Receding horizon output feedback control for constrained uncertain systems using periodic invariance

In this article, we consider a receding horizon output feedback control (RHOC) method for linear discrete-time systems with polytopic model uncertainties and input constraints. First, we derive a set of estimator gains and then we obtain, on the basis of the periodic invariance, a series of state feedback gains stabilising the augmented output feedback system with these estimator gains. These procedures are formulated as linear matrix inequalities. An RHOC strategy is proposed based on these state feedback and state estimator gains in conjunction with their corresponding periodically invariant sets. The proposed RHOC strategy enhances the performance in comparison with the case in which static periodic gains are used, and increases the size of the stabilisable region by introducing a degree of freedom to steer the augmented state into periodically invariant sets.     

A novel gain design method to improve the consensus performance of output-feedback multi-agent systems

This paper considers the consensus problem of a group of homogeneous agents. These agents are governed by a general linear system and can only directly measure the output, instead of the state. In order to achieve the consensus goal, each agent estimates its state through a Luenberger observer, exchanges its estimated state with neighbors, and constructs the control input with the estimated states of its own and neighbors. Due to the existence of observation and process noises, only practical consensus, instead of asymptotical consensus, can be achieved in such multi-agent systems. The performance of the achieved practical consensus can be measured by the ultimate mean square deviation of the states of agents. That performance is closely related to the observation gains of the state observers and the control gains of agents. This paper proposes a method to optimize such performance with respect to the concerned observation and control gains. That method starts with a set of feasible observation and control gains and formulates a group of linear matrix inequalities (LMIs). Solving these LMIs gives some intermediate matrix variables. By perturbing observation and control gains, and the intermediate matrix variables, the original LMIs yield another group of LMIs, which can be solved to provide a descent direction of observation and control gains. Moving along that descent direction, observation and control gains can be improved to yield better performance and work as the starting point of the next iteration. By iteratively repeating this procedure, we can hopefully improve the consensus performance of the concerned multi-agent system. Simulations are done to demonstrate the effectiveness of the proposed method.     

Anti-windup design of uncertain discrete-time Markovian jump systems with partially known transition probabilities and saturating actuator

This paper carries out a study on the design of anti-windup gains for uncertain discrete-time Markovian jump systems subject to both actuator saturation and partially known transition probabilities. The parameter uncertainties appearing in both the state and input matrices are assumed to be time-varying and norm-bounded. Under the assumption that a set of linear dynamic output feedback controllers have been designed to stabilise the Markovian jump system in the absence of actuator saturation, anti-windup compensation gains are designed for maximising the domain of attraction of the closed-loop system with actuator saturation. Then, by solving a convex optimisation problem with constraints of a set of linear matrix inequalities, the anti-windup compensation gains are obtained. A simulation example is provided to illustrate the effectiveness of the proposed technique.     

Decentralized control and state estimation of linear time-periodic systems

The main contributions of this article are the design of a decentralized controller and state estimator for linear time-periodic systems with fixed network topologies. The proposed method to tackle both problems consists of reformulating the linear periodic dynamics as a linear time-invariant system by applying a time-lifting technique and designing a discrete-time decentralized controller and state estimator for the time-lifted formulation. The problem of designing the decentralized estimator is formulated as a discrete-time Kalman filter subject to sparsity constraints on the gains. Two different algorithms for the computation of steady-state observer gains are tested and compared. The control problem is posed as a state feedback gain optimization problem over an infinite-horizon quadratic cost, subject to a sparsity constraint on the gains. An equivalent formulation that consists in the optimization of the steady-state solution of a matrix difference equation is presented and an algorithm for the computation of the decentralized gain is detailed. Simulation results for the practical cases of the quadruple-tank process and an extended 40-tank process are presented that illustrate the performance of the proposed solutions, complemented with numerical simulations using the Monte Carlo method.     

Receding Horizon Estimation for Linear Discrete-time Systems with Multi-channel Observation Delays

This paper investigates the receding horizon state estimation for the linear discrete-time system with multi-channel observation delays. The receding horizon estimation is designed by the reorganized observation technique and the linear unbiased estimation method. The estimation gains are developed by solving a set of Riccati equations, and a stability result about the state estimation is shown. Finally, an example is given to illustrate the efficiency of the receding horizon state estimation.      

An algorithm for computing the minimum-time regulator of multivariable discrete linear systems

This paper constructs an algorithm in general form for computing time-invariant feedback laws which assume deadbeat regulation in minimum time of multivariable discrete-time linear systems. The algorithm simply assumes that the system is irreducible. The key idea is the division of the state space into sub-statespaces according to the time needed to reach the equilibrium state. Based on the spans of all sub-statespaces, iterative formulae for computing all the feedback gains are obtained. The formulae can be programmed easily, and the transient response can be shaped by choosing different sets of feedback gains. An example is worked out to demonstrate the feasibility of the proposed method.     

A theory of state covariance assignment for discrete systems

In many regulation control problems it is desired to design the controller so that various system states have acceptable root mean squared values. This is a multiple objective problem. One way to satisfy these objectives is to assign a specified state covariance to the system. This paper introduces and solves the following problem: 1) characterize the entire set of state covariances which may be assigned to a linear discrete-time system by state feedback; and 2) find the set of all state feedback gains which will assign an admissible state covariance to the system. Extensions are also presented for state estimate feedback.     

On the exact model matching controller design

The problem of designing a static state feedback controller which matches a given multivariable system to a desired ideal system (model) is treated. The system under control is assumed in state space form while the model is assumed in transfer matrix form. An algorithm is developed which separates the conditions which must be satisfied by the system under control and the model to be matched from the equations which must be solved to find the gains of the feedback controller. Two examples are included.     

基于强跟踪UKF 的自适应SLAM 算法

针对无迹卡尔曼滤波（UKF）缺乏在线自适应调整能力,导致系统状态估计精度较低的问题,提出了 一种将强跟踪滤波器（STF）与UKF 相结合的SLAM 算法．该算法对于UKF 中每个采样点采用STF 进行更新,获 得优化滤波增益,抑制噪声对系统状态估计的影响,使系统状态估计迅速收敛到真实值附近．仿真实验对比了当前 几种SLAM 算法在不同噪声环境下的性能,实验表明,基于强跟踪UKF 的自适应SLAM 算法具有更好的鲁棒性和 自适应性．     

The use of model following methods to generate suboptimal feedback control†

Implementation of linear optimal control laws oftentimes requires that all system state variables be physically available for measurement and feedback. The well known impracticality of this requirement motivates the work described in this paper which is addressed to the use of model following methods in the synthesis of sub-optimal feedback controllers which do not require sensing all of the system state variables. The approach presented here consists of first computing a complete set of optimal feedback gains and thus generating optimum system response which is then used as a model toward which a suboptimal design can strive. A suboptimal control is postulated with zero feedback gains as desired, the remaining gains being as yet arbitrary. The average integrated difference between the model closed loop response and the suboptimal closed loop response is then minimized by selection of these remaining feedback gains. For a given feedback configuration, the method thus determines the suboptimal closed loop control yielding a response which is as close as possible in a given well-defined sense to the model response. Defining equations are derived and parameter optimisation methods are utilized to compute the free feedback gains. The method is particularly well suited to digital computation requiring only the use of standard parameter optimization algorithms as well as an algorithm to solve a set of bilinear matrix equations. An example involving regulation of the longitudinal modes of a VTOL flight vehicle is presented to illustrate the model following capabilities of the synthesis procedure.     

存在数据丢包的网络控制系统的控制

将存在数据丢包的网络控制系统描述为跳跃系统。基于一个李雅普诺夫泛函,只需满足4个线性矩阵不等式,便可通过带状态观测的状态反馈控制使闭环系统达到稳定。由于得到的条件不是严格的线性矩阵不等式条件,将不具有严格线性矩阵不等式条件的非凸可行解问题转化为具有严格线性不等式的非线性最小化问题,得到了求解状态反馈控制器增益和状态观测器增益的算法。数值仿真结果验证了该算法的有效性。在所设计的状态反馈控制器的校正作用下,闭环系统的响应是渐近稳定的。     

含结构参数扰动的线性连续系统的鲁棒约束方差状态估计*

本文考虑含结构参数扰动的线性连续随机系统的鲁棒约束方差状态估计问题，即设计滤波增益，使受扰系统每个状态分量的估计误差方差的稳态值不大于预先给定值，同时滤波矩阵具有期望的稳定裕度。本文给出了上述性能鲁棒滤波增益的存在条件及解析表达式，并提供了相应的数值例子。     

Control of Teleoperators with Communication Time Delay through State Convergence

This paper describes a new control method of teleoperation systems with communication time delay. This method models the teleoperation system in the state space, considering all the possible interactions that could appear in the operator‐master‐slave‐environment set, and it uses the Taylor expansion to model the time delay. The control system allows that the slave manipulator follows the master in spite of the time delay in the communication channel. The tracking is achieved by state convergence between the master and the slave. The method is also able to establish the desired dynamics of this convergence and the dynamics of the slave manipulator. Furthermore, a simple design procedure is provided to obtain the control system gains. These control gains are calculated solving a set of seven equations. The control method is robust to the uncertainty of the design parameters, so it is not necessary to obtain good estimations of these parameters. Simulations and experiments with a one DOF teleoperation system are presented to verify the control method. © 2004 Wiley Periodicals, Inc.     

Application of stochastic optimal control to a hydrofoil boat problem

In this paper the solution of a stochastic optimal control problem described by linear equations of motion and a nonquadratic performance index is presented. The theory is then applied to the dynamics of a single-foil and a hydrofoil boat flying on rough water. The random disturbances caused by sea waves are represented as the response of an auxiliary system to a white noise input. The control objective is formulated as an integral performance index containing a quadratic acceleration term and a nonquadratic term of the submergence deviation of the foil from calm water submergence. The stochastic version of the maximum principle is used in the formulation of a feedback control law. The Riccati equations and the feedback gains associated with a nonquadratic performance index are non-linear functions of the state and auxiliary state variables. These equations are integrated forward with the state equations for the steady-state solution of the problem. The controller for a nonquadratic performance index contains computing elements which perform the integration of the Riccati equations to generate the instantaneous values of the feedback gains. The effect of a nonquadratic penalty on the submergence deviation and the effect of a nonquadratic control penalty on the response of the system are investigated. A comparison between an optimal nonlinear control law and a suboptimal linear control law is presented.     

Robust Output Feedback Model Predictive Control: A Stochastic Approach

This paper addresses the robust explicit model predictive control scheme for linear systems with input and output constraint in the presence of disturbances and noise. Conditions for disturbance rejection are established by incorporating a full state/disturbance observer. The separation principle is applied to design an optimal observer in the unconstrained problem. Then, an efficient algorithm is developed to explicitly design observer gains by minimizing a quadratic performance criterion. It is shown that the solution includes a set of regions with piecewise affine functions of the state and reference vectors and a set of regions with optimal observers. In the proposed method, two sets of partitions associated with the control law and the observer gains are obtained. Therefore, the online computation includes finding the active regions of both observer and control law partitions in which the current state is located. The proposed technique is particularly attractive for a wide range of practical problems where the exact model of the actual system is not available.     

机器人非线性连续变增益H∞控制器设计

本文针对n关节的刚性机器人,提出了一种设计连续变增益控制器的新方法．这种方法结合 了变增益和H∞理论,通过在平衡点附近线性化系统,利用具有极点配置的状态反馈H∞ 技术,对应每个运动区域,设计满足H∞性能和动态特性的状态反馈增益,这些增益通过 泰勒级数展开拟合成与运动点有关的连续函数．随着系统状态的变化,拟合成的增益函数可 使控制器获得连续的增益,使得所设计的控制器同样适合系统状态变化较快的对象,而且系 统随状态的变化始终具有很高的动态性能,克服了传统变增益控制器中存在的不足．仿真结 果验证了此控制器的有效性．     

Reduced-order filters for limited state estimation from measurements containing coloured noise

The design of optimal fixed-configuration filters for estimating, without bias, a linear transformation of the state of a dynamic system in the presence of coloured measurement noise is studied. The performance index employed is the integral of error variance, and this leads to a matrix variational problem in the filter gains. It is demonstrated that the optimal time-varying filter gains may be computed by solving this variational problem using standard conjugate gradient algorithms. Consideration is also given to both algebraic and differential approximation of the optimal filter gains. The problem is formulated as one of ordinary minimization in parameters defining the approximation, and the required gradient expressions are derived for its solution using standard function minimization algorithms. An illustrative numerical example is presented.     

基于降维观测器的起重机吊重防摇系统研究

对直流电压控制桥门式起重机小车驱动电机的小车吊重动力学系统,设置降维观测器,用小车位置和速度信息对摆角、摆角角速度和驱动力进行估计,从而解决了工程实际中这些状态变量不易直接测得的问题.为了防止吊重摇摆,采用全状态反馈形成吊重防摇的闭环控制系统,并给出了控制系统结构以及降维观测器和反馈控制器增益参数的确定方法.仿真结果表明:各状态变量能从观测时间开始消除重构误差;吊重摆角能在小车指定位置和时间内衰减为零,其余状态变量也有良好的动态特性.     

A new method of recursive estimation in discrete linear systems

Let the measurementz(i)at instantibe of formz(i) = y(i) + eta(i)whereeta(i)is the noise andy(i)is the signal obeying a system of coupled linear difference equations. A method is given for computing the gains of the predictor and filter for the signaly(i)and the corresponding statex(i). The gains are computed recursively from the previous gains without involving the covariance matrix of the state. The computational advantages of the scheme are also discussed.     

On the design of optimal constrained dynamic compensators for linear constant systems

The design of linear time-invariant dynamic compensators of fixed dimensionalitys, which are to be used for the regulation of annth-order linear time-invariant plant, is dealt with. A modified quadratic cost criterion is employed in which a quadratic penalty on the system state as well as all compensator gains is used; the effects of the initial state are averaged out. The optimal compensator gains are specified by a set of simultaneous nonlinear matrix algebraic equations. The numerical solution of these equations would specify the gain matrices of the dynamic compensator. The proposed method may prove useful in the design of low-orderscompensators for high-ordernplants that have fewroutputs, so that the dimension of the compensator is less than that obtained through the use of the associated Kalman-Bucy filternor the Luenberger observern - r.