Model predictive control for max-plus-linear discrete event systems (Q5939330)

The model predictive control (MPC) method is extended to the max-plus linear discrete system NEWLINE\[NEWLINE x(k+1)=A \otimes x(k) \oplus B \otimes u(k) , NEWLINE\]NEWLINE NEWLINE\[NEWLINE y(k)=C \otimes x(k) , NEWLINE\]NEWLINE where \(x \oplus y = \max \{x , y \}\), \(x \otimes y = x + y\), \(A \in \mathbb{R}^n \times n_{\varepsilon}\), \(B \in \mathbb{R}^{n \times m}_{\varepsilon}\), \(C \in \mathbb{R}^{l \times n}_{\varepsilon}\), (\(m\) is the number of inputs and \(l\) is the number of outputs), the counter \(k\) is an event counter. NEWLINENEWLINENEWLINESome methods to solve the max-plus-algebraic MPC problem are presented.