Theoretical Study of Double Cost Function Linear Quadratic Regulator(LQR)

Double cost function linear quadratic regulator (DLQR) is developed from LQR theory to solve an optimal control problem with a general nonlinear cost function. In addition to the traditional LQ cost function, another free form cost function was introduced to express the physical need plainly and optimize weights of LQ cost function using the search algorithms. As an instance, DLQR was applied in determining the control input in the front steering angle compensation control (FSAC) model for heavy duty vehicles. The brief simulations show that DLQR is powerful enough to specify the engineering requirements correctly and balance many factors effectively. The concept and applicable field of LQR are expanded by DLQR to optimize the system with a free form cost function.

Arterial traffic signal coordination model considering buses and social vehicles

Considering the difference in driving parameters of buses and social vehicles on the arterial,an arterial traffic signal coordination model that takes into account social vehicles and buses on the basis of the maximum bandwidth is proposed.By using the pre-set parameters of a common cycle,green/red duration and known parameters of bus dwell time distribution,link length and vehicle speed and solving the mixed-integer-linear programming and optimizing the signal offsets,the model obtains the signal control parameters of the green bands both of social vehicles and buses.Finally,taking Wangjiang Road in Hefei as an example,simulation and evaluation are carried out by VISSIM.The results show that the new model has 15.2%and 13.2%reduction in average person delay and number of stops,respectively,compared with the traditional coordinated control method.

Method for secondary spring load equalization of railway vehicles with two-stage spring suspension: Modeling and optimal regulation

To ensure running safety,the secondary spring loads of railway vehicles must be well equalized.Due to the coupling interactive effects of these hyper static suspended structures,the equalization adjustment through shimming procedure is quite complex.Therefore,an effective and reliable method in application is developed in this paper.Firstly,the best regulation of spring load is solved based on a mechanical model of the secondary suspension system,providing a target for actual adjustment.To reveal the relationship between secondary spring load distribution and shim quantity sequence,a forecasting model is constructed and then modified experimentally with consideration of car body’s elastic deformation.Further,a gradient-based algorithm with a momentum operation is proposed for the load optimization.Effectiveness of the whole method has been verified on a test rig.It is experimentally confirmed that this research provides an important basis for achieving an optimal regulation of spring load distribution for multiple types of railway vehicles.

A Dynamic Job Shop Scheduling Method Based on Ant Colony Coordination System

Due to the stubborn nature of dynamic job shop scheduling problem,a novel ant colony coordination mechanism is proposed in this paper to search for an optimal schedule in dynamic environment.In ant colony coordination mechanism,the dynamic job shop is composed of several autonomous ants.These ants coordinate with each other by simulating the ant foraging behavior of spreading pheromone on the trails,by which they can make information available globally,and further more guide ants make optimal decisions.The proposed mechanism is tested by several instances and the results confirm the validity of it.

Attitude controller for reentry vehicles using state-dependent Riccati equation method

To get better tracking performance of attitude command over the reentry phase of vehicles, the use of state-dependent Riccati equation (SDRE) method for attitude controller design of reentry vehicles was investigated. Guidance commands are generated based on optimal guidance law. SDRE control method employs factorization of the nonlinear dynamics into a state vector and state dependent matrix valued function. State-dependent coefficients are derived based on reentry motion equations in pitch and yaw channels. Unlike constant weighting matrix Q, elements of Q are set as the functions of state error so as to get satisfactory feedback and eliminate state error rapidly, then formulation of SDRE is realized. Riccati equation is solved real-timely with Schur algorithm. State feedback control law u(x) is derived with linear quadratic regulator (LQR) method. Simulation results show that SDRE controller steadily tracks attitude command, and impact point error of reentry vehicle is acceptable. Compared with PID controller, tracking performance of attitude command using SDRE controller is better with smaller control surface deflection. The attitude tracking error with SDRE controller is within 5°, and the control deflection is within 30°.

Cyclic beamforming using fractional Fourier transform domain cyclostationarity

A minimum mean-squared error （MSE） beamforming algorithm employing the optimum fractional Fourier transform （Opt-FrFT） domain second-order cyclostationarity is proposed. This method can efficiently filter out the compact desired chirp signal, with a consequence that the cyclically uncorrelated interferences and stationary （colored） Gaussian noise are greatly suppressed in the Opt- FrFT domain. This improves the MSE minimization cyclic beamformer by reducing effectively the Opt-FrFY domain signal-noise cross terms in the presence of finite data length de-correlation operation. Simulation results show that the new method works well under a wide range of signal-to-noise ratio （SNR） and signal-to-interference ratio （SIR）.

A Graph-based Ant Colony Optimization Approach for Integrated Process Planning and Scheduling

This paper considers an ant colony optimization algorithm based on AND/OR graph for integrated process planning and scheduling(IPPS). Generally, the process planning and scheduling are studied separately. Due to the complexity of manufacturing system, IPPS combining both process planning and scheduling can depict the real situation of a manufacturing system. The IPPS is represented on AND/OR graph consisting of nodes, and undirected and directed arcs. The nodes denote operations of jobs, and undirected/directed arcs denote possible visiting path among the nodes. Ant colony goes through the necessary nodes on the graph from the starting node to the end node to obtain the optimal solution with the objective of minimizing makespan. In order to avoid local convergence and low convergence, some improved strategy is incorporated in the standard ant colony optimization algorithm. Extensive computational experiments are carried out to study the influence of various parameters on the system performance.

A Parameter Determination Method of Distribution Voltage Regulators Considering Tap Change and Voltage Profile

This paper proposes a parameter determination method of distribution voltage regulators load ratio control transformers （LRT） and step voltage regulators （SVR） considering the tap change and voltage profile. The method takes two procedures in order to simplify the optimization problem and to reduce calculation time. One is to simultaneously determine the control parameters of LRT and SVR minimizing voltage violations and voltage variations. The algorithm is based on particle swarm optimization （PSO）, which is one of non-linear optimization methods by using a concept of swarm intelligence. Another is to determine the dead-band width of LRT and SVR on the basis of bi-evaluation of tap change and voltage margin. The concept of a Pareto optimal solution is used for the decision of the best dead-band width. As the results of numerical simulations using distribution network model, the validity of the proposed method has been affirmed.

一道例题解法的思考

《中学生数理化》高中版2000年第10期《直线倾斜角和斜率的求解及活用》一文中例4的解法,笔者认为有商榷之处.题求函数f(x):(x2-2x+5)/(x+1)(x≥0)的值域.题求函数f(x)=(x2-2x+5)/(x+1)(x≥0)的值域原解函数表达式(x2-2x+5)/(x+1)=(x2-2x-(-5))/(x-(-1))

Inequalities for the Gaussian hypergeometric function

we study the monotonicity of certain combinations of the Gaussian hypergeometric functions F(-1/2,1/2;1;1- xc) and F(-1/2- δ,1/2 + δ;1;1- xd) on(0,1) for given 0 < c 5d/6 < ∞ andδ∈(-1/2,1/2),and find the largest value δ1 = δ1(c,d) such that inequality F(-1/2,1/2;1;1- xc) <F(-1/2- δ,1/2 + δ;1;1- xd) holds for all x ∈(0,1). Besides,we also consider the Gaussian hypergeometric functions F(a- 1- δ,1- a + δ;1;1- x3) and F(a- 1,1- a;1;1- x2) for given a ∈ [1/29,1) and δ∈(a- 1,a),and obtain the analogous results.

Optimization of formation for multi-agent systems based on LQR

In this paper,three optimal linear formation control algorithms are proposed for first-order linear multiagent systems from a linear quadratic regulator(LQR) perspective with cost functions consisting of both interaction energy cost and individual energy cost,because both the collective ob ject(such as formation or consensus) and the individual goal of each agent are very important for the overall system.First,we propose the optimal formation algorithm for first-order multi-agent systems without initial physical couplings.The optimal control parameter matrix of the algorithm is the solution to an algebraic Riccati equation(ARE).It is shown that the matrix is the sum of a Laplacian matrix and a positive definite diagonal matrix.Next,for physically interconnected multi-agent systems,the optimal formation algorithm is presented,and the corresponding parameter matrix is given from the solution to a group of quadratic equations with one unknown.Finally,if the communication topology between agents is fixed,the local feedback gain is obtained from the solution to a quadratic equation with one unknown.The equation is derived from the derivative of the cost function with respect to the local feedback gain.Numerical examples are provided to validate the effectiveness of the proposed approaches and to illustrate the geometrical performances of multi-agent systems.