Researchers in  introduced a linear quadratic regulator (LQR) based dynamic yaw-moment control (DYC) method to generate global yaw moment needed to track the desired lateral response of a reference model under the input of driver's steering and vehicle speed.
This would lead to a linear time-invariant (LTI) system approximation of the nonlinear system that we will use to build a linear quadratic regulator (LQR) controller that will be updated at each sample time , The LTI system between time steps k and k+1 is given by:
Then a locally linearized rigid body model is used to design an on-line updated linear quadratic regulator that generates the desired global control efforts that can closely track the desired motion state responses.
Linear Quadratic Regulator (LQR) and Particle Swarm Optimization (PSO) were used in the thesis.
To solve these problems,  use part of feedback linear technology level 2 inverted pendulum swing control, realize the balance of the linear zed complete, using linear quadratic regulator balance control.
For the linear system Equation (2), the linear quadratic regulator is given by:
McLellan, "Effect of Process Nonlinearity on Linear Quadratic Regulator Performance," J.
The position control based on linear quadratic regulator is presented in Section 3.
Lee, "Optimal tuning of linear quadratic regulators using quantum particle swarm optimization," in Proceedings of the International Conference on Control, Dynamic Systems, andRobotics (CDSR '14), Paperno.