboptimal observer-based measurement feedback controllers. Both full-order as well as reduced-order observer-based controllers are developed. For a given H ₂-suboptimal state feedback gain, a sequence of observer gains for either a full-order or reduced-order observer can be constructed by merely dualizing Algorithm A1. The direct method of constructing H ₂-suboptimal controllers developed here has a number of advantages over the perturbation method, e.g., it has the ability to design both full-order and reduced-order observer-based controllers while still maintaining throughout the design the computational simplicity of it.     

基于混合时滞观测器的混合反馈控制

对于一类具有状态和有限自动机输出时滞的离散混合系统,研究基于混合时滞观测器的混合反馈控制问题.通过系统线性部分和离散事件部分的Lyapunov函数构造了整个时滞系统的混合Lyapunov函数,进一步,给出混合反馈控制的设计方法且证明了闭环系统的稳定性.仿真例子说明该方法的有效性.     

Power-series approximations for the optimal feedback control of noisy nonlinear systems

Power-series methods are developed for designing approximately optimal state regulators for a nonlinear system subject to white Gaussian random disturbances. The performance index of the control is an ensemble average of a quadratic form. A perfect observation of the system state is assumed. When the system nonlinearity is small and it is characterized by a polynomial function of the state, a definite method is presented to construct a suboptimal feedback control of a power-series form in a small nonlinearity parameter. If the variance of noise is small, an alternative method is also applicable which yields a suboptimal control in a power series with respect to a variance parameter. A simple one-dimensional problem is examined to make comparison between controls of the two different forms.     

Adaptive output feedback asymptotic stabilization of nonholonomic systems with uncertainties

A global adaptive output feedback control strategy is presented for a class of nonholonomic systems in generalized chained form with drift nonlinearity and unknown virtual control parameters. The purpose is to design a nonlinear output feedback switching controller such that the closed-loop system is globally asymptotically stable. By using the input-state scaling technique and an integrator back-stepping approach, an output feedback controller is given. A filter of observer gain is introduced for state and parameter estimates. Meanwhile, in order to avoid the over-parameters, a tuning function technique is utilized. A novel switching control strategy based on the output measurement of the first subsystem rather than time is used to overcome the uncontrollability of the x₀-subsystem in the origin. The proposed controller can guarantee that all the system states globally converge to the origin, while other signals maintain bounded. The numerical simulation testifies the effectiveness.     

广义分布参数系统的状态反馈稳定性问题(1)

关于系统的状态反馈稳定性问题的研究一直是现代控制理论研究的重要问题之一.广义分布参数系统是比分布参数系统更广的一类系统,在研究复合材料热导体中的温度分布等问题时会出现这样的系统.本文讨论了H ilbert空间中一阶广义分布参数系统的状态反馈稳定性问题.应用泛函分析及线性算子半群理论的方法给出了使闭环广义分布参数系统渐进稳定的充要条件,充分条件及状态反馈的构造性表达式.这对研究广义分布参数系统的状态反馈稳定性问题具有重要的理论价值.     

An entire strategy for precise system tracking control of a revolving thin flexural link,part I: Finite element modeling and direct tuning controller design

An entire control strategy including a design based model, controller design, and system output modification for a distributed parameter system is illuminated by application to feedback control of a revolving thin flexural link. In Part I, a very realizable actuator and a sensor, which uses a motor and a tachometer, are applied to design the control system. The finite element modeling and the state space representation are obtained for the purpose of control system analysis and computer simulation. Instead of relying on parameter identification subroutines, a controller design based on directly tuning the parameter of the gain makes the closed-loop absolutely stable and good for system tracking control. This control system design scheme is robust, insensitive to system parameter changes, and this algorithm cannot depend on traditionally priori knowledge such as the system dimension, exact model, or observer design. The performance included in the presence of all the high frequency dynamics can be effectively shown through the computer simulation, and one is led to speculate that this design scheme may perform quite well in the real world implementation.     

Real-time nonlinear global state observer design for solar heating systems

Nowadays it is important to investigate and develop solar water heating systems as an environmentally friendly technology. For this reason we introduce a physically-based nonlinear mathematical model that applies to a wide range of solar heating systems. In commercial solar heating systems not all state variables are monitored by direct measurements, since some of them may be technically difficult or expensive to measure. For a better monitoring and more efficient control of the system it may be useful to estimate the unmeasured state variables.As a novelty, we apply a global nonlinear state observer to a solar domestic water heating system. The state observer has been established relatively recently in the field of control theory. The state observer we worked out enables us to estimate the unmeasured state variables in real-time. This observer is global in the sense that it works starting from any initial state. A further contribution of this work is a rather general algorithm for the practical application of the real-time estimation process, and we also give bounds of the estimation error and a practical method to decrease this error.Comparing calculated and measured values for a real particular solar heating system, we justify the usability of the state observer and the estimation process.On the basis of measured data, we show that the nonlinear mathematical model corresponding to the applied nonlinear observer is more accurate than the linear model corresponding to the classical linear Luenberger-type observer, so it is reasonable to apply the nonlinear observer.     

Iterative learning control for MIMO nonlinear systems with arbitrary relative degree and no states measurement

This article presents a state observer based iterative learning control to solve the trajectory tracking problem of a class of time‐varying Multi‐Input‐Multi‐Output nonlinear systems with arbitrary relative degree. For this purpose, an asymptotically stable observer is derived for the system under consideration. There after, this observer is integrated with the iterative learning controller by replacing the state in the control law with its estimation yielded by the state observer. Hence, the stability of the whole control (nonlinear system plus controller plus observer) is guaranteed. Simulation result on nonlinear system shows that the trajectory tracking error decreases through the iterations. © 2013 Wiley Periodicals, Inc. Complexity 19: 37–45, 2013     

Active Disturbance Rejection Control of Quadrotor UAVs Based on Joint Observation and Feedforward Compensation北大核心CSCD

为解决模型参数不确定与外界干扰影响下,四旋翼无人机飞控作业中姿态与轨迹跟踪精度下降,反应迟缓的问题,利用拓展Kalman滤波应对非线性系统问题出色的适应能力和噪声抑制能力,对四旋翼状态信息进行初步估算来抑制高频信号干扰,从而降低了扩张状态观测器的估计负担.同时,与扩张状态观测器联合估计由系统不确定性参数与外界扰动联合组成的“总扰动”,使系统对于精确模型的依赖性降低,并利用扰动估计的微分值进行前馈补偿,以提高对突变扰动的跟踪精度,克服了突变干扰下的相位滞后现象.综合联合观测器、带前馈补偿的LESO及带误差补偿的PD控制律,形成了一种利用拓展Kalman滤波与前馈补偿后的扩张状态观测器联合观测扰动,能较大程度抑制高频噪声和突变扰动的改进型自抗扰控制器.仿真与实验结果表明,联合观测器能有效地减小观测误差幅值且能超前校正观测相位滞后,从而更好地得到更精确的状态信息,改进型自抗扰控制器能更好地满足四旋翼飞行器快速反应、高效稳定的控制要求,精准高效地完成复杂轨迹跟踪.     

基于输出反馈的一类大型互联Holder非线性系统的全局实际镇定

本文研究基于输出反馈的一类大型互联Holder连续非线性系统的全局实际镇定问题.通过构造每个子系统的状态观测器,并对观测器的状态作线性变换,得到分散输出反馈控制器.当输出反馈控制律作用于该系统时,闭环系统是全局实际稳定的.     

基于输出反馈的一类大型互联非线性系统的鲁棒全局指数稳定

研究基于输出反馈的一类新的大型互联非线性不确定系统的鲁棒全局指数稳定问题,通过构造每个子系统收敛的状态观测器,并对观测器的状态作线性变换,得到鲁棒分散输出反馈控制器.当该反馈控制律作用于该系统时,闭环系统是全局指数稳定的.     

A decentralized volume variations observer for open channels

This paper derives a linear model of open channels enabling to design a decentralized volume variations observer. The proposed observer allows to implement decentralized constant volume controllers under the realistic assumption of non-measurable state. The main advantage of this approach is that each state variable may be reconstructed on the base of only local measurements, thus not vanishing the advantage of decentralization in the controller.Since the fundamental property which must be retained for all possible perturbations of the plant is stability of the feedback system, this paper studies whether a given decentralized controller used in conjunction with the proposed observer is robust when output-multiplicative perturbations occur due to the low-frequency approximations and to the variations with respect to the reference configuration of uniform flow.