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• A Polynomial State-Space model for fish population dynamics in areas affected by the golden mussel. • Model identification validation for ten different species. • Discussion of real-life applicable control strategies with a Nonlinear Model Predictive Control framework. • Numerical simulations. The invasion of exotic species in aquatic environments is one of the several disturbance factors responsible for altering the dynamics of fish communities. The golden mussel Limnoperna fortunei was first recorded in the upper Uruguay river, Brazil, in 2012 and, since then, it has been needed to discuss and evaluate how this invasive species interferes with the dynamics of the ten most abundant fishes of this region. Literature lacks works that investigate how to model and control the effect of such kind of invasion. This paper proposes a polynomial-nonlinear state-space representation to model the dynamics of the these fish communities, whose parameters are identified with the use of Least Squares procedures, considering in loci collected data from 2007 to 2016. This work also evaluates quantitatively, by relying on simulation results, how the (sudden) presence of the golden mussel medelled with the aquatic life of the upper Uruguay river. The obtained model allows some ambitious automatic control objectives. Using a Nonlinear Model Predictive Control (NMPC) approach, an automatic controller is designed to determine how much and how often the golden mussel should be removed from the water in order for the most affected species to once again exhibit sustainable life conditions, in terms of its K Condition Factor and abundance. The NMPC strategy is synthesized considering performance constraints and piecewise-constant control trajectories. By relying on simulation results, this work elucidates how an automatic controller could be implemented as management policies established by environmental agencies to gradually restore the fish ecological balance of the upper Uruguay river, previously unsettled by an exotic invasor. [ABSTRACT FROM AUTHOR]