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Kristian Ye

Asked on: July 1, 2025

Answers (1)

• 

  Wallon Lenos • July 2, 2025

  $$$$\vspace{-2mm} \begin{equation}\label{eq:MPC} \begin{aligned} \min_{u, y} \quad & \sum_{t=0}^{T-1} \left( \| y(t) - \mathcal{P}(t) \|_Q^2 + \| u(t) \|_R^2 \right) \\ \text{s.t.} \quad & x(t+1) = A x(t) + B u(t), \quad \forall t \in \{0, \dots, T-1\}, \\ & y(t) = C x(t) + D u(t), \quad \forall t \in \{0, \dots, T-1\}, \\ & x(0) = x_{init}, \\ & x(t) \in \mathcal{X}, \quad \forall t \in \{0, \dots, T-1\}, \\ & u(t) \in \mathcal{U}, \quad \forall t \in \{0, \dots, T-1\}, \\ & y(t) \in \mathcal{Y}, \quad \forall k \in \{0, \dots, N-1\}. \end{aligned} \end{equation}$$$$test

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