Sheng Zhang

Sheng Zhang, Yan-Qing Chenq, Wei-Qi Qian

Studies regarding the computation of Optimal Control Problems (OCPs) with terminal inequality constraint, under the frame of the Variation Evolving Method (VEM), are carried out. The attributes of equality constraints and inequality constraints in the generalized optimization problem is traversed, and the intrinsic relations to the multipliers are uncovered. Upon these preliminaries, the right Evolution Partial Differential Equation (EPDE) is derived, and the costate-free optimality conditions are established. Besides the analytic expression for the costates in the classic treatment, they also reveal the analytic relations between the states, the controls and the (Lagrange and KKT) multipliers, which adjoin the terminal (equality and inequality) constraints. Moreover, in solving the transformed Initial-value Problems (IVPs) with common Ordinary Differential Equation (ODE) integration methods, the numerical soft barrier is proposed to eliminate the numerical error resulting from the suddenly triggered inequality constraint and it is shown to be effective.

Sheng Zhang, Fei Liao, Kai-Feng He

The Variation Evolving Method (VEM) that originates from the continuous-time dynamics stability theory seeks the optimal solutions with variation evolution principle. After establishing the first and the second evolution equations within its frame, the third evolution equation is developed. This equation only solves the control variables along the variation time to get the optimal solution, and its definite conditions may be arbitrary since the equation can eliminate possible infeasibilities. With this equation, the dimension of the resulting Initial-value Problem (IVP), transformed via the semi-discrete method, is greatly reduced. Therefore it might relieve the computation burden in seeking solutions. Illustrative examples are solved and it is shown that the proposed equation may produce more precise numerical solutions than the second evolution equation, and its computation time may be shorter for the dense discretization.

Sheng Zhang, Fei Liao, Wei-Qi Qian

The first evolution equation is derived under the Variation Evolving Method (VEM) that seeks optimal solutions with the variation evolution principle. To improve the performance, its compact form is developed. By replacing the states and costates variation evolution with that of the controls, the dimension-reduced Evolution Partial Differential Equation (EPDE) only solves the control variables along the variation time to get the optimal solution, and its definite conditions may be arbitrary. With this equation, the scale of the resulting Initial-value Problem (IVP), transformed via the semi-discrete method, is significantly reduced. Illustrative examples are solved and it is shown that the compact form evolution equation outperforms the primary form in the precision, and the efficiency may be higher for the dense discretization. Moreover, in discussing the connections to the classic iteration methods, it is uncovered that the computation scheme of the gradient method is the discrete implementation of the third evolution equation, and the compact form of the first evolution equation is a continuous realization of the Newton type iteration mechanism.

Sheng Zhang, Yang Nan, Yingying Fang et al.

Automatic lung organ segmentation on CT images is crucial for lung disease diagnosis. However, the unlimited voxel values and class imbalance of lung organs can lead to false-negative/positive and leakage issues in advanced methods. Additionally, some slender lung organs are easily lost during the recycled down/up-sample procedure, e.g., bronchioles & arterioles, causing severe discontinuity issue. Inspired by these, this paper introduces an effective lung organ segmentation method called Fuzzy Attention-based Border Rendering (FABR) network. Since fuzzy logic can handle the uncertainty in feature extraction, hence the fusion of deep networks and fuzzy sets should be a viable solution for better performance. Meanwhile, unlike prior top-tier methods that operate on all regular dense points, our FABR depicts lung organ regions as cube-trees, focusing only on recycle-sampled border vulnerable points, rendering the severely discontinuous, false-negative/positive organ regions with a novel Global-Local Cube-tree Fusion (GLCF) module. All experimental results, on four challenging datasets of airway & artery, demonstrate that our method can achieve the favorable performance significantly.