A Comparison Between Robust Control Design LMIs for Grid-Connected Converters

This paper is focused on a comparison between two linear matrix inequality conditions for design of robust state feedback controllers applied for current regulation of gridconnected converters with LCL filters, operating under uncertain grid impedance at the point of common coupling. The first condition is the well known quadratic stability and the second one is the polyquadratic stability, which uses extra matrix variables. It is shown that the condition with slack variables can provide superior performance in terms of ensuring stable and suitable operation for a larger set of uncertainties.

Support vector machines for oil classification link with polyaromatic hydrocarbon contamination in the environment

The main focus of this study is exploring the spatial distribution of polyaromatics hydrocarbon links between oil spills in the environment via Support Vector Machines based on Kernel-Radial Basis Function (RBF) approach for high precision classification of oil spill type from its sample fingerprinting in Peninsular Malaysia. The results show the highest concentrations of Σ Alkylated PAHs and Σ EPA PAHs in ΣTAH concentration in diesel from the oil samples PP3_liquid and GP6_Jetty achieving 100% classification output, corresponding to coherent decision boundary and projective subspace estimation. The high dimensional nature of this approach has led to the existence of a perfect separability of the oil type classification from four clustered oil type components; i.e diesel, bunker C, Mixture Oil (MO), lube oil and Waste Oil (WO) with the slack variables of ξ ≠ 0. Of the four clusters, only the SVs of two are correctly predicted, namely diesel and MO. The kernel-RBF approach provides efficient and reliable oil sample classification, enabling the oil classification to be optimally performed within a relatively short period of execution and a faster dataset classification where the slack variables ξ are non-zero.

A stabilizing gradient-based economic MPC for unstable processes: toward the enlargement of the domain of attraction

This work proposes a stabilizing gradient-based economic MPC with enlargement of the domain of attraction, based on the novel combination of three ingredients: terminal equality constraints solely on open-loop non-stable states, an admissible articial steady-state, and a terminal cost. A further enlargement of the domain of attraction is achieved by including slack variables to soften the bound constraints of states, without affecting the stabilizing propertiesor capacity to drive the closed-loop system toward the economic target. Finally, a case study based on an unstable reactor is used to demonstrate the properties of the proposed strategy.

DEA Analysis of Municipal Hospital Services and Scale After Hierarchical Medical Treatment Policy Was Implemented in China

Background: We aimed to provide decision basis for optimizing resource allocation by hospital administrators in China.Methods: The samples were 18 municipal TCM hospitals of all public TCM hospitals of Gansu province in 2017. The BCC DEA model was employed to evaluate the relative efficiency of hospital operation. The slack variables in non DEA effective hospitals were employed to give the guidance how to achieve to the DEA effective.Results: Firstly, the demands for medical services kept surging will lead to the scale return of most municipal-level TCM hospitals tend to the stable although part of it appear the decline or increase in return scale. Therefore, these municipal-level TCM hospitals should further pay attention to make full use of existing resources. Secondly, some municipal-level TCM hospitals with decline in return scale or increase in return scale should adopt different management measures for different situations, which in details in results and discussions sections.Conclusion: After the implementation of healthcare policy such as graded diagnosis and treatment, hospital managers should learn advanced management concepts, use scientific management tools and software, carry out closed-loop management, make constant adjustments according to evaluation indicators, reduce management costs, and ensure the vitality of hospital operation.

Constructive generalization of classical sufficient second-order optimality conditions

In this paper, we consider new sufficient conditions of optimality of the second-order for equality constrained optimization problems, which essentially enhance and complement the classical ones and are constructive. For example, they establish equivalence between sufficient conditions in the equality constrained optimization problems and sufficient conditions for optimality in equality constrained problems by reducing the latter to equalities with the help of introducing slack variables. Previously, when using the classical sufficient optimality conditions, this fact was not considered to be true, that is, the existing classical sufficient conditions were not complete, so the proposed optimality conditions complement the classical ones and close the question of the equivalence of the problems with inequalities and the problems with equalities when reducing the first to the second by introducing slack variables.

Robustra: Training Provable Robust Neural Networks over Reference Adversarial Space

Machine learning techniques, especially deep neural networks (DNNs), have been widely adopted in various applications. However, DNNs are recently found to be vulnerable against adversarial examples, i.e., maliciously perturbed inputs that can mislead the models to make arbitrary prediction errors. Empirical defenses have been studied, but many of them can be adaptively attacked again. Provable defenses provide provable error bound of DNNs, while such bound so far is far from satisfaction. To address this issue, in this paper, we present our approach named Robustra for effectively improving the provable error bound of DNNs. We leverage the adversarial space of a reference model as the feasible region to solve the min-max game between the attackers and defenders. We solve its dual problem by linearly approximating the attackers' best strategy and utilizing the monotonicity of the slack variables introduced by the reference model. The evaluation results show that our approach can provide significantly better provable adversarial error bounds on MNIST and CIFAR10 datasets, compared to the state-of-the-art results. In particular, bounded by L^infty, with epsilon = 0.1, on MNIST we reduce the error bound from 2.74% to 2.09%; with epsilon = 0.3, we reduce the error bound from 24.19% to 16.91%.

Suboptimal trajectory programming for unmanned aerial vehicles with dynamic obstacle avoidance

With regard to the dynamic obstacles current unmanned aerial vehicles encountered in practical applications, an integral suboptimal trajectory programming method was proposed. It tackled with multiple constraints simultaneously while guiding the unmanned aerial vehicle to execute autonomous avoidance maneuver. The kinetics of both unmanned aerial vehicle and dynamic obstacles were established with appropriate hypotheses. Then it was assumed that the unmanned aerial vehicle was faced with terminal constraints and control constraints in the whole duration. Meanwhile, the performance index was established as minimum control efforts. The initial trajectory was generated according to optimized model predictive static programming. Next, the slack variables were introduced to transform the inequality constraints arising from dynamic obstacle avoidance into equality constraints. In addition, sliding mode control theory was utilized to determine these slack variables' dynamics by designing the approaching law of sliding mode. Then the avoidance trajectory for single or multiple dynamic obstacles was developed by this combined method. At last, a further trajectory optimization was conducted by differential dynamic programming. Consequently, the integral problem was solved step by step and numerical simulations demonstrated that the integral method possessed high computational efficiency.

Toward a More Complete, Flexible, and Safer Speed Planning for Autonomous Driving via Convex Optimization

In this paper, we present a complete, flexible and safe convex-optimization-based method to solve speed planning problems over a fixed path for autonomous driving in both static and dynamic environments. Our contributions are five fold. First, we summarize the most common constraints raised in various autonomous driving scenarios as the requirements for speed planner developments and metrics to measure the capacity of existing speed planners roughly for autonomous driving. Second, we introduce a more general, flexible and complete speed planning mathematical model including all the summarized constraints compared to the state-of-the-art speed planners, which addresses limitations of existing methods and is able to provide smooth, safety-guaranteed, dynamic-feasible, and time-efficient speed profiles. Third, we emphasize comfort while guaranteeing fundamental motion safety without sacrificing the mobility of cars by treating the comfort box constraint as a semi-hard constraint in optimization via slack variables and penalty functions, which distinguishes our method from existing ones. Fourth, we demonstrate that our problem preserves convexity with the added constraints, thus global optimality of solutions is guaranteed. Fifth, we showcase how our formulation can be used in various autonomous driving scenarios by providing several challenging case studies in both static and dynamic environments. A range of numerical experiments and challenging realistic speed planning case studies have depicted that the proposed method outperforms existing speed planners for autonomous driving in terms of constraint type covered, optimality, safety, mobility and flexibility.