A nonsmooth Newton’s method for control-state constrained optimal control problems

We investigate optimal control problems subject to mixed control-state constraints. The necessary conditions are stated in terms of a local minimum principle. By use of the Fischer–Burmeister function the minimum principle is transformed into an equivalent nonlinear and nonsmooth equation in appropriate Banach spaces. This nonlinear and nonsmooth equation is solved by a nonsmooth Newton’s method. We will show the local quadratic convergence under certain regularity conditions and suggest a globalization strategy based on the minimization of the squared residual norm. A numerical example for the Rayleigh problem concludes the article.     

基于多速率内插和最小二乘法的精确同步方法

最小二乘法可以利用PN序列相关曲线的对称性实现对接收端接收到的PN序列的相位精确测量。然而实际应用中无线信道带宽有限,接收端还原出来的PN序列只能在极性上和原来的方波形式保持一致,这样导致了相关曲线的变形,因而限制了最小二乘法的实际测量精度。为了进一步改善最小二乘法的测量精度,引入了多速率处理的方法,在不提高前端AD采样频率的基础上,通过增加鉴相曲线零点附近的鉴相点个数,使所用于拟合直线的点更靠近零点,从而提高系统测量精度。仿真结果表明,经过两倍内插后的方法相比内插前在测量性能上有三倍左右的提高。因此经过多速率处理改进后的方法可以显著提高系统对PN相位的测量性能。     

An adaptive edge-based smoothed point interpolation method for mechanics problems

This paper develops a smoothing domain-based energy (SDE) error indicator and an efficient adaptive procedure using edge-based smoothed point interpolation methods (ES-PIM), in which the strain field is constructed via the generalized smoothing operation over smoothing domains associated with edges of three-node triangular background cells. Because the ES-PIM can produce a close-to-exact stiffness and achieve ‘super-convergence’ and ‘ultra-accurate’ solutions, it is an ideal candidate for adaptive analysis. A SDE error indicator is first devised to make use of the features of the ES-PIM. A local refinement technique based on the Delaunay algorithm is then implemented to achieve high efficiency. The refinement of nodal neighbourhood is accomplished simply by adjusting a scaling factor assigned to control local nodal density. Intensive numerical studies, including the problems with stress concentration and solution singularity, demonstrate that the proposed adaptive procedure is effective and efficient in producing solutions with desired accuracy.     

An optimal control method for applications using wireless sensor/actuator networks

The wireless sensor/actuator networks (WSANs) can be used for spatially distributed control systems. With smart sensors and actuators, the WSANs are able to not only sense the control system states and report measurements, but also perform control and actuation. This paper investigates WSANs on their ability of control. A centralized controller is introduced into WSANs to make up closed-loop control systems, in which control decisions are made based on global network-wide information. A model of the control and communication over WSANs is made theoretically, based on which we achieved an optimal control method. It is demonstrated by simulations that the control method proposed could stabilize the control system quickly.     

气体流速流向传感器及其温度补偿的研究

设计了一种内燃机用气体流速、流向传感器,阐述了传感器的工作原理;介绍了应用单片机对传感器输出信号进行线性化和温度补偿处理的方法。试验结果表明:该传感器在-20~100℃温度范围内,温度稳定性高,零点温度漂移为4.0×10-3%FS/℃,准确度可达到±1.0%FS,性能指标达到了设计要求。     

Hybrid method for a general optimal sensor scheduling problem in discrete time

In this paper, we consider a general class of optimal sensor scheduling problems in discrete time. There are N₁ sensors available for acquiring data so as to estimate the needed but unknown signal. Only N₂ out of the N₁ sensors can be turned on at any moment, while different weights can be assigned to different sensors. This problem is formulated as a discrete time deterministic optimal control problem involving both discrete and continuous valued controls. A computational method is developed for solving this discrete time deterministic optimal control problem based on a branch and bound method in conjunction with a gradient-based method. The branch and bound method is used to determine the optimal schedule of sensors, where a sequence of lower bound dynamic systems is introduced so as to provide effective lower bounds for the construction of the branching rules. Each of the branches is an optimal weight vector assignment problem and a gradient-based method is developed for solving this optimal control problem. For illustration, two numerical examples are solved.     

An element-free smoothed radial point interpolation method (EFS-RPIM) for 2D and 3D solid mechanics problems

This paper presents a novel element-free smoothed radial point interpolation method (EFS-RPIM) for solving 2D and 3D solid mechanics problems. The idea of the present technique is that field nodes and smoothing cells (SCs) used for smoothing operations are created independently and without using a background grid, which saves tedious mesh generation efforts and makes the pre-process more flexible. In the formulation, we use the generalized smoothed Galerkin (GS-Galerkin) weak-form that requires only discrete values of shape functions that can be created using the RPIM. By varying the amount of nodes and SCs as well as their ratio, the accuracy can be improved and upper bound or lower bound solutions can be obtained by design. The SCs can be of regular or irregular polygons. In this work we tested triangular, quadrangle, $n$-sided polygon and tetrahedron as examples. Stability condition is examined and some criteria are found to avoid the presence of spurious zero-energy modes. This paper is the first time to create GS-Galerkin weak-form models without using a background mesh that tied with nodes, and hence the EFS-RPIM is a true meshfree approach. The proposed EFS-RPIM is so far the only technique that can offer both upper and lower bound solutions. Numerical results show that the EFS-RPIM gives accurate results and desirable convergence rate when comparing with the standard finite element method (FEM) and the cell-based smoothed FEM (CS-FEM).     

An adaptive wavelet collocation method for solving optimal control of elliptic variational inequalities of the obstacle type

This paper presents a fast computational technique based on the wavelet collocation method for the numerical solution of an optimal control problem governed by elliptic variational inequalities of obstacle type. In this problem, the solution divides the domain into contact and noncontact sets. The boundary between the contact and noncontact sets is a free boundary, which is not known a priori and the solution is not smooth on it. Accordingly, a very fine grid is needed in order to obtain a solution with a reasonable accuracy. In this paper, our aim is to propose an adaptive scheme in order to generate an appropriate and economic irregular dyadic mesh for finding the optimal control and state functions. The irregular mesh will be generated such that its density around the free boundary is higher than in other places and high-resolution computations are focused on these zones. To this aim, we use an adaptive wavelet collocation method and take advantage of the fast wavelet transform of compact-supported interpolating wavelets to develop a multi-level algorithm, which generates an adaptive computational grid. Using this adaptive grid takes less CPU time than using a full regular mesh. At each step of the algorithm, the active set method is used for solving the optimality system of the obstacle problem on the adapted mesh. Finally, the numerical examples are presented to show the validity and efficiency of the technique.     

An optimal hierarchical control scheme for smart generation units: An application to combined steam and electricity generation

Optimal management of thermal and energy grids with fluctuating demand and prices requires to orchestrate the generation units (GU) among all their operating modes. A hierarchical approach is proposed to control coupled energy nonlinear systems. The high level hybrid optimization defines the unit commitment, with the optimal transition strategy, and best production profiles. The low level dynamic model predictive control (MPC), receiving the set-points from the upper layer, safely governs the systems considering process constraints. To enhance the overall efficiency of the system, a method to optimal start-up the GU is here presented: a linear parameter-varying MPC computes the optimal trajectory in closed-loop by iteratively linearizing the system along the previous optimal solution. The introduction of an intermediate equilibrium state as additional decision variable permits the reduction of the optimization horizon, while a terminal cost term steers the system to the target set-point. Simulation results show the effectiveness of the proposed approach.     

An integrated state space partition and optimal control method of multi-model for nonlinear systems based on hybrid systems

Multilinear model approach turns out to be an ideal candidate for dealing with nonlinear systems control problem. However, how to identify the optimal active state subspace of each linear subsystem is an open problem due to that the closed-loop performance of nonlinear systems interacts with these subspaces ranges. In this paper, a new systematic method of integrated state space partition and optimal control of multi-model for nonlinear systems based on hybrid systems is initially proposed, which can deal with the state space partition and associated optimal control simultaneously and guarantee an overall performance of nonlinear systems consequently. The proposed method is based on the framework of hybrid systems which synthesizes the multilinear model, produced by nonlinear systems, in a unified criterion and poses a two-level structure. At the upper level, the active state subspace of each linear subsystem is determined under the optimal control index of a hybrid system over infinite horizon, which is executed off-line. At the low level, the optimal control is implemented online via solving the optimal control of hybrid system over finite horizon. The finite horizon optimal control problem is numerically computed by simultaneous method for speeding up computation. Meanwhile, the model mismatch produced by simultaneous method is avoided by using the strategy of receding-horizon. Simulations on CSTR (Continuous Stirred Tank Reactor) confirm that a superior performance can be obtained by using the presented method.     

An optimal approach to multiple tool selection and their numerical control path generation for aggressive rough machining of pockets with free-form boundaries

To machine pockets, especially ones with closed free-form boundary curves, roughing is crucial to part productivity, for this operation alone could take more than 60% of the total machining time. At present, there is a high demand from industry for a new machining technique that can efficiently cut pockets. Aggressive rough machining, in which the largest possible cutters are always employed and are fully immersed in workpieces, can be a solution. Although aggressive roughing is by far the most efficient machining strategy, compared to prior pocketing methods, no computer numerical control (CNC) programming technique has been developed to support it, resulting in few applications in machine shops. To address this urgent industrial need, based on the medial axis transform of a pocket, this work proposes an optimal approach to multiple tool selection and their numerical control (NC) path generation for aggressive roughing of the pocket. First, the NC paths of a specific tool are quickly generated using the pocket’s medial axis transform. Thanks to the unique characteristic of the medial axis transform, the paths can ensure the tool the largest accessible space for pocketing. At the same time, they can guarantee the tool to be free of gouging and interference. Then, an optimization model of selecting multiple cutters and generating their NC paths is built in order to achieve the highest efficiency of the aggressive rough machining. To demonstrate the advantages of this innovative approach, two examples are rendered, and their results are compared to those obtained by the existing methods. This approach can be directly implemented into current CAD/CAM software to promote aggressive rough machining of pockets in industry.     

An integrated probabilistic linguistic projection method for MCGDM based on ELECTRE III and the weighted convex median voting rule

In the multi-criteria group decision-making (MCGDM) problems with great uncertainty, making full use of participants' evaluation information could help improve the accuracy and reliability of decision results. Probabilistic linguistic term set (PLTS) is an effective tool to represent qualitative data and can fully express the hesitation and preference of decision makers. Therefore, this paper aims to propose an MCGDM method based on PLTSs. In the proposed method, the projection of PLTSs is explored to measure the distance and angle differences between two objects, and Bayesian best–worst method (Bayesian BWM) is used to determine the aggregated final weights of criteria. Besides, the elimination and choice translating reality III (ELECTRE III) method combined with distillation algorithm deals with the projection of PLTSs to obtain the alternatives' ranking of each decision maker. Then, the weighted convex median voting rule is developed to integrate the rankings results regarding all decision makers, which can solve the conflict of ranking results among experts and ensure that the comprehensive ranking results are reasonable and practical. Finally, a case study of health-care waste management is designed and comparative analyses are implemented to show the effectiveness and advantages of the proposed method.     

An extended FMEA approach based on the Z-MOORA and fuzzy BWM for prioritization of failures

Identification and prioritization of failure modes in a system and planning for corrective actions are among the most important components of risk management in any organization. Meanwhile, conventional Failure Mode and Effects Analysis (FMEA) is one of the most commonly used methods for prioritization of the failures. Despite the widespread applications of this method in various industries, FMEA is associated with some shortcomings that can lead to unrealistic results. In this study, a proposed approach is presented in three phases to cover some of the shortcomings of the FMEA technique. In the first phase, FMEA is used to identify the failure modes and assign values to the Risk Priority Number (RPN) determinant factors. In the second phase, the Fuzzy Best-Worst Method (FBWM) based on the experts’ opinions is used to measure the weights of these factors. In the third phase, the outputs of the previous phases are used as a basis to prioritize the failures using the proposed Multi-Objective Optimization by Ratio Analysis based on the Z-number theory (Z-MOORA). In addition to assigning different weights to the RPN determinant factors and considering uncertainties of them, the Z-number theory is used in this approach to cover reliability in different failure modes. The proposed approach was implemented in the automotive spare parts industry, and the results indicate a full prioritization of the failures in comparison with other conventional methods such as FMEA and fuzzy MOORA.