*7.2. MPC-LQR Dual Controller*

To reduce the computational load of the algorithm, when the current states reach a terminal invariant set around the equilibrium point, the MPC algorithm does not need to be computed. Instead, an LQR gain can be computed based on the value of the actual prediction parameter to cope with the small error that may be present inside the terminal invariant set. The control law is then presented as:

$$\boldsymbol{u}(k) = \begin{cases} \mathbf{U\_{mpc}} & \mathbf{x}(k) \notin \mathbf{T} \\ \mathbf{K\_{LQR}}(\rho\_1)\mathbf{x}(k) & \mathbf{x}(k) \in \mathbf{T} \end{cases} \tag{35}$$

where **KLQR**(*ρ*1) is the LQR gain dependent on the scheduling parameter *ρ*<sup>1</sup> and **T** is the terminal invariant set defined around the equilibrium point of the system.

Figure 3 presents the block diagram for the proposed LPV-MPC-LQR control strategy. Additionally, the LPV-MPC-LQR algorithm is shown in the flowchart presented in Figure 4.

**Figure 3.** Block diagram of the proposed LPV-MPC-LQR control strategy for the Active Suspension system.

**Figure 4.** Flow diagram of the LPV-MPC-LQR control strategy.
