Minimum Principle for Plurisubharmonic Functions and Related Topics

This is a survey about some recent developments of the minimum principle for plurisub- harmonic functions and related topics.

Minimum Normal Force Principle Based Quantitive Optimization of Clamping Forces for Thin Walled Part

Based on the stability criteria of workpiece-fixture system, quantitative optimization of clamping forces during precise machining process for thin walled part is studied considering the contact condition between wokpiece and locator, the contact mechanical model is achieved, which is further been used to calculate the entire passive forces acting on the statically undetermined workpiece by means of the force screw theory as well as minimum norm force principle. Furthermore, a new methodology to optimize clamping forces is put forward, on the criteria of keeping the stability of workpiece during cutting process. By this way, the intensity of clamping forces is decreased dramatically, which will be most beneficial for improving the machining quality of thin-walled parts. Finally, a case study is used to support and validate the proposed model.

Flexible predictive power-split control for battery-supercapacitor systems of electric vehicles using IVHS

The utilization of traffic information received from intelligent vehicle highway systems(IVHS) to plan velocity and split output power for multi-source vehicles is currently a research hotspot. However, it is an open issue to plan vehicle velocity and distribute output power between different supply units simultaneously due to the strongly coupling characteristic of the velocity planning and the power distribution. To address this issue, a flexible predictive power-split control strategy based on IVHS is proposed for electric vehicles(EVs) equipped with battery-supercapacitor system(BSS). Unlike hierarchical strategies to plan vehicle velocity and distribute output power separately, a monolayer model predictive control(MPC) method is employed to optimize them online at the same time. Firstly, a flexible velocity planning strategy is designed based on the signal phase and time(SPAT) information received from IVHS and then the Pontryagin’s minimum principle(PMP) is adopted to formulate the optimal control problem of the BSS. Then, the flexible velocity planning strategy and the optimal control problem of BSS are embedded into an MPC framework, which is online solved using the shooting method in a fashion of receding horizon. Simulation results verify that the proposed strategy achieves a superior performance compared with the hierarchical strategy in terms of transportation efficiency, battery capacity loss, energy consumption and computation time.

A fast computational method for the landing footprints of space-to-ground vehicles

Fast computation of the landing footprint of a space-to-ground vehicle is a basic requirement for the deployment of parking orbits, as well as for enabling decision makers to develop real-time programs of transfer trajectories. In order to address the usually slow computational time for the determination of the landing footprint of a space-to-ground vehicle under finite thrust, this work proposes a method that uses polynomial equations to describe the boundaries of the landing footprint and uses back propagation(BP) neural networks to quickly determine the landing footprint of the space-to-ground vehicle. First, given orbital parameters and a manoeuvre moment, the solution model of the landing footprint of a space-to-ground vehicle under finite thrust is established. Second, given arbitrary orbital parameters and an arbitrary manoeuvre moment, a fast computational model for the landing footprint of a space-to-ground vehicle based on BP neural networks is provided.Finally, the simulation results demonstrate that under the premise of ensuring accuracy, the proposed method can quickly determine the landing footprint of a space-to-ground vehicle with arbitrary orbital parameters and arbitrary manoeuvre moments. The proposed fast computational method for determining a landing footprint lays a foundation for the parking-orbit configuration and supports the design of real-time transfer trajectories.

Optimal feedback based control for Mars entry trajectory tracking

The various uncertainties of Mars environment have great impact on the process of vehicles entering the atmosphere.To improve the robustness of control system against the model errors and to reduce the computational burden, an optimal feedback based tracking control law is developed. The control scheme presented in this paper determines the amplitude and the reversals of bank angle respectively in the longitudinal and lateral flight plane. At each control cycle, the amplitude of the bank angle is obtained by an optimal feedback controller to minimize tracking errors. The control gains are tuned according to the closed-loop error dynamics by using optimization methods. The bank reversals are executed if the crossrange exceeds a predetermined corridor which is designed by setting a boundary function. The accuracy and robustness of the proposed closed-loop optimal feedback based control law in tracking the reference trajectory is verified via500 deviation simulations, in which modeling errors and external disturbances are considered.

Study of optimal control problems for hybrid dynamical systems

From the viewpoint of continuous systems, optimal control problem is proposed for a class of controlled Hybrid dynamical systems. Then a mathematical method- HDS minimum principle is put forward, which can solve the above problem. The HDS minimum principle is proved by means of Ekeland＇ s variational principle.

Receding horizon H_∞ control for discrete-time Markovian jump linear systems

Receding horizon H∞ control scheme which can deal with both the H∞ disturbance attenuation and mean square stability is proposed for a class of discrete-time Markovian jump linear systems when minimizing a given quadratic performance criteria. First, a control law is established for jump systems based on pontryagin’s minimum principle and it can be constructed through numerical solution of iterative equations. The aim of this control strategy is to obtain an optimal control which can minimize the cost function under the worst disturbance at every sampling time. Due to the difficulty of the assurance of stability, then the above mentioned approach is improved by determining terminal weighting matrix which satisfies cost monotonicity condition. The control move which is calculated by using this type of terminal weighting matrix as boundary condition naturally guarantees the mean square stability of the closed-loop system. A sufficient condition for the existence of the terminal weighting matrix is presented in linear matrix inequality （LMI） form which can be solved efficiently by available software toolbox. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.

SEPARATING COUPLED PHYSIC QUANTITY BYPOTENTIAL OPERATOR

In the present paper, using the method of separating coupled physic quantity bypotential operator, we derive two special minmum principles in coupled thermoelastodynamics.

Optimal Control of Heterogeneous-Susceptible-Exposed-Infectious-Recovered-Susceptible Malware Propagation Model in Heterogeneous Degree-Based Wireless Sensor Networks

Heterogeneous wireless sensor networks(HWSNs)are vulnerable to malware propagation,because of their low configuration and weak defense mechanism.Therefore,an optimality system for HWSNs is developed to suppress malware propagation in this paper.Firstly,a heterogeneous-susceptible-exposed-infectious-recovered-susceptible(HSEIRS)model is proposed to describe the state dynamics of heterogeneous sensor nodes(HSNs)in HWSNs.Secondly,the existence of an optimal control problem with installing antivirus on HSNs to minimize the sum of the cumulative infection probabilities of HWSNs at a low cost based on the HSEIRS model is proved,and then an optimal control strategy for the problem is derived by the optimal control theory.Thirdly,the optimal control strategy based on the HSEIRS model is transformed into corresponding Hamiltonian by the Pontryagin’s minimum principle,and the corresponding optimality system is derived.Finally,the effectiveness of the optimality system is validated by the experimental simulations,and the results show that the infectious HSNs will fall to an extremely low level at a low cost.

ANOMALOUS BEHAVIOR REVISITED:DYNAMIC RESPONSE OF ELASTIC-PLASTIC STRUCTURES

Based on the minimum principle of acceleration in the elastic-plastic continua under finite def ormation, the dynamic response of an elastic-perfectly plastic pin-ended beam subjected to rectangular impulse loading is studied with the help of a numerical approach. The calculated results once again show the anomalous behavior of the beam during its response process, which was previously found in [1]. By carefully analyzing the instantaneous distribution of the bending moment, the membrane force, the curvature and displacement during the response process, it is concluded that the interactive effect between the geometry and materials nonlinearities of the structure is the key reason for leading to the anomalous behavior. This will be helpful for clarifying some misunderstandings in explaining the problem before.

Generalized mixed finite element method for 3D elasticity problems

Without applying any stable element techniques in the mixed methods, two simple generalized mixed element(GME) formulations were derived by combining the minimum potential energy principle and Hellinger–Reissner(H–R) variational principle. The main features of the GME formulations are that the common C0-continuous polynomial shape functions for displacement methods are used to express both displacement and stress variables, and the coefficient matrix of these formulations is not only automatically symmetric but also invertible. Hence, the numerical results of the generalized mixed methods based on the GME formulations are stable. Displacement as well as stress results can be obtained directly from the algebraic system for finite element analysis after introducing stress and displacement boundary conditions simultaneously. Numerical examples show that displacement and stress results retain the same accuracy. The results of the noncompatible generalized mixed method proposed herein are more accurate than those of the standard noncompatible displacement method. The noncompatible generalized mixed element is less sensitive to element geometric distortions.

Is There a Minimum Electrophilicity Principle in Chemical Reactions？

For 25 simple reactions, the changes of the hardness （△η）, polarizability （△α） and electrophilicity index （△ω） and their cube-roots （△η^1/3, △α^1/3, △ω^1/3） were calculated. It is shown that although the Maximum Hardness and Minimum Polarizability Principles are not valid for all reactions, but in most cases △ω^1/3〈0, whereas we always find △ω〈0. Our observation implies to this fact that for those chemical reactions in which the number of moles decreases or at least remains constant, the most stable species （reactants or products） have the lowest sum of electrophilicities. In other words ＂the natural direction of a chemical reaction is toward a state of minimum electrophilicity＂. This fact may be called Minimum Electrophilicity Principle （MEP）.

Motion Equation and Solution of Mushroom Cloud

Using model like hot air bloom with zero-weighted membrane wrapped hot air, surrounded by cold air, this paper sets up a partial differential equation (PDE) of motion of mushroom cloud by modifying Navier-Stokes (N-S) equations. The obtained equation is a vector PDE. It states that the derivative of velocity is with respect to time proportions to the gradient of temperature with respect to trace. Its solution is obtained by the method of separating variables for scalar function. These results have been compared with well agreement with literatures. Highlight: The Principle of Minimum Energy Release (PMER) is used to prove the pulse-mode of explosion of nuclear weapon, as great Earthquake, and optimum path problems.

A NEW HIGH-ORDER MULTI-JOINT FINITE ELEMENTFOR THIN-WALLED BAR

A new high-order multi-joint finite element for thin-walled bar was derived from the Hermite interpolation polynomial and minimum potential energy principle. This element's characteristics are that it is of high accuracy and can be used in finite method analysis of bridge, tall mega-structure building.

HOMOTOPY CONTINUATION ALGORITHM FOR STRUCTURAL DAMAGE IDENTIFICATION

A new method is put forward for structural damage identification based on the homotopy continuation algorithm. A numerical example is presented to verify the method. The beams with different damage locations and different damage extents are identified by this method. The numerical examples have proved that this new method is capable of easy convergence, which is not sensitive to the initial iterative values. It is effective for accurately identifying multiple damages. By incorporating the finite element method into the homotopy continuation algorithm, the damage identifying ability of the new method can be greatly enhanced.

Generalized stress field in granular soils heap with RayleigheRitz method

The stress field in granular soils heap(including piled coal) will have a non-negligible impact on the settlement of the underlying soils. It is usually obtained by measurements and numerical simulations.Because the former method is not reliable as pressure cells instrumented on the interface between piled coal and the underlying soft soil do not work well, results from numerical methods alone are necessary to be doubly checked with one more method before they are extended to more complex cases. The generalized stress field in granular soils heap is analyzed with Rayleighe Ritz method. The problem is divided into two cases: case A without horizontal constraint on the base and case B with horizontal constraint on the base. In both cases, the displacement functions u(x, y) and v(x, y) are assumed to be cubic polynomials with 12 undetermined parameters, which will satisfy the Cauchy’s partial differential equations, generalized Hooke’s law and boundary equations. A function is built with the Rayleighe Ritz method according to the principle of minimum potential energy, and the problem is converted into solving two undetermined parameters through the variation of the function, while the other parameters are expressed in terms of these two parameters. By comparison of results from the Rayleighe Ritz method and numerical simulations, it is demonstrated that the Rayleighe Ritz method is feasible to study the generalized stress field in granular soils heap. Solutions from numerical methods are verified before being extended to more complicated cases.

Time-optimal control of multiple unmanned aerial vehicles with human control input

Purpose–The purpose of this paper is to investigate time-optimal control problems for multiple unmanned aerial vehicle(UAV)systems to achieve predefined flying shape.Design/methodology/approach–Two time-optimal protocols are proposed for the situations with or without human control input,respectively.Then,Pontryagin’s minimum principle approach is applied to deal with the time-optimal control problems for UAV systems,where the cost function,the initial and terminal conditions are given in advance.Moreover,necessary conditions are derived to ensure that the given performance index is optimal.Findings–The effectiveness of the obtained time-optimal control protocols is verified by two contrastive numerical simulation examples.Consequently,the proposed protocolscan successfully achieve the prescribed flying shape.Originality/value–This paper proposes a solution to solve the time-optimal control problems for multiple UAV systems to achieve predefined flying shape.

Basics of estimation

This paper outlines a theory of estimation,where optimality is defined for all sizes of data—not only asymptotically.Also one principle is needed to cover estimation of both real-valued parameters and their number.To achieve this we have to abandon the traditional assumption that the observed data have been generated by a“true”distribution,and that the objective of estimation is to recover this from the data.Instead,the objective in this theory is to fit‘models’as distributions to the data in order to find the regular statistical features.The performance of the fitted models is measured by the probability they assign to the data:a large probability means a good fit and a small probability a bad fit.Equivalently,the negative logarithm of the probability should be minimized,which has the interpretation of code length.There are three equivalent characterizations of optimal estimators,the first defined by estimation capacity,the second to satisfy necessary conditions for optimality for all data,and the third by the complete Minimum Description Length(MDL)principle.