Globally Optimal Distributed Fusion Filter for Descriptor Systems with Time-Correlated Measurement Noises.

This paper concerns the distributed fusion filtering problem for descriptor systems with time-correlated measurement noises. The original descriptor is transformed into two reduced-order subsystems (ROSs) based on singular value decomposition. For the first ROS, a new measurement is obtained using measurement difference technology. Each sensor produces a local filter based on the fusion predictor from the fusion center and its own new measurement and then sends it to the fusion center. In the fusion center, based on local filters, a distributed fusion filter with feedback (DFFWF) in the linear minimum variance (LMV) sense is proposed by applying an innovative approach. The DFFWF for the second ROS is also obtained based on the DFFWF for the first ROS. Then, the DFFWF for the original descriptor is obtained. The proposed DFFWF can achieve the same estimation accuracy as the centralized fusion filter (CFF) under the condition that all local filter gain matrices are of full column rank. Its optimality is strictly proved. Moreover, it has robustness and reliability due to the parallel processing of local filters. Two simulation examples demonstrate the effectiveness of the developed fusion algorithm.

Steady-state sequence optimization with incremental input constraints in two-layer model predictive control.

Steady-state optimization is of vital importance in two-layer model predictive control for bringing better steady-state and dynamic performance. However, the global optimality of steady-state sequences provided by local steady-state optimization cannot be guaranteed. Therefore, a new steady-state sequence optimization approach is proposed in the paper, to improve the global optimality of steady-state sequences. First, the non-global optimality of local steady-state sequences is discussed using an example. Subsequently, aiming at improving the global optimality, a novel sequence optimization strategy designed for steady-state optimization is proposed. Its basic formulation is given and the lower bound of the introduced parameter is analyzed. Then, the relation and difference between the proposed steady-state sequence optimization and the existing global steady-state optimization and local steady-state optimization are discussed. Finally, the steady-state performance, dynamic performance, and computational burden of the proposed approach are studied. The proposed approach provides engineers a brand-new way to realize steady-state optimization and effectively improves the global optimality of calculated steady-state sequences. Extensive simulations verify the effectiveness and reliability of the proposed method.

Global optimal hybrid geometric active contour for automated lung segmentation on CT images.

Lung segmentation on thoracic CT images plays an important role in early detection, diagnosis and 3D visualization of lung cancer. The segmentation accuracy, stability, and efficiency of serial CT scans have a significant impact on the performance of computer-aided detection. This paper proposes a global optimal hybrid geometric active contour model for automated lung segmentation on CT images. Firstly, the combination of global region and edge information leads to high segmentation accuracy in lung regions with weak boundaries or narrow bands. Secondly, due to the global optimality of energy functional, the proposed model is robust to the initial position of level set function and requires fewer iterations. Thus, the stability and efficiency of lung segmentation on serial CT slices can be greatly improved by taking advantage of the information between adjacent slices. In addition, to achieve the whole process of automated segmentation for lung cancer, two assistant algorithms based on prior shape and anatomical knowledge are proposed. The algorithms not only automatically separate the left and right lungs, but also include juxta-pleural tumors into the segmentation result. The proposed method was quantitatively validated on subjects from the publicly available LIDC-IDRI and our own data sets. Exhaustive experimental results demonstrate the superiority and competency of our method, especially compared with the typical edge-based geometric active contour model.

Input and state estimation for linear systems with a rank-deficient direct feedthrough matrix.

The problem of joint input and state estimation for linear stochastic systems with a rank-deficient direct feedthrough matrix is discussed in this paper. Results from previous studies only solve the state estimation problem; globally optimal estimation of the unknown input is not provided. Based on linear minimum-variance unbiased estimation, a five-step recursive filter with global optimality is proposed to estimate both the unknown input and the state. The relationship between the proposed filter and the existing results is addressed. We show that the unbiased input estimation does not require any new information or additional constraints. Both the state and the unknown input can be estimated under the same unbiasedness condition. Global optimalities of both the state estimator and the unknown input estimator are proven in the minimum-variance unbiased sense.

Synchronic interval Gaussian mixed-integer programming for air quality management.

To reveal the synchronism of interval uncertainties, the tradeoff between system optimality and security, the discreteness of facility-expansion options, the uncertainty of pollutant dispersion processes, and the seasonality of wind features in air quality management (AQM) systems, a synchronic interval Gaussian mixed-integer programming (SIGMIP) approach is proposed in this study. A robust interval Gaussian dispersion model is developed for approaching the pollutant dispersion process under interval uncertainties and seasonal variations. The reflection of synchronic effects of interval uncertainties in the programming objective is enabled through introducing interval functions. The proposition of constraint violation degrees helps quantify the tradeoff between system optimality and constraint violation under interval uncertainties. The overall optimality of system profits of an SIGMIP model is achieved based on the definition of an integrally optimal solution. Integer variables in the SIGMIP model are resolved by the existing cutting-plane method. Combining these efforts leads to an effective algorithm for the SIGMIP model. An application to an AQM problem in a region in Shandong Province, China, reveals that the proposed SIGMIP model can facilitate identifying the desired scheme for AQM. The enhancement of the robustness of optimization exercises may be helpful for increasing the reliability of suggested schemes for AQM under these complexities. The interrelated tradeoffs among control measures, emission sources, flow processes, receptors, influencing factors, and economic and environmental goals are effectively balanced. Interests of many stakeholders are reasonably coordinated. The harmony between economic development and air quality control is enabled. Results also indicate that the constraint violation degree is effective at reflecting the compromise relationship between constraint-violation risks and system optimality under interval uncertainties. This can help decision makers mitigate potential risks, e.g. insufficiency of pollutant treatment capabilities, exceedance of air quality standards, deficiency of pollution control fund, or imbalance of economic or environmental stress, in the process of guiding AQM.

Optimal Exact Least Squares Rank Minimization.

In multivariate analysis, rank minimization emerges when a low-rank structure of matrices is desired as well as a small estimation error. Rank minimization is nonconvex and generally NP-hard, imposing one major challenge. In this paper, we consider a nonconvex least squares formulation, which seeks to minimize the least squares loss function with the rank constraint. Computationally, we develop efficient algorithms to compute a global solution as well as an entire regularization solution path. Theoretically, we show that our method reconstructs the oracle estimator exactly from noisy data. As a result, it recovers the true rank optimally against any method and leads to sharper parameter estimation over its counterpart. Finally, the utility of the proposed method is demonstrated by simulations and image reconstruction from noisy background.