【Paper】2015_ Coordinated cruise control for high-speed train movements based on a multi-agent model

2015_Coordinated cruise control for high-speed train movements based on a multi-agent model

1. Introduction

2. The dynamic model of high-speed trains and some preliminaries

$$\{\begin{array}{rl}{\dot{x}}_i(t)& =v_i,i=1,2,\cdots ,n_1\\ m_i{\dot{v}}_i(t)& =u_i-m_i(c_{i0}+c_{i1}{v}_i(t)+c_{i2}{v}_i^2(t)),i=1,2,3,\cdots ,n\end{array}\text{\hspace{1em}(2)}$$

The symbol is ：
$x_i$： Indicate location ,
$v_i$： It means speed ,
$m_i$： Indicates quality ,
$u_i$： It means control .

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Then the nominal control force in the equilibrium state is
$${\bar{u}}_i=c_{i0}{m}_i+c_{i1}{m}_i{v}_r+c_{i2}{m}_i{v}_r^2,i=1,2,\cdots ,n\text{\hspace{1em}(3)}$$

3. Coordinated cruise control design

$$u_i(t)={\bar{u}}_i+u_{1i}(t)+u_{2i}(t)+u_{3i}(t)\text{\hspace{1em}(7)}$$

$$\begin{array}{rl}{u}_{1i}(t)& =m_i\alpha \sum _{j=1}^n{a}_{ij}(v_j(t)-v_i(t))\\ u_{2i}(t)& =-m_i\beta \sum _{j=1}^n{a}_{ij}{\nabla }_{x_i}{U}_{ij}\\ u_{3i}(t)& =m_{i}k(v_i(t)-v_r)\end{array}$$

4. Numerical simulations

Example 4.1.