Application of Feedback Linearization to Tracking and Almost Disturbance Decoupling Control of the AMIRA Ball and Beam System

This paper studies the tracking and almost disturbance decoupling problem of the nonlinear AMIRA ball and beam system based on the feedback linearization approach. The main contribution of this study is to construct a controller, under appropriate conditions, such that the resulting closed-loop system is valid for any initial condition and bounded tracking signal with the following characteristics: input-to-state stability with respect to disturbance inputs and almost disturbance decoupling. Two examples on the almost disturbance decoupling problem, which cannot be solved via Ref. 1, are proposed in this paper exploiting the fact that the tracking and the almost disturbance decoupling performances are easily achieved by our proposed approach.     

Finite-time H∞ control for a class of discrete-time switched time-delay systems with quantized feedback

This paper is concerned with the finite-time quantized H_∞ control problem for a class of discrete-time switched time-delay systems with time-varying exogenous disturbances. By using the sector bound approach and the average dwell time method, sufficient conditions are derived for the switched system to be finite-time bounded and ensure a prescribed H_∞ disturbance attenuation level, and a mode-dependent quantized state feedback controller is designed by solving an optimization problem. Two illustrative examples are provided to demonstrate the effectiveness of the proposed theoretical results.     

Robust finite-time H∞ control for a class of uncertain switched neutral systems

This paper investigates the robust finite-time H_∞ control problem for a class of uncertain switched neutral systems with unknown time-varying disturbance. The uncertainties under consideration are norm bounded. By using the average dwell time approach, a sufficient condition for finite-time boundedness of switched neutral systems is derived. Then, finite-time H_∞ performance analysis for switched neutral systems is developed, and a robust finite-time H_∞ state feedback controller is proposed to guarantee that the closed-loop system is finite-time bounded with H_∞ disturbance attenuation level γ. All the results are given in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to show the effectiveness of the proposed method.     

永磁同步电机伺服系统的有限时间位置控制

研究了永磁同步电机伺服系统的位置跟踪问题.利用反馈线性化的思想,对永磁同步电机的数学模型进行分析,实现了电机模型的精确线性化和解耦.首先,将永磁同步电机位置跟踪系统采用反馈线性化技术变换为两个线性子系统,分别对其设计相应的基于连续状态反馈线性化的有限时间控制器,并设计了有限时间负载观测器来观测估计外部负载扰动.对永磁同步电机位置跟踪的闭环系统进行了稳定性的分析.与对应的渐近稳定控制的方案相比,基于有限时间的控制方案实现了永磁同步电机对期望信号的有限时间跟踪,获得了更好的动态响应和抗扰动性能.仿真结果表明了该控制方案的有效性.     

Robust H∞ control for linear Markovian jump systems with unknown nonlinearities

This paper studies the problem of stochastic stability and disturbance attenuation for a class of linear continuous-time uncertain systems with Markovian jumping parameters. The uncertainties are assumed to be nonlinear and state, control and external disturbance dependent. A sufficient condition is provided to solve the above problem. An H_∞ controller is designed such that the resulting closed-loop system is stochastically stable and has a disturbance attenuation γ for all admissible uncertainties. It is shown that the control law is in terms of the solutions of a set of coupled Riccati inequalities. A numerical example is included to demonstrate the potential of the proposed technique.     

A dual control problem and application to marketing

The general approach to adaptive and dual control is to formulate an optimal stochastic control problem. However, for such an approach only mathematical representations of the solution are available which allow little insight into the structure of the optimal controller. Here, an alternative deterministic approach is presented based upon determining a control in which a disturbance attenuation function remains bounded for all allowable (L₂ functions) disturbances. The disturbance attenuation function is composed of the ratio of an L₂ function of the desired outputs over an L₂ function of the disturbance inputs. This disturbance attenuation problem is converted to a differential game. For this game, the optimal control law, in a closed-form, is obtained by performing a minmax operation with respect to a quadratic cost function subjected to a bilinear system. The resulting controller is time-varying and depends nonlinearly on the state and the parameter estimates vector, and on an associated Riccati-type matrix. We provide insights into the structure of the resulting dual controller and illustrate the method by two examples. One of the examples is an application to marketing, to set promotional spending of a company, considering that the effect of promotional effort on sales is unknown.     

State estimation with guaranteed performance for switching-type fuzzy neural networks in presence of sensor nonlinearities

This paper investigates the state estimation with guaranteed performance for a class of switching fuzzy neural networks. A switching-type fuzzy neural networks (STFNNs) model is proposed which captures external disturbances, sensor nonlinearities, and mode switching phenomenon of the fuzzy neural networks without the Markovian process assumption. For such a model, a state estimation problem is formulated to achieve the guaranteed performance: the estimation error system is exponentially stable with certain decay rate and a prescribed H_∞ disturbance attenuation level. A novel sufficient condition for this problem is established using the Lyapunov functional method and the average dwell time approach, and the estimator parameters are explicitly given. A numerical example is presented to show the effectiveness of the developed results.     

Control with a Guide in the Guarantee Optimization Problem under Functional Constraints on the Disturbance

A motion control problem for a dynamic system under disturbances is considered on a finite time interval. There are compact geometric constraints on the values of the control and disturbance. The equilibrium condition in the small game is not assumed. The aim of the control is to minimize a given terminal performance index. The guaranteed result optimization problem is posed in the context of the game-theoretical approach. In the case when realizations of the disturbance belong to some a priori unknown compact subset of L₁ (the space of functions that are Lebesgue summable with the norm), we propose a new discrete-time control procedure with a guide. The proximity between the motions of the system and the guide is provided by the dynamic reconstruction of the disturbance. The quality of the control process is achieved by using an optimal counter-strategy in the guide. Conditions on the equations of motion under which this procedure ensures an optimal guaranteed result in the class of quasi-strategies are given. The scheme of the proof makes it possible to estimate the deviation of the realized value of the performance index from the value of the optimal result depending on the discretization parameter. Illustrative examples are given.     

Robust reliable H∞ control for neural networks with mixed time delays

This paper considers the problem of robust reliable H_∞ control for neural networks. The system has time-varying delays, parametric uncertainties and faulty actuators. The faulty actuators are considered as a disturbance signal to the system which is augmented with system disturbance input. Based on the LMI technique and the Lyapunov stability theory, a new set of sufficient conditions is obtained for the existence of the robust reliable H_∞ controller. An example is also presented illustrate the results.     

Two-grid finite element method for the dual-permeability-Stokes fluid flow model

In this paper, two-grid finite element method for the steady dual-permeability-Stokes fluid flow model is proposed and analyzed. Dual-permeability-Stokes interface system has vast applications in many areas such as hydrocarbon recovery process, especially in hydraulically fractured tight/shale oil/gas reservoirs. Two-grid method is popular and convenient to solve a large multiphysics interface system by decoupling the coupled problem into several subproblems. Herein, the two-grid approach is used to reduce the coding task substantially, which provides computational flexibility without losing the approximate accuracy. Firstly, we solve a global problem through standard P_k ? P_k??1 ? P_k ? P_k finite elements on the coarse grid. After that, a coarse grid solution is applied for the decoupling between the interface terms and the mass exchange terms to solve three independent subproblems on the fine grid. The three independent parallel subproblems are the Stokes equations, the microfracture equations, and the matrix equations, respectively. Four numerical tests are presented to validate the numerical methods and illustrate the features of the dual-permeability-Stokes model.

     

An Efficient Algorithm to Identify DNA Motifs

We consider the problem of identifying motifs that abstracts the task of finding short conserved sites in genomic DNA. The planted (l, d)-motif problem, PMP, is the mathematical abstraction of this problem, which consists of finding a substring of length l that occurs in each s _i in a set of input sequences S = {s ₁, s ₂, . . . ,s _t } with at most d substitutions. Our propose algorithm combines the voting algorithm and pattern matching algorithm to find exact motifs. The combined algorithm is achieved by running the voting algorithm on t′ sequences, t′ < t. After that we use the pattern matching on the output of the voting algorithm and the reminder sequences, t ? t′. Two values of t′ are calculated. The first value of t′ makes the running time of our proposed algorithm less than the running time of voting algorithm. The second value of t′ makes the running time of our proposed algorithm is minimal. We show that our proposed algorithm is faster than the voting algorithm by testing both algorithms on simulated data from (9, d ≤ 2) to (19, d ≤ 7). Finally, we test the performance of the combined algorithm on realistic biological data.     

Reliability of disturbance rejection control based on the geometrical disturbance decoupling

In this note, a reliable disturbance decoupled control system based on the geometrical technique is proposed. For this purpose, first, the conditions for nominal disturbance detection and rejection is introduced by using invariant subspaces. Then, the fragility issue of the controller/observer is addressed with appropriate H_∞ constraints in the form of some linear matrix inequalities (LMIs). In contrast to conventional pole placement method suitable for systems by neglecting sources of uncertainty, in the presented method, the disturbance rejection problem reduces to a quadratic stability problem. It is observed that the proposed method has a better attenuation performance than classical observer-based non-fragile controller. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

L2 − L∞ filtering for Markovian jump systems with time-varying delays and partly unknown transition probabilities

This paper considers the L₂ − L_∞ filtering problem for Markovian jump systems. The systems under consideration involve time-varying delays, disturbance signal and partly unknown transition probabilities. The aim of this paper is to design a filter, which is suitable for exactly known and partly unknown transition probabilities, such that the filtering error system is stochastically stable and a prescribed L₂ − L_∞ disturbance attenuation level is guaranteed. By using the Lyapunov-Krasovskii functional, sufficient conditions are formulated in terms of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed main results. All these results are expected to be of use in the study of filter design for Markovian jump systems with partly unknown transition probabilities.     

Iterative learning control design of nonlinear multiple time-delay systems

Most available results on iterative learning control address trajectory tracking problem for systems without multiple time-delay. This paper is concerned with iterative learning control design for nonlinear systems with multiple delays, in which external disturbances and output measurement noises are involved. We obtain some new and interesting criteria to guarantee the convergence of the tracking error in the sense of the λ − norm. It will be shown that the convergence of the system outputs to the desired trajectory is ensured in the absence of disturbances and output measurement noises. In the presence of disturbance and measurement noises, we estimate the upper bound of the tracking error. In order to confirm the validity of the present results, numerical simulation is also presented.     

Adjustable dimension descriptor observer based fault estimation for switched nonlinear systems with partially unknown nonlinear dynamics

This paper focuses on the fault estimation problem for switched systems with partially unknown nonlinear dynamics, actuator and sensor faults, simultaneously. The fault estimation observers are constructed, in which the observer dimension is not fixed and can be selected in a certain range. Both the disturbance decoupling and disturbance attenuation are considered, where the unknown nonlinear dynamics can be decoupled and the effect of modeling error and measurement disturbance is attenuated. Based on the average dwell time and the piecewise Lyapunov function, the observer parameter matrices can be calculated by solving LMIs and matrix equations. Finally, two examples are listed to verify the proposed fault estimation approach.     

航天器编队飞行多目标姿态快速跟踪鲁棒控制

研究了航天器编队飞行多目标姿态跟踪鲁棒控制问题．主航天器装有一个快速机动天线和一个星载相机．考虑相机对地面目标跟踪,同时考虑天线与从航天器通信的空间任务．通过引入角速度约束和姿态角约束,分别推导了相机和天线的参考姿态角、角速度和角加速度．提出期望逆系统的概念,将三维空间姿态跟踪问题转化为调节问题,简化了控制器的设计．考虑存在参数摄动和外部干扰力矩的情况,基于期望逆系统和滑模控制,设计了鲁棒姿态跟踪控制器,并利用Liapunov稳定性理论证明了控制系统的渐近稳定性．以两航天器编队飞行多目标跟踪为例进行数值仿真,结果表明所设计的控制器具有良好的鲁棒性和优越的跟踪性能．     

Robust L2–L∞ filtering for switched systems under asynchronous switching

This paper investigates the problem of robust L₂–L_∞ filtering for continuous-time switched systems under asynchronous switching. When there exists asynchronous switching between the filter and the system, based on the average dwell time approach, sufficient conditions for the existence of a linear filter that guarantee the filtering error system to be exponentially stable with a prescribed weighted L₂–L_∞ performance for switched systems are derived, and filter parameters can be obtained by solving a set of matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.     

Feedforward Design and Optimality Aspects for the Control of Mechatronic Systems

This paper considers the tracking controller design for a mechatronic handling system. The presented approach is based on Port-Hamiltonian systems and it achieves good tracking as well as good disturbance rejection based on a polynomial approach. A PBC controller stabilizes the trajectory and the feedforward part has to fulfill the given limitations and the time optimality. This approach avoids the solution of a boundary value problem and a real-time integration of the internal dynamics. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Adaptive robust synchronization of Rossler systems in the presence of unknown matched time-varying parameters

This paper deals with the problem of adaptive robust synchronization of chaotic systems based on the Lyapunov theory. A controller is designed for a feedback linearizable error system with matched uncertainties. The proposed method shows that the drive and response systems are synchronized and states of the response system track the states of the drive system as time tends to infinity. Since this approach does not require any information about the bound of uncertainties, this information is not needed in advance. In order to prevent the frequent switching phenomenon in the control signal, the method is modified such that the norm of tracking error is bounded. Numerical simulations on two uncertain Rossler systems with matched uncertainties show fast responses of tracking error, while the errors are Uniformly Ultimately Bounded, and the control signal is reasonably smooth.