Table 2 Parameters and symbols of MPC problems
Parameters | Symbols |
|---|---|
\(t\) | Current moment |
\(N_{p}\) | Prediction horizon |
\(N_{c}\) | Control horizon |
\(J_{t}\) | The objective function of the longitudinal motion planning |
\(x(0)\) | The state vector at the current moment |
\(u_{t - 1}\) | The control vector at the previous moment |
\(y_{{t + it_{p} \left| t \right.}}\) | The predictive output of longitudinal position and velocity corresponding to each predictive step in the prediction horizon at the current step |
\(y_{{{\text{ref}},t + it_{p} \left| t \right.}}\) | The desired output of longitudinal position and velocity of each predictive step in the prediction horizon |
\(u_{{t + jt_{c} \left| t \right.}}\) | The output of acceleration corresponding to each predictive step in the control horizon at the current step |
\({\Delta }u_{{t + it_{c} \left| t \right.}}\) | The output of jerk corresponding to each predictive step in the control horizon at the current step |
\(\varepsilon\) | Relaxation factor |
\(Q,R_{u} ,R_{du} ,\rho\) | Weights of each optimization objectives |
\(1_{p \times 1} ,1_{n \times 1}\) | A unit column vector of dimension n and p |