A Nash game approach to mixed $$\mathcal {H}_{2}/\mathcal {H}_{\infty }$$ H 2 / H ∞ model predictive control: part 1—state feedback linear system

Abstract

In this paper, the mixed \(\mathcal {H}_{2}/\mathcal {H}_{\infty }\) model predictive control (MPC) using Nash game approach for linear systems is proposed (Aadaleesan in PhD Dissertation, IIT Guwahati 2011, Aadaleesan and Saha in Proceedings of annual meeting of American institute of chemical engineers. Philadelphia 2008). Two-player game strategy is adopted by using two separate cost functions, viz., \(\mathcal {H}_{2}\) and \(\mathcal {H}_{\infty }\) cost functions for the minimizing and maximizing players of the game, respectively. The problem ultimately reduces to solving a pair of cross-coupled Riccati equations. Although solving the coupled Riccati equations resulting from LQ games is by itself of theoretical importance, in the present work it has been extended, for the first of its kind, to the regime of receding horizon control. Numerical examples are provided for disturbance rejection case to check the efficiency of the present algorithm against another established robust MPC (Orukpe et al. in Proceedings of American control conference. New York, pp 6147–6150 2007).