Marine population dynamics problem

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Marine population dynamics problem
Algebraic states:  n_s
Continuous control values:  2 n_s
Path constraints:  4 n_s

The Marine population dynamics problem estimates growth and mortality rates of a marine species at each stage (for example ages or development stage) given the population as a function of time.( Problem taken from the COPS library)

Mathematical formulation

The problem is given by

 \displaystyle \min_{g, m} & \sum\limits_{j=1}^{n_s} &&||y(\tau_j; g, m) - z_j||^2   \\[1.5ex]
 & \dot{y}_j & = &  g_{j-1} y_{j-1} - (m_j + g_j) y_j \qquad \forall j \in 1, ..., n_s,\\
 & g_j, m_j &\in&  [0,1].

where  g_j and  m_j are the growth and mortality rates at stage  j respectively and the initial conditions are unknown. The error between computed and observed data is minimized.


There are  n_s stages and  n_m timepoints at which the error is minimized.

Source Code

Model descriptions are available in