Robust performance analysis for systems with structured uncertainty

This paper analyses robust performance measures for linear time-invariant systems with norm-bounded time-varying structured uncertainty. We consider two robust performance measures. One is the worst-case peak value of the error signal in response to the disturbance with a known energy. The other is the worst-case energy of the error signal in response to impulsive disturbance. In both cases, the ‘worst case’ is taken over all admissible uncertainties and disturbances. The notion of robust stability is Q-stability, or the scaled H_∞ norm bound. Our main results provide an upper bound for each of the robust performance measures in terms of a positive definite matrix which satisfies a linear matrix inequality (LMI) together with a scaling matrix. Hence, the best bound in this LMI formulation can be computed by convex programming.     

Bayesian approach to neural-network modeling with input uncertainty

It is generally assumed when using Bayesian inference methods for neural networks that the input data contains no noise or corruption. For real-world (errors in variable) problems this is clearly an unsafe assumption. This paper presents a Bayesian neural-network framework which allows for input noise provided that some model of the noise process exists. In the limit where the noise process is small and symmetric it is shown, using the Laplace approximation, that this method gives an additional term to the usual Bayesian error bar which depends on the variance of the input noise process. Further, by treating the true (noiseless) input as a hidden variable and sampling this jointly with the network weights using a Markov chain Monte Carlo method, it is demonstrated that it is possible to infer the regression over the noiseless input.     

On controllability of diagonal systems with one-dimensional input space

This paper deals with diagonal systems on a Hilbert state space with a one-dimensional input space and a (possibly unbounded) control operator. A priori it is not assumed that the input operator is admissible. Necessary and sufficient conditions for different notions of controllability such as null-controllability, exact controllability and approximate controllability are presented. These conditions, which are given in terms of the eigenvalues of the diagonal operator and in terms of the control operator, are linked with the theory of interpolation in Hardy spaces.     

Analysis of H2 performance robustness with respect todisturbance model uncertainty

A method for evaluating the H₂ performance robustness of an LTI SISO feedback system with respect to parametric uncertainties in the disturbance model is developed. The disturbance is assumed to be colored noise obtained by passing standard white noise through a linear finite-dimensional filter with uncertain coefficients. The method is based on the converse of a spectral factorization problem. The main result obtained is an explicit formula for the output variance in terms of the uncertain parameters of the coloring filter. This result is illustrated on a ship roll stabilization problem     

Robust PI controller design with respect to fuzzy sensitivity margins

The paper deals with PI controller design for linear systems with parametric uncertainty with respect to sensitivity margin. The plant is considered as possibility distribution on a plant space and the closed loop specifications are given in terms of the peak of sensitivity function described by fuzzy numbers. The controller design is understood as the inclusion of respective α-cuts. Such consideration makes it possible to degrade the closed loop specifications towards the uncertainty that occurs very rarely. The proposed procedure is applied on the speed control of a hydraulic turbine – a non-minimum phase system.     

Multiple kernel k-means clustering with block diagonal property

Pattern Analysis and Applications - Multiple kernel k-means clustering (MKKC) is proposed to efficiently incorporate multiple base kernels to generate an optimal kernel. However, many existing MKKC...     

Robust performance analysis with LMI-based methods for realparametric uncertainty via parameter-dependent Lyapunov functions

Robust performance analysis for linear time-invariant systems with linear fractional transformation real parametric uncertainty is considered. New conditions of robust stability/performance based on parameter-dependent Lyapunov functions are proposed. The robust stability/performance measures are: robust pole location, robust H_∞ performance and robust H₂ performance. Linear matrix inequality (LMI)-based sufficient conditions for the existence of parameter-dependent Lyapunov functions are derived by using the quadratic separation concept. The performances of the proposed conditions are compared with existing tests     

Robust controller synthesis for systems with input nonlinearities: a trade-off between gain variation and parametric uncertainty

A feedback control-system design problem involving input nonlinearities and structured plant parameter uncertainities is considered. Multivariable absolute stability theory is merged with the guaranteed cost control approach to robust stability and performance to obtain a theory of full- and reduced-order robust control design that accounts for input time-varying sector bounded nonlinearities. The principal result is a sufficient condition for characterizing dynamic controllers of a fixed dimension which are guaranteed to provide robust stability for plant parametric variations and absolute stabilization for input nonlinearities. The proposed framework provides a systematic design trade-off between classical robustness guarantees (i.e., gain and phase margins) versus parametric robustness. Furthermore, the framework is directly applicable to uncertain systems with saturating controls and provides fixed-order dynamic output feedback controllers with guaranteed domains of attraction. © 1998 John Wiley & Sons, Ltd.     

输出反馈实现一类带不确定输入动态非线性系统的鲁棒几乎干扰解耦

研究一类带不确定输入动态非线性系统的输出反馈干扰抑制问题并基于观测器给出了输出反馈控制器 构造性的设计方法.所设计的控制器具有对可允许不确定动态的鲁棒性.不仅在L₂增益意义上抑制了干扰对输出 的影响,同时在ISS镇定意义上抑制了干扰对状态的影响.     

Robust stability with time-varying structured uncertainty

Considers the problem of assessing robust stability in the presence of block-diagonally structured time-varying dynamic uncertainty. It is shown that robust stability holds only if there exist constant scalings which lead to a small gain condition. The notion of stability here is finite-gain stability over finite-energy signals. In sharp contrast to the case of time-invariant dynamic uncertainty, this result is not limited by the number uncertainty blocks. These results parallel previous results regarding finite-gain stability over persistent bounded signals     

Robust control with respect to coprime factors ofinfinite-dimensional positive real systems

It is shown that infinite-dimensional positive real systems can be robustly stabilized with respect to coprime factor perturbations with a robustness margin of at least 1/√2. This result is applied to dissipative colocated systems which arise in PDE models of flexible structures     

融合块对角约束的鲁棒低秩多核聚类

针对现有的多核学习(multiple kernel learning, MKL)子空间聚类方法忽略噪声和特征空间中数据的低秩结构问题,提出一种新的鲁棒多核子空间聚类方法(low-rank robust multiple kernel clustering, LRMKC),该方法结合块对角表示(block diagonal representation, BDR)与低秩共识核(low-rank consensus kernel, LRCK)学习,可以更好地挖掘数据的潜在结构.为了学习最优共识核,设计一种基于混合相关熵度量(mixture correntropy induced metric,MCIM)的自动加权策略,其不仅为每个核设置最优权重,而且通过抑制噪声提高模型的鲁棒性;为了探索特征空间数据的低秩结构,提出一种非凸低秩共识核学习方法;考虑到亲和度矩阵的块对角性质,对系数矩阵应用块对角约束. LRMKC将MKL、LRCK与BDR巧妙融合,以迭代提高各种方法的效率,最终形成一个处理非线性结构数据的全局优化方法.与最先进的MKL子空间聚类方法相比,通过在图像和文本数据集上的大量实验验证了...     

Robust robot control with bounded input torques

A new scheme is presented to achieve effective on-line tracking control of robot manipulators in the presence of model uncertainty and torque limitations. Pointwise optimization techniques are incorporated into a “slow” feedback loop in order to generate feasible desired trajectories, optimally close to the original desired trajectories. A suction controller is used in the “fast” main feedback loop, allowing to combine robust tracking with simple controller design. Simulations show very significant performance improvement over standard techniques. The algorithm is computationally cheap and can easily be implemented on-line.     

Transfer matrix approach to the structural block diagonal decoupling problem

The block diagonal decoupling problem for structured systems is treated using the transfer matrix approach. An associated graph, which displays the internal structure of the system (invariant and interconnection), is used to establish necessary and sufficient conditions for the solution of the problem. These conditions are expressed in the graph in terms of shortest input-output paths, which are related to the infinite structure of the system.     

Robust diagonal stabilization: an LMI approach

Addresses the problem of robust diagonal stabilization for discrete-time systems. Linear matrix inequality (LMI) conditions are derived for the search of a diagonal solution to the associated Lyapunov equation. This approach can be applied to guarantee stability of quantized systems and to find numerous illustrative applications, e.g., for the design of robust digital filters     

Robust Wiener filtering with non-parametric spectral uncertainty

In this article, robust least-squares filtering problems are considered for non-parametric multivariate spectral uncertainty defined by the so-called spectral band and generalised-moment constraints. Its major aim is to provide a basis for computing approximate solutions to worst-case, Wiener-filtering optimisation problems involving causal filters and multivariate signals. It hinges upon associating upper and lower bounds on the minimum worst-case performance achievable with causal filters with linear-cost/linear matrix inequality (LC/LMI)-constraint optimisation problems. On the basis of a Lagrangean duality formulation for the worst-case, least-squares performance of a given filter, upper bounds on it are obtained as the optimal values of LC/LMI problems. Then, for linearly parameterised classes of filter transfer functions, a causal filter which optimises such an upper bound on worst-case performance can also be obtained from an LC/LMI optimisation problem. To estimate the amount of conservatism incurred when relying on such upper bounds, optimal, nominal, least-squares performance for a given pair of power spectral densities (for the information and noise signal) is maximised over finite-dimensional, linearly parameterised classes of the latter. Again, such problems are shown to be equivalent to LC/LMI problems and the corresponding optimal values are lower bounds on the minimum worst-case, least-squares error achievable in the original robust filtering problem (say, μ_*). Finally, two simple numerical examples are presented to illustrate how causal filters can be obtained whose worst-case, least-squares performance is quite close to the optimal one (i.e. μ_*).     

联合松弛块对角表示矩阵回归的遮挡人脸识别

基于核范数矩阵回归的方法能够有效解决人脸识别中连续遮挡的问题,然而该类方法仅关注误差图像的低秩结构信息,忽略了样本图像表示的相关性。为了有效解决自然场景下的遮挡人脸识别问题,考虑到这一特点,提出一种联合松弛块对角表示的矩阵回归模型（RBDMR）学习图像的松弛块对角表示,并通过动态优化表示矩阵的块对角分量加强类内表示的相关性和类间表示的差异性。此外,通过联合优化训练样本和测试样本的表示持续提高类内表示的一致性。通过在三个不同的数据集进行验证,实验结果表明,该方法优于其他对比算法,在真实遮挡和光照变化的情况下有较好的性能。     

Robust design optimization with design-dependent random input variables

Structural and Multidisciplinary Optimization - This paper addresses the dependency of design parameters and random variables within robust design optimization. If the stochastic distributions of...     

Latent block diagonal representation for subspace clustering

Pattern Analysis and Applications - Spectral-type subspace clustering algorithms have attracted wide attention because of their excellent performance displayed in a great deal of applications in...     

Quantitative non‐diagonal controller design for multivariable systems with uncertainty

The loop coupling reduction of multivariable systems under the presence of plant uncertainty is currently a most discussed topic. Following the ideas suggested by Horowitz, in this paper the role played by the non‐diagonal controller elements is analysed in order to state a design methodology. Thus, the definition of a coupling matrix and a quality function of the non‐diagonal elements come into use to quantify the amount of loop interaction and to design the controllers, respectively. This yields a criterion that makes possible to propose a sequential design methodology of the fully populated matrix controller, in the quantitative feedback theory (QFT) robust control frame. Finally, a real example with the heat exchanger of a pasteurization plant is included to show the practical use of this technique. Copyright © 2002 John Wiley & Sons, Ltd.