VARIATIONAL METHOD AND COMPUTATION FOR H_∞ CONTROL

ＩｎｔｒｏｄｕｃｔｉｏｎＨ∞ｃｏｎｔｒｏｌｔｈｅｏｒｙｈａｓｂｅｅｎｗｅｌｌｄｅｖｅｌｏｐｅｄｓｉｎｃｅｔｈｅＤＧＫＦｐａｐｅｒ[1],ｗｈｅｒｅｔｈｅｆｕｎｄａｍｅｎｔａｌｅｑｕａｔｉｏｎｓｆｏｒＨ∞ ｍｅａｓｕｒｅｍｅｎｔｆｅｅｄｂａｃｋｃｏｎｔｒｏｌａｒｅｄｅｒｉｖｅｄｆｒｏｍｔｈｅｓｅｐａｒａｔｉｏｎｐｒｉｎｃｉｐｌｅ ,ａｓｉｎＬＱＧｃｏｎｔｒｏｌｔｈｅｏｒｙ[2～ 5 ].Ｈｏｗｅｖｅｒ,ｔｈｅｃｏｍｐｕｔａｔｉｏｎｆｏｒｆｉｎｉｔｅｈｏｒｉｚｏｎ [0 ,ｔｆ]ｐｒｏｂｌｅｍａｎｄｔｈｅｄｅｔｅｒｍｉ…     

Generalized passivity-based chaos synchronization

In this paper, a new passivity-based synchronization method for a general class of chaotic systems is proposed. Based on the Lyapunov theory and the linear matrix inequality （LMI） approach, the passivity-based controller is presented to make the synchronization error system not only passive but also asymptotically stable. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. Simulation studies for the Genesio-Tesi chaotic system and the Qi chaotic system are presented to demonstrate the effectiveness of the proposed scheme.     

Sensitivity analysis of composite laminated plates with bonding imperfection in Hamilton system

Sensitivity analysis of composite laminated plates with bonding imperfection is carried out based on the radial point interpolation method （RPIM） in a Hamilton system. A set of hybrid governing equations of response and sensitivity quantities is reduced using the spring-layer model and the modified Hellinger-Reissner （H-R） variational principle. The analytical method （AM）, the semi-analytical method （SAM）, and the finite difference method （FDM） are used for sensitivity analysis based on the reduced set of hybrid governing equations. A major advantage of the hybrid governing equations is that the convolution algorithm is avoided in sensitivity analysis. In addition, sensitivity analysis using this set of hybrid governing equations can obtain response values and sensitivity coefficients simultaneously, and accounts for bonding imperfection of composite laminated plates.     

Semi-inverse method and generalized variational principles with multi-variables in elasticity

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ 1 954,Ｈｕ[1,2 ]ｄｅｄｕｃｅｄＨｕ＿Ｗａｓｈｉｚｕｐｒｉｎｃｉｐｌｅｂｙｓｏ＿ｃａｌｌｅｄｔｒｉａｌ＿ａｎｄ＿ｅｒｒｏｒｍｅｔｈｏｄ ,ａｎｄｉｎ1 964 ,Ｃｈｉｅｎ[3]ｓｙｓｔｅｍａｔｉｃａｌｌｙｄｉｓｃｕｓｓｅｄｔｈｅＬａｇｒａｎｇｅｍｕｌｔｉｐｌｉｅｒｍｅｔｈｏｄ ,ｂｙｗｈｉｃｈｈｅｓｕｃｃｅｓｓｆｕｌｌｙｄｅｄｕｃｅｄＨｕ＿Ｗａｓｈｉｚｕｐｒｉｎｃｉｐｌｅ.Ａｆｔｅｒｔｈａｔｇｅｎｅｒａｌｉｚｅｄｖａｒｉａｔｉｏｎａｌｐｒｉｎｃｉｐｌｅｓｃａｎｂｅａｒｒｉｖｅｄａｔ…     

THE HLDER CONTINUITY FOR THE GRADIENT OF SOLUTIONS TO ONE-SIDED OBSTACLE PROBLEMS

The Hǒlder continuity is proved for the gradient of the solution to the one-sided obstacle problem of the following variational inequality in the case 1相似文献   

THE HLDER CONTINUITY FOR THE GRADIENT OF SOLUTIONS TO ONE-SIDED OBSTACLE PROBLEMS

The Hölder continuity is proved for the gradient of the solution Jo the one-sided obstacle problem of the following variational inequality in the case 1相似文献   

A stabilized complementarity formulation for nonlinear analysis of 3D bimodular materials

Bi-modulus materials with different mechanical responses in tension and compression are often found in civil, composite, and biological engineering. Numerical analysis of bimodular materials is strongly nonlinear and convergence is usually a problem for traditional iterative schemes. This paper aims to develop a stabilized computational method for nonlinear analysis of 3D bimodular materials. Based on the parametric variational principle, a unified constitutive equa-tion of 3D bimodular materials is proposed, which allows the eight principal stress states to be indicated by three para-metric variables introduced in the principal stress directions. The original problem is transformed into a standard linear complementarity problem (LCP) by the parametric virtual work principle and a quadratic programming algorithm is developed by solving the LCP with the classic Lemke’s algo-rithm. Update of elasticity and stiffness matrices is avoided and, thus, the proposed algorithm shows an excellent conver-gence behavior compared with traditional iterative schemes. Numerical examples show that the proposed method is valid and can accurately analyze mechanical responses of 3D bimodular materials. Also, stability of the algorithm is greatly improved.     

BASIC THEOREMS IN LINEAR MICROMORPHIC THERMOELECTROELASTICITY AND THEIR PRIMARY APPLICATION

As a natural extension of the micromorphic continuum theory, the linear theory of micromorphic thermoelectroelasticity is developed to characterize the nano-micro scale behavior of thermoelectroelastic materials with remarkable microstructures. After the basic governing equations are given and the reciprocal theorem is deduced, both the generalized variational principle and the generalized Hamilton principle for mixed boundary-initial value problems of micromorphic thermoelectroelastodynamics in convolution form are established. Finally, as a primary application, steady state responses of an unbounded homogeneous isotropic micromorphic thermoelectroelastic body to external concentrated loads with mechanical, electric, and thermal origins are analyzed.     

输入受限LQ控制的参变量变分原理和算法

在最优控制理论中根据模拟理论思想发展了塑性力学和接触力学中的参变量变分原理, 并建立了控制输入受限的线性二次(linear quadratic, LQ)最优控制问题的求解新方程---耦合的Hamilton正则方程与线性互补方程. 通过将连续时间离散成一系列等间距时间区段, 在离散时域内采用参数二次规划方法给出数值求解输入受限的LQ最优控制问题的新算法. 数值仿真验证了该算法在求解控制输入受限的LQ最优控制问题中的有效性, 并且该算法具有较快的收敛性, 在大步长下具有较高的计算精度.     

Optimal control of parabolic variational inequalities with state constraint

1　IntroductionandProblemWeshallstudytheoptimalcontrolproblemsgovernedbynonlinearparabolicvariationalinequalitiesoftheformy′+Ay +β(y) ∈Bu+f(a.e .(x,t)∈Q =Ω× [0 ,t]) ,y(0 ) =y0 , ( )withthestateconstraintF(y) S ,andthecostfunctionalI(y,u) .Whereβisadiscontinuous,nonlinearandnonmonotonemulti_valuedmapping .Theoptimalcontrolproblemsofthedifferentialsystemshavebeenstudiedforalongtime.Manyscholars,suchasJ.L .Lions ,V .Barbu ,D .Tiba,andF .Mignotetal.,haveresearchedtheoptimalcontrolpr…     

The optimal control variational principle and finite elements analysis for viscoplastic dynamics

This paper presents the optimal control variational principle for Perzyna model which is one of the main constitutive relation of viscoplasticity in dynamics. And it could also be transformed to solve the parametric quadratic programming problem. The FEM form of this problem and its implementation have also been discussed in the paper.     

Optimal control of hyperbolic H-hemivariational inequalities with state constraints

The optimal control problems of hyperbolic H-hemivariational inequalities with the state constraints and nonnornotone multivalued mapping term are considered. The optimal solutions are obtained. In addition, their approximating problems are also studied.     

PARAMETRIC VARIATIONAL PRINCIPLE BASED ELASTIC-PLASTIC ANALYSIS OF HETEROGENEOUS MATERIALS WITH VORONOI FINITE ELEMENT METHOD

The Voronoi cell finite element method (VCFEM) is adopted to overcome the limitations of the classic displacement based finite element method in the numerical simulation of heterogeneous materials. The parametric variational principle and quadratic programming method are developed for elastic-plastic Voronoi finite element analysis of two-dimensional problems. Finite element formulations are derived and a standard quadratic programming model is deduced from the elastic-plastic equations. Influence of microscopic heterogeneities on the overall mechanical response of heterogeneous materials is studied in detail. The overall properties of heterogeneous materials depend mostly on the size, shape and distribution of the material phases of the microstructure. Numerical examples are presented to demonstrate the validity and effectiveness of the method developed.     

Symplectic multi-level method for solving nonlinear optimal control problem

By converting an optimal control problem for nonlinear systems to a Hamiltonian system,a symplecitc-preserving method is proposed.The state and costate variables are approximated by the Lagrange polynomial.The state variables at two ends of the time interval are taken as independent variables.Based on the dual variable principle,nonlinear optimal control problems are replaced with nonlinear equations.Furthermore,in the implementation of the symplectic algorithm,based on the 2N algorithm,a multilevel method is proposed.When the time grid is refined from low level to high level,the initial state and costate variables of the nonlinear equations can be obtained from the Lagrange interpolation at the low level grid to improve efficiency.Numerical simulations show the precision and the efficiency of the proposed algorithm in this paper.     

Numerical solution of plane and axially symmetric jet flow problems based on the variational inequality formulation

The numerical analysis of plane and axially symmetric jet flows of an incompressible inviscid fluid is treated. A new formulation of the variational inequality type is developed from the variational principle associated with jet problems. A successive approximation method is formulated by the combined use of variational inequality and the finite element method. Numerical examples based on the iterative method are presented. The results obtained agree well with those by other methods.     

Asymptotic approximation method for elliptic variational inequality of first kind简

An asymptotic approximation method is proposed to solve a particular elliptic variational inequality of first kind associated with unilateral obstacle problems. In this method, the free boundary is first captured, and then the method of the fundamental solution (MFS) is used to find the solution of the Dirichlet problem for Laplace’s equation in the non-coincidence set. Numerical examples are given to show the efficiency of the method.     

EQUIVALENT BOUNDARY INTEGRAL EQUATIONS WITH INDIRECT VARIABLES FOR PLANE ELASTICITY PROBLEMS

IntroductionIthasbeenratheralonghistorythattheBoundaryElementMethod (BEM )isappliedtosolvetheplaneelasticityproblems[1～2 ].However,theEBIE ,whichisequivalenttotheoriginalboundaryvalueproblem ,hasnotbeenfullyappreciatedandsolvedinBEMcommunity .TheconventionalboundaryintegralequationswithindirectvariablesarediscussedthoroughlyanditisshownthatthepreviousresultsarenotEBIE ,i.e .,sometimes,thereexistsnosolutionormorethanonesolutiontothem .Themainkeyliesintheexactformoftheexteriorproblems.I…     

Optimal prestress of structures with frictional unilateral contact interfaces

Summary The problem of optimal prestress stabilization of elastic structures with frictional contact interfaces subject to static loads is studied in this paper. A linear elastic structure with given unilateral contact at frictional interfaces is considered. The prestressing control is modelled by the pin-load method. The static problem is formulated as a nonsymmetric variational inequality. The goal of the optimal control design is closing of the unilateral contact joints as well as minimization of the friction induced slips with a minimum effort. The resulting optimal control problem is nonsmooth and nonconvex, as it concerns the control of structures governed by variational inequalities. Appropriate techniques of nonsmooth analysis are used for its numerical solution. Effective computer realization and integration into existing finite element software is facilitated by appropriate static condensation techniques, which are outlined in the paper. Numerical examples illustrate the theory.