Fair-MPC: a control-oriented framework for socially just decision-making

Abstract: Control theory can play a pivotal role in tackling many of the global challenges currently affecting our society, representing an actionable tool to help policymakers in shaping our future. At the same time, for this to be possible, elements of social justice must be accounted for within a control theoretical framework, so as not to exacerbate the existing divide in our society. In turn, this requires the formulation of new constraints and control objectives and their integration into existing or new control design strategies. Devising a formally sound framework to ensure social fairness can enable a leap in the comprehension of the meaning of such goals and their non-trivial relation with the usual notion of performance in control. In this new and challenging context, we propose Fair-MPC, an economic model predictive control scheme to promote fairness in control design and model-based decision-making. Moving beyond traditional measures of performance, Fair-MPC enables the integration of social fairness metrics, articulated in equality and equity, allowing the design of optimal input sequences to trade-off fairness and efficiency, which are often in conflict. By establishing a theoretical link between Fair-MPC and the standard model predictive control framework (quadratic cost and linear constraints), we provide insights into the impact of social justice objectives on the final control action, which is ultimately assessed along the efficiency of the controller over two numerical examples.