Schur-Cohn多项式的鲁棒稳定半径

研究离散线性时不变系统的特征多项式的鲁棒稳定性, 给出用求多项式最小值的方法来估计Schur_Cohn多项式的鲁棒稳定半径, 在一定条件下估计为最优估计. 最后, 给出若干算例.     

集中式与分布式鲁棒状态融合估计

研究不确定多传感器系统的鲁棒估计问题是多传感器融合估计理论的一个重要研究方向.本文以鲁棒滤波理论为基础,给出了不确定多传感器系统的多胞型描述模型,并利用LMI方法给出集中式鲁棒状态融合估计问题的解,证明了将集中式鲁棒融合估计转化为相同估计性能的分布式融合估计算法的条件.最后给出了分布式不确定多传感器系统的状态融合估计的一个算例.     

鲁棒逆奈奎斯特方法中鲁棒Gershgori带的近似估计

针对多输入多输出线性系统的鲁棒逆奈奎斯特阵列分析,提出一种保守性较小的鲁棒Gershgorin带近似估计方法.首先给出一个保守性较小的鲁棒对角优势性引理,基于此引理,对具有参数不确定性的传递函数矩阵,推导了鲁棒Gershgorin带的近似估计方法,降低了估计结果的保守性.最后给出了仿真验证.     

鲁棒稳定性和鲁棒对角优势的关系

本文研究了多输入多输出系统的鲁棒稳定性和鲁棒对角优势的关系.不仅给出了使系统 鲁棒对角优势所需的鲁棒稳定性条件,而且还得出了系统鲁棒对角优势一定保证系统鲁棒稳 定这个一般性的结论.并可根据本文所给的结果,对允许摄动的最大边界进行估计,包括非结 构摄动的范数上界和结构性摄动的摄动矩阵的各元素的模的估计.本文得出的鲁棒对角优势 保证鲁棒稳定的结果是较少保守性的.     

不确定性离散时间系统非保守自适应鲁棒控制

研究含未知干扰和互质因子摄动离散时间不确定性系统的自适应鲁棒控制问题，为非保守的自适应鲁棒镇定提出一种广义参数递推估计方法，基于确定性等价原理，并利用ι1设计方法提出一种自适应鲁棒控制策略，证明了自适应算法的全局收敛性，给出了一个可验算的鲁棒稳定性条件，证明了该鲁棒稳定性条件是非保守和最优的。     

离散系统状态和参数鲁棒滤波分离算法

提出了一种离散系统的鲁棒分离滤波方法.为了对状态向量进行较准确估计,将鲁棒滤波器分为:1)零误差状态估计器;2)不确定矩阵估计器;3)鲁棒合成器.零偏差状态估计器是假定系统的不确定部分为零时的状态估计器;其新息作为不确定部分的估计变量,并由此估计系统的不确定部分;最后,根据系统不确定部分估计误差的上下界,用鲁棒合成器对状态向量的估计值进行鲁棒修正.为了在合成器中得到鲁棒滤波的逼近计算式,通过变换状态估计误差的协方差阵,得到了系统矩阵不确定部分的误差上界不等式逼近,并且得到了估计误差协方差阵逆阵的下界不等式逼近,从而给出了鲁棒合成滤波的完整算法.     

一类结构不确定采样系统的鲁棒H∞控制

本文针对一类结构不确定线性采样系统,研究了鲁棒H∞控制问题,给出了系统鲁棒稳定的充分条件及响应的鲁棒H∞控制律和最优鲁棒H∞控制律,控制律的求取通过借助一类线性矩阵不等式(LMI),或通过求取满足线性矩阵不等式约束的优化问题.仿真结果表明,系统在受到扰动后仍然是稳定的,同时给出了最优性能指标随外部扰动加权矩阵的变化规律.     

感应电机调速系统的鲁棒最优控制

提出了一种新的鲁棒最优控制器的设计方法 ,该控制器包括一个鲁棒抗扰调节器和一个跟随型最优调节器 ,使用H∞ 鲁棒控制理论设计抗扰调节器 ,使用二次型最优控制理论设计跟随调节器 ,给出了具体的设计方法 .并将其应用于感应电机调速系统中 ,给出了仿真结果     

球形对象族的最优鲁棒镇定

本文对球形对象族系统最优鲁棒镇定问题进行了研究.利用最小范数解方法求解球形对象族的可镇定性半径.可镇定性半径是系统稳定性半径的上界,最优控制器的稳定性半径等于镇定性半径.文中给出球形对象族最优鲁棒控制器的形式,并通过示例具体说明球形对象族最优鲁棒控制器的设计方法.     

基于鲁棒正不变集的传感器故障区间估计

针对具有传感器故障和未知扰动与测量噪声的线性离散系统, 提出了一种传感器故障区间估计方法. 将传感器故障视为增广状态, 原始系统转化为一个等效的广义系统. 为了得到故障的点估计同时抑制扰动和噪声的影响, 基于有界实引理设计了一个针对广义系统的鲁棒状态观测器. 然后, 通过中心对称多胞体技术实现对故障的区间估计并基于鲁棒正不变集给出了一种降低区间估计计算量的方法. 最后, 通过一个垂直起降(Vertical take-off and landing, VTOL)飞行器线性化模型的仿真算例验证了所提出方法的有效性与优越性.     

Robust filtering under stochastic parametric uncertainties

This paper is concerned with a polynomial approach to robust deconvolution filtering of linear discrete-time systems with random modeling uncertainties. The modeling errors appear in the coefficients of the numerators and denominators of both the input signal and system transfer function models in the form of random variables with zero means and known upper bounds of the covariances. The robust filtering problem is to find an estimator that minimizes the maximum mean square estimation error over the random parameter uncertainties and input and measurement noises. The key to our solution is to quantify the effect of the random parameter uncertainties by introducing two fictitious noises for which a simple way is given to calculate their covariances. The optimal robust estimator is then computed by solving one spectral factorization and one polynomial equation as in the standard optimal estimator design using a polynomial approach. An example of signal detection in mobile communication is given to illustrate the effectiveness of our approach.     

Optimal guaranteed cost filtering for uncertain discrete-time linear systems

This paper presents a result on the design of a steady-state robust state estimator for a class of uncertain discrete-time linear systems with normal bounded uncertainty. This result extends the steady state Kalman filter to the case in which the underlying system is uncertain. A procedure is given for the construction of a state estimator which minimizes a bound on the state error covariance. It is shown that this leads to a state estimator which is optimal with respect to a notion of quadratic guaranteed cost state estimation.     

Robust end-point optimizing feedback for nonlinear dynamic processes

The paper suggests two novel approaches to the synthesis of robust end-point optimizing feedback for nonlinear dynamic processes. Classically, end-point optimization is performed only for the nominal process model using optimal control methods, and the question of performance robustness to disturbances and model-plant mismatch remains unaddressed. The present contribution addresses the end-point optimization problem for nonlinear affine systems with fixed final time through robust optimal feedback methods. In the first approach, a nonlinear state feedback is derived that robustly optimizes the final process state. This solution is obtained through series expansion of the Hamilton-Jacobi-Bellman PDE with an active opponent disturbance. As reliable measurements or estimates of all states may not always be available, the second approach also robustly optimizes the process end-point, but uses output rather than state information. This direct use of measurement information is preferred since the choice of a state estimator for robust state feedback is non-trivial even when the observability issue is addressed. A linear time-variant output corrector is obtained by feedback parametrization and numerical optimization of a nonlinear H _∞ cost functional. A number of possible variations and alternatives to both approaches are also discussed. As model-plant mismatch is particularly common with chemical batch processes, the suitability of the robust optimizing feedback is demonstrated on a semi-batch reactor simulation example, where robustness to several realistic mismatches is investigated and the results are compared against those for the optimal open-loop policy and the optimal feedback designed for the nominal model.     

A robust continuous‐time fixed‐lag smoother for nonlinear uncertain systems

This paper presents a scheme for the design of a robust fixed‐lag smoother for a class of nonlinear uncertain systems. The proposed approach combines a nonlinear robust estimator with a stable fixed‐lag smoother, to improve the estimation error covariance. The robust fixed‐lag smoother is based on the use of integral quadratic constraints and minimax linear quadratic regulator estimation and control theory. The state estimator uses a copy of the system nonlinearity in the estimator and combines an approximate model of the delayed states to produce a smoother signal. Also in this work, a characterization of the delay approximation error is presented, and the corresponding integral quadratic constraint is included in the design, which gives a guaranteed bound on the performance cost function. In order to see the effectiveness of the method, it is applied to a quantum optical phase estimation problem. Results show a significant improvement in the error covariance of the estimator when compared with a robust nonlinear filter. Copyright © 2015 John Wiley & Sons, Ltd.     

On Robust H2 Estimation

The problem of state estimation for uncertain systems has attracted a recurring interest in the past decade. In this paper, we shall give an overview on some of the recent development in the area by focusing on the robust H2 (Kalman) filtering of uncertain discrete-time systems. The robust H2 estimation is concerned with the design of a fixed estimator for a family of plants under consideration such that the estimation error covariance is of a minimal upper bound. The uncertainty under consideration includes norm-bounded uncertainty and polytopic uncertainty. In the finite horizon case, we shall discuss a parameterized difference Riccati equation approach for systems with norm-bounded uncertainty and pinpoint the difference of state estimation between systems without uncertainty and those with uncertainty. In the infinite horizon case, we shall deal with both the norm-bounded and polytopic uncertainties using a linear matrix inequality (LMI) approach. In particular, we shall demonstrate how the conservatism of design can be improved using a slack variable technique. We also propose an iterative algorithm to refine a designed estimator. An example will be given to compare estimators designed using various techniques.     

Robust fusion time‐varying Kalman estimators for multisensor networked systems with mixed uncertainties

This paper addresses the problem of designing robust fusion time‐varying Kalman estimators for a class of multisensor networked systems with mixed uncertainties including multiplicative noises, missing measurements, packet dropouts, and uncertain‐variance linearly correlated measurement and process white noises. By the augmented approach, the original system is converted into a stochastic parameter system with uncertain noise variances. Furthermore, applying the fictitious noise approach, the original system is converted into one with constant parameters and uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case system with the conservative upper bounds of the noise variances, the five robust fusion time‐varying Kalman estimators (predictor, filter, and smoother) are presented by using a unified design approach that the robust filter and smoother are designed based on the robust Kalman predictor, which include three robust weighted state fusion estimators with matrix weights, diagonal matrix weights, and scalar weights, a modified robust covariance intersection fusion estimator, and robust centralized fusion estimator. Their robustness is proved by using a combination method, which consists of Lyapunov equation approach, augmented noise approach, and decomposition approach of nonnegative definite matrix, such that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. The accuracy relations among the robust local and fused time‐varying Kalman estimators are proved. A simulation example is shown with application to the continuous stirred tank reactor system to show the effectiveness and correctness of the proposed results.     

Design and analysis of optimal controller for fuzzy systems with input constraint

In this paper, we present a design method of the optimal and robust controller subject to the constraint on control inputs for continuous-time Takagi-Sugeno (TS) fuzzy systems. In order to establish this design method, we consider an optimal and robust control problem for nonlinear dynamic systems. For this problem, we present an analytic way which can provide the optimal controller for nonlinear dynamic systems by the dynamic programming approach and the inverse optimal approach. Moreover, we analyze the robustness property of the proposed optimal controller with respect to a class of input uncertainties by the passivity approach. Then, based on the theoretical results presented in this paper, we formulate the design problem of the optimal and robust controller with input constraint for continuous-time TS fuzzy systems as the semidefinite programming problem, and find the controller by solving it. The usefulness of the proposed approach is illustrated by considering the three-axis attitude stabilization problem of rigid spacecraft.     

On estimation of nonlinear functionals from discrete noisy measurements

The principal objective of this paper is to estimate a nonlinear functional of state vector (NFS) in dynamical system. The NFS represents a multivariate functional of state variables which carries useful information of a target system for control. The paper focuses on estimation of the NFS in linear continuous-discrete systems. The optimal nonlinear estimator based on the minimum mean square error approach is derived. The estimator depends on the Kalman estimate of a state vector and its error covariance. Some challenging computational aspects of the optimal nonlinear estimator are solved by usage of the unscented transformation for implementation of the nonlinear estimator. The special quadratic functional of state vector (QFS) is studied in detail. We derive effective matrix formulas for the optimal quadratic estimator and mean square error. The quadratic estimator has a simple closed-form calculation procedure and it is easy to implement in practice. The obtained results we demonstrate on theoretical and practical examples with different types of an nonlinear functionals. Comparison analysis of the optimal and suboptimal estimators is presented. The subsequent application of the proposed optimal nonlinear and quadratic estimators demonstrates their effectiveness.     

A new PI-based optimal linear quadratic state-estimate tracker for discrete-time non-square non-minimum phase systems

A new proportional–integral (PI)-based optimal linear quadratic state-estimate tracker, derived using a proportional–integral–derivative (PID) filter-based frequency-domain shaping approach, is proposed in this paper for discrete-time non-square non-minimum phase multi-input-multi-output systems. Subsequently, a new integrated PID filter-shaped optimal PI state estimator is presented for the aforementioned systems, so that both the proposed state estimator and the state-estimate tracker are able to achieve satisfactory minimum phase-like tracking performance, for the case of arbitrary command inputs with significant variations at some isolated time instants.     

LINEAR OPTIMAL FEEDBACK AND LOAD‐DECOUPLED CONTROL OF A BUCK DC‐DC CONVERTER

This paper describes a new controller design procedure and tuning method for a PWM buck dc‐dc converter. First, linear optimal feedback is designed using the LQR approach. Then the designed control law is implemented using a PID controller incorporated with a load‐decoupled PD compensator. The PID controller is tuned to achieve the optimal design based on the output error voltage directly, instead of using an estimator. When the proposed PD compensator is used, the converter is robust with respect to the input voltage and output current changes and the parameter perturbations. We also provide the conditions for the robust stability assurance of the closed‐loop system.