Mixed H_2/H_∞ State Feedback Attitude Control of Microsatellite Based on Extended LMI Method

For the appearance of the additive perturbation of controller gain when the controller parameter has minute adjustment at the initial running stage of system,to avoid the adverse effects,this paper investigates the mixed H_2/H_∞ state feedback attitude control problem of microsatellite based on extended LMI method.Firstly,the microsatellite attitude control system is established and transformed into corresponding state space form.Then,without the equivalence restriction of the two Lyapunov variables of H_2 and H∞performance,this paper introduces additional variables to design the mixed H_2/H_∞ control method based on LMI which can also reduce the conservatives.Finally,numerical simulations are analyzed to show that the proposed method can make the satellite stable within 20 s whether there is additive perturbation of the controller gain or not.The comparative analysis of the simulation results between extended LMI method and traditional LMI method also demonstrates the effectiveness and feasibility of the proposed method in this paper.

Design of Poiseuille Flow Controllers Using the Method of Inequalities

This paper investigates the use of the method of inequalities （MoI） to design output-feedback compensators for the problem of the control of instabilities in a laminar plane Poiseuille flow. In common with many flows, the dynamics of streamwise vortices in plane Poiseuille flow are very non-normal. Consequently, small perturbations grow rapidly with a large transient that may trigger nonlinearities and lead to turbulence even though such perturbations would, in a linear flow model, eventually decay. Such a system can be described as a conditionally linear system. The sensitivity is measured using the maximum transient energy growth, which is widely used in the fluid dynamics community. The paper considers two approaches. In the first approach, the MoI is used to design low-order proportional and proportional-integral （PI） controllers. In the second one, the MoI is combined with McFarlane and Glover＇s H∞ loop-shaping design procedure in a mixed-optimization approach.

Superconvergence and L^(∞)-Error Estimates of RT1Mixed Methods for Semilinear Elliptic Control Problems with an Integral Constraint

In this paper,we investigate the superconvergence property and the L∞-error estimates of mixed finite element methods for a semilinear elliptic control problem with an integral constraint.The state and co-state are approximated by the order one Raviart-Thomas mixed finite element space and the control variable is approximated by piecewise constant functions or piecewise linear functions.We derive some superconvergence results for the control variable and the state variables when the control is approximated by piecewise constant functions.Moreover,we derive L∞-error estimates for both the control variable and the state variables when the control is discretized by piecewise linear functions.Finally,some numerical examples are given to demonstrate the theoretical results.

Higher Order Triangular Mixed Finite Element Methods for Semilinear Quadratic Optimal Control Problems

In this paper,we investigate a priori error estimates for the quadratic optimal control problems governed by semilinear elliptic partial differential equations using higher order triangular mixed finite element methods.The state and the co-state are approximated by the order k Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise polynomials of order k(k≥0).A priori error estimates for the mixed finite element approximation of semilinear control problems are obtained.Finally,we present some numerical examples which confirm our theoretical results.

Error Estimates and Superconvergence of RT0Mixed Methods for a Class of Semilinear Elliptic Optimal Control Problems

In this paper,we will investigate the error estimates and the superconvergence property of mixed finite element methods for a semilinear elliptic control problem with an integral constraint on control.The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element and the control variable is approximated by piecewise constant functions.We derive some superconvergence properties for the control variable and the state variables.Moreover,we derive L∞-and H−1-error estimates both for the control variable and the state variables.Finally,a numerical example is given to demonstrate the theoretical results.

MIXED DISCONTINUOUS GALERKIN TIME-STEPPING METHOD FOR LINEAR PARABOLIC OPTIMAL CONTROL PROBLEMS

In this paper, we discuss the mixed discontinuous Galerkin （DG） finite element ap- proximation to linear parabolic optimal control problems. For the state variables and the co-state variables, the discontinuous finite element method is used for the time dis- cretization and the Raviart-Thomas mixed finite element method is used for the space discretization. We do not discretize the space of admissible control but implicitly utilize the relation between co-state and control for the discretization of the control. We de- rive a priori error estimates for the lowest order mixed DG finite element approximation. Moveover, for the element of arbitrary order in space and time, we derive a posteriori L2（O, T; L2（Ω）） error estimates for the scalar functions, assuming that only the underlying mesh is static. Finally, we present an example to confirm the theoretical result on a priori error estimates.

Error estimates of triangular mixed finite element methods for quasilinear optimal control problems

The goal of this paper is to study a mixed finite element approximation of the general convex optimal control problems governed by quasilinear elliptic partial differential equations. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive a priori error estimates both for the state variables and the control variable. Finally, some numerical examples are given to demonstrate the theoretical results.

Superconvergence and L^(∞)-Error Estimates of the Lowest Order Mixed Methods for Distributed Optimal Control Problems Governed by Semilinear Elliptic Equations

In this paper, we investigate the superconvergence property and the L∞-errorestimates of mixed finite element methods for a semilinear elliptic control problem. Thestate and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions.We derive some superconvergence results for the control variable. Moreover, we derive L^(∞)-error estimates both for the control variable and the state variables. Finally, anumerical example is given to demonstrate the theoretical results.

Fully Discrete H^(1) -Galerkin Mixed Finite Element Methods for Parabolic Optimal Control Problems

In this paper,we investigate a priori and a posteriori error estimates of fully discrete H^(1)-Galerkin mixed finite element methods for parabolic optimal control prob-lems.The state variables and co-state variables are approximated by the lowest order Raviart-Thomas mixed finite element and linear finite element,and the control vari-able is approximated by piecewise constant functions.The time discretization of the state and co-state are based on finite difference methods.First,we derive a priori error estimates for the control variable,the state variables and the adjoint state variables.Second,by use of energy approach,we derive a posteriori error estimates for optimal control problems,assuming that only the underlying mesh is static.A numerical example is presented to verify the theoretical results on a priori error estimates.

ON THE EVOLUTION OF LARGE SCALE STRUCTURES IN THREE-DIMENSIONAL MIXING LAYERS

In this paper, several mathematical models for the large scale structures in some special kinds of mixing layers, which might be practically useful for enhancing the mixing, are proposed. First, the linear growth rate of the large scale structures in the mixing layers was calculated. Then, using the much improved weakly non-linear theory, combined with the energy method, the non-linear evolution of large scale structures in two special mixing layer configurations is calculated. One of the mixing lavers has equal magnitudes of the upstream velocity vectors, while the angles between the velocity vectors and the trailing edge were pi /2 - phi and pi /2 + phi, respectively. The other mixing layer was generated by a splitter-plate with a 45-degree-sweep trailing edge.

L∞-ESTIMATES OF MIXED FINITE ELEMENT METHODS FOR GENERAL NONLINEAR OPTIMAL CONTROL PROBLEMS

This paper investigates L∞--estimates for the general optimal control problems governed by two-dimensional nonlinear elliptic equations with pointwise control constraints using mixed finite element methods. The state and the co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. The authors derive L∞--estimates for the mixed finite element approximation of nonlinear optimal control problems. Finally, the numerical examples are given.

A Posteriori Error Estimates of Mixed Methods for Quadratic Optimal Control Problems Governed by Parabolic Equations

In this paper,we discuss the a posteriori error estimates of the mixed finite element method for quadratic optimal control problems governed by linear parabolic equations.The state and the co-state are discretized by the high order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions.We derive a posteriori error estimates for both the state and the control approximation.Such estimates,which are apparently not available in the literature,are an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.

Error Estimates and Superconvergence of Mixed Finite Element Methods for Optimal Control Problems with Low Regularity

In this paper,we investigate the error estimates and superconvergence property of mixed finite element methods for elliptic optimal control problems.The state and co-state are approximated by the lowest order Raviart-Thomas mixed fi-nite element spaces and the control variable is approximated by piecewise constant functions.We derive L^(2) and L^(∞)-error estimates for the control variable.Moreover,using a recovery operator,we also derive some superconvergence results for the control variable.Finally,a numerical example is given to demonstrate the theoretical results.

Superconvergence of Rectangular Mixed Finite Element Methods for Constrained Optimal Control Problem

We investigate the superconvergence properties of the constrained quadratic elliptic optimal control problem which is solved by using rectangular mixed finite element methods.We use the lowest order Raviart-Thomas mixed finite element spaces to approximate the state and co-state variables and use piecewise constant functions to approximate the control variable.We obtain the superconvergence of O(h^(1+s))(0<s≤1)for the control variable.Finally,we present two numerical examples to confirm our superconvergence results.

Error Estimates ofMixedMethods forOptimal Control Problems Governed by General Elliptic Equations

In this paper,we investigate the error estimates of mixed finite element methods for optimal control problems governed by general elliptic equations.The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions.We derive L2 and H−1-error estimates both for the control variable and the state variables.Finally,a numerical example is given to demonstrate the theoretical results.

A Posteriori Error Estimates of Triangular Mixed Finite Element Methods for Semilinear Optimal Control Problems

In this paper,we present an a posteriori error estimates of semilinear quadratic constrained optimal control problems using triangular mixed finite element methods.The state and co-state are approximated by the order k≤1 RaviartThomas mixed finite element spaces and the control is approximated by piecewise constant element.We derive a posteriori error estimates for the coupled state and control approximations.A numerical example is presented in confirmation of the theory.

平行流交叉口车道控制与信号配时组合优化

为了提升平行流交叉口实际应用的灵活性,提出车道控制与信号配时组合优化方法,将单向、非对称双向、对称双向、三向、四向设置与布设方向组合共16种方案整合到优化模型中,通过修正交通冲突矩阵自动生成相位相序方案.构建混合整数线性规划模型,实现交叉口设置方案选择、车道分配和信号配时的组合优化.结果表明,在各种流量场景下,对称双向、三向、四向设置方案相较于常规交叉口分别能够提升约20%、20%、50%的通行能力,单向、非对称双向设置方案通行能力与常规交叉口接近,说明平行流交叉口不宜采用单向、非对称双向设置.四向设置方案通行能力的提升幅度最大,最大值能达到70.51%.对称双向和三向设置方案的通行能力提升相差不大,但三向设置在不对称流量场景中的表现优于对称双向设置.

混行交叉口自动驾驶专用车道与相位优化研究

文中提出了面向HDV/CAV混行交叉口的车道组织与信号控制协同优化模型,支持交叉口CAV专用车道及相位协同优化.以典型城市道路交叉口为例,分析了不同CAV渗透率下交叉口车道配置及信号控制策略的变化规律.结果表明:当CAV渗透率超过60%时,设置CAV专用车道及相位将显著降低交叉口车均延误.且CAV渗透率在70%~90%时,车均延误降幅超过30%;当CAV渗透率在60%~80%时,HDV车辆的延误降幅更为明显.

Superconvergence of RT1 mixed finite element approximations for elliptic control problems

In this paper,we investigate the superconvergence property of the numerical solution to a quadratic elliptic control problem by using mixed finite element methods.The state and co-state are approximated by the order k=1 Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions.We prove the superconvergence error estimate of h3/2 in L2-norm between the approximated solution and the average L2 projection of the control.Moreover,by the postprocessing technique,a quadratic superconvergence result of the control is derived.