中考控分题的命题理念与教学对策

本文分析了中考控分题的常见形式、设计理念及特点,并提出了相应的教学对策。

Optimal design of coordination control strategy for distributed generation system

This paper presents a novel design procedure for optimizing the power distribution strategy in distributed generation system. A coordinating controller, responsible to distribute the total load power request among multiple DG units, is suggested based on the conception of hierarchical control structure in the dynamic system. The optimal control problem was formulated as a nonlinear optimization problem subject to set of constraints. The resulting problem was solved using the Kuhn-Tucker method. Computer simulation results demonstrate that the proposed method can provide better efficiency in terms of reducing total costs compared to existing methods. In addition, the proposed optimal load distribution strategy can be easily implemented in real-time thanks to the simplicity of closed-form solutions.

Metro passenger flow control with station-to-station cooperation based on stop-skipping and boarding limiting

Metro passenger flow control problem is studied under given total inbound demand in this work,which considers passenger demand control and train capacity supply.Relevant connotations are analyzed and a mathematical model is developed.The decision variables are boarding limiting and stop-skipping strategies and the objective is the maximal passenger profit.And a passenger original station choice model based on utility theory is built to modify the inbound passenger distribution among stations.Algorithm of metro passenger flow control scheme is designed,where two key technologies of stopping-station choice and headway adjustment are given and boarding limiting and train stopping-station scheme are optimized.Finally,a real case of Beijing metro is taken for example to verify validity.The results show that in the three scenarios with different ratios of normal trains to stop-skipping trains,the total limited passenger volume is the smallest and the systematic profit is the largest in scenario 3.

The State Equations Methods for Stochastic Control Problems

The state equations of stochastic control problems,which are controlled stochastic differential equations,are proposed to be discretized by the weak midpoint rule and predictor-corrector methods for the Markov chain approximation approach. Local consistency of the methods are proved.Numerical tests on a simplified Merton's portfolio model show better simulation to feedback control rules by these two methods, as compared with the weak Euler-Maruyama discretisation used by Krawczyk.This suggests a new approach of improving accuracy of approximating Markov chains for stochastic control problems.

A utility-optimal backoff algorithm for wireless sensor networks

A novel backoff algorithm in CSMA/CA-based medium access control (MAC) protocols for clustered sensor networks was proposed. The algorithm requires that all sensor nodes have the same value of contention window (CW) in a cluster, which is revealed by formulating resource allocation as a network utility maximization problem. Then, by maximizing the total network utility with constrains of minimizing collision probability, the optimal value of CW (Wopt) can be computed according to the number of sensor nodes. The new backoff algorithm uses the common optimal value Wopt and leads to fewer collisions than binary exponential backoff algorithm. The simulation results show that the proposed algorithm outperforms standard 802.11 DCF and S-MAC in average collision times, packet delay, total energy consumption, and system throughput.

A QUADRATIC OBJECTIVE PENALTY FUNCTION FOR BILEVEL PROGRAMMING

The bilevel programming is applied to solve hierarchical intelligence control problems in such fields as industry, agriculture, transportation, military, and so on. This paper presents a quadratic objective penalty function with two penalty parameters for inequality constrained bilevel programming. Under some conditions, the optimal solution to the bilevel programming defined by the quadratic objective penalty function is proved to be an optimal solution to the original bilevel programming. Moreover, based on the quadratic objective penalty function, an algorithm is developed to l^nd an optimal solution to the original bilevel programming, and its convergence proved under some conditions. Furthermore, under the assumption of convexity at function without lower level problems is defined and lower level problems, a quadratic objective penalty is proved equal to the original bilevel programming.

FINITE ELEMENT APPROXIMATION FOR A CLASS OF PARAMETER ESTIMATION PROBLEMS

This paper investigates the finite element approximation of a class of parameter estimation problems which is the form of performance as the optimal control problems governed by bilinear parabolic equations,where the state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions.The authors derive some a priori error estimates for both the control and state approximations.Finally,the numerical experiments verify the theoretical results.

An alternating direction method of multipliers for elliptic equation constrained optimization problem

We propose an alternating direction method of multipliers(ADMM)for solving the state constrained optimization problems governed by elliptic equations.The unconstrained as well as box-constrained cases of the Dirichlet boundary control,Robin boundary control,and right-hand side control problems are considered here.These continuous optimization problems are transformed into discrete optimization problems by the finite element method discretization,then are solved by ADMM.The ADMM is an efficient first order algorithm with global convergence,which combines the decomposability of dual ascent with the superior convergence properties of the method of multipliers.We shall present exhaustive convergence analysis of ADMM for these different type optimization problems.The numerical experiments are performed to verify the efficiency of the method.

Matrix perturbation based approach for sensitivity analysis of eigen-solutions in a microgrid

Sensitivities of eigen-solutions to control variables play an important role in microgrid studies,such as coordinated optimal design of controllers and parameters,robust stability analysis on control variables,oscillation modes analysis on a system,etc.Considering the importance of sensitivities and the complexity of state matrix in a microgrid,parameter perturbations are utilized in this paper to analyze the construction characteristics of state matrix.Then,the sensitivities of eigenvalues and eigenvectors to control variables are obtained based on the first-order matrix perturbation theory,which makes the complex derivations of sensitivity formulas and repeated solutions of eigenvalue problem unnecessary.Finally,the effectiveness of the matrix perturbation based approach for sensitivity calculation in a microgrid is verified by a numerical example on a low-voltage microgrid prototype.

THE MAXIMUM PRINCIPLE FOR PARTIALLY OBSERVED OPTIMAL CONTROL OF FORWARD-BACKWARD STOCHASTIC SYSTEMS WITH RANDOM JUMPS

This paper studies the problem of partially observed optimal control for forward-backward stochastic systems which are driven both by Brownian motions and an independent Poisson random measure. Combining forward-backward stochastic differential equation theory with certain classical convex variational techniques, the necessary maximum principle is proved for the partially observed optimal control, where the control domain is a nonempty convex set. Under certain convexity assumptions, the author also gives the sufficient conditions of an optimal control for the aforementioned optimal optimal problem. To illustrate the theoretical result, the author also works out an example of partial information linear-quadratic optimal control, and finds an explicit expression of the corresponding optimal control by applying the necessary and sufficient maximum principle.

OPTIMAL CONTROL OF MULTISOLUTION ORDINARY DIFFERENTIAL EQUATIONS IN THE ABSENCE OF CONVEXITY

In this paper,the authors study an optimal control problem governed by a class of multistateordinary differential equations in the absence of convexity.To overcome the difficulty that thecorresponding approximate optimal control problem may have no solution,relaxed controls are introduced.With the help of relaxation theory,Pontryagin's maximum principle for the optimal pairs ofthe original control problem is obtained.In the end of this paper,the authors discuss the applicationof the maximum principle by an example.

STOCHASTIC DIFFERENTIAL EQUATIONS AND STOCHASTIC LINEAR QUADRATIC OPTIMAL CONTROL PROBLEM WITH LEVY PROCESSES

In this paper, tile authors first study two kinds of stochastic differential equations （SDEs） with Levy processes as noise source. Based on the existence and uniqueness of the solutions of these SDEs and multi-dimensional backward stochastic differential equations （BSDEs） driven by Levy pro- cesses, the authors proceed to study a stochastic linear quadratic （LQ） optimal control problem with a Levy process, where the cost weighting matrices of the state and control are allowed to be indefinite. One kind of new stochastic Riccati equation that involves equality and inequality constraints is derived from the idea of square completion and its solvability is proved to be sufficient for the well-posedness and the existence of optimal control which can be of either state feedback or open-loop form of the LQ problems. Moreover, the authors obtain the existence and uniqueness of the solution to the Riccati equation for some special cases. Finally, two examples are presented to illustrate these theoretical results.

Improvement of contact calculation in spherical discontinuous deformation analysis

Discontinuous deformation analysis （DDA） method is a newly developed discrete element method which employs the implicit time-integration scheme to solve the governing equations and the open-close iteration （OCI） method to deal with contact prob- lem, its computational efficiency is relatively low. However, spherical element based discontinuous deformation analysis （SDDA）, which uses very simple contact type like point-to-point contact, has higher calculation speed. In the framework of SDDA, this paper presents a very simple contact calculation approach by removing the OCI scheme and by adopting the maximal displacement increment （MDI）. Through some verification examples, it is proved that the proposed method is correct and effective, and a higher computational efficiency is obtained.

Constrained LQ Problem with a Random Jump and Application to Portfolio Selection

This paper deals with a constrained stochastic linear-quadratic（LQ for short）optimal control problem where the control is constrained in a closed cone. The state process is governed by a controlled SDE with random coefficients. Moreover, there is a random jump of the state process. In mathematical finance, the random jump often represents the default of a counter party. Thanks to the Ito-Tanaka formula, optimal control and optimal value can be obtained by solutions of a system of backward stochastic differential equations（BSDEs for short）. The solvability of the BSDEs is obtained by solving a recursive system of BSDEs driven by the Brownian motions. The author also applies the result to the mean variance portfolio selection problem in which the stock price can be affected by the default of a counterparty.

New Results on H_∞ Control of Linear Systems with Interval Time-Varying Delays

This paper is focused on the H_(∞) control problem for linear systems with interval timevarying delays.By employing a reciprocally convex combination approach and a delay decomposition approach,some new delay-dependent bounded real lemmas(BRLs) are derived such that the closedloop system is asymptotically stable with a prescribed H_(∞) level.The BRLs are then used to solve the H_(∞) controller design by incorporating with the cone complementary approach.Three numerical examples are finally given to show the validity of the proposed method.

Distributed adaptive attitude synchronization of multiple spacecraft

This paper addresses the distributed attitude synchronization problem of multiple spacecraft with unknown inertia matrices. Two distributed adaptive controllers are proposed for the cases with and without a virtual leader to which a time-varying reference attitude is assigned. The first controller achieves attitude synchronization for a group of spacecraft with a leaderless communication topology having a directed spanning tree. The second controller guarantees that all spacecraft track the reference attitude if the virtual leader has a directed path to all other spacecraft. Simulation examples are presented to illustrate the effectiveness of the results.

Peng's maximum principle for a stochastic control problem driven by a fractional and a standard Brownian motion

We study a stochastic control system involving both a standard and a fractional Brownian motion with Hurst parameter less than 1/2.We apply an anticipative Girsanov transformation to transform the system into another one,driven only by the standard Brownian motion with coefficients depending on both the fractional Brownian motion and the standard Brownian motion.We derive a maximum principle and the associated stochastic variational inequality,which both are generalizations of the classical case.

Discrete-Time Mean-Field Stochastic H_2/H_∞ Control

The finite horizon H_2/H_∞ control problem of mean-field type for discrete-time systems is considered in this paper. Firstly, the authors derive a mean-field stochastic bounded real lemma(SBRL). Secondly, a sufficient condition for the solvability of discrete-time mean-field stochastic linearquadratic(LQ) optimal control is presented. Thirdly, based on SBRL and LQ results, this paper establishes a sufficient condition for the existence of discrete-time stochastic H_2/H_∞ control of meanfield type via the solvability of coupled matrix-valued equations.

Stochastic maximum principle for mean-field forward-backward stochastic control system with terminal state constraints

In this paper,we consider an optimal control problem with state constraints,where the control system is described by a mean-field forward-backward stochastic differential equation(MFFBSDE,for short)and the admissible control is mean-field type.Making full use of the backward stochastic differential equation theory,we transform the original control system into an equivalent backward form,i.e.,the equations in the control system are all backward.In addition,Ekeland's variational principle helps us deal with the state constraints so that we get a stochastic maximum principle which characterizes the necessary condition of the optimal control.We also study a stochastic linear quadratic control problem with state constraints.

A Type of General Forward-Backward Stochastic Differential Equations and Applications

The authors discuss one type of general forward-backward stochastic differential equations (FBSDEs) with Ito's stochastic delayed equations as the forward equations and anticipated backward stochastic differential equations as the backward equations.The existence and uniqueness results of the general FBSDEs are obtained.In the framework of the general FBSDEs in this paper,the explicit form of the optimal control for linear-quadratic stochastic optimal control problem with delay and the Nash equilibrium point for nonzero sum differential games problem with delay are obtained.