A Nash game approach to mixed $${\mathcal {H}}_{2}/{\mathcal {H}}_{\infty }$$ H 2 / H ∞ model predictive control: part 2—stability and robustness

Abstract

This paper is a note on the stability and robustness of the Nash Game (Vamvoudakis et al. in Adaptive optimal control algorithm for zero-sum nash games with integral reinforcement learning, 2012; Ning et al. in Optim Control Appl Methods. doi:10.1002/oca.2042, 2012; Bouyer et al. in Concurrent games with ordered objectives, 2012) based mixed \({\mathcal {H}}_{2}/{\mathcal {H}}_{\infty }\) Model Predictive Controllers (Aadaleesan and Saha in Mixed \(\mathcal {H}_{2}/\mathcal {H}_{\infty }\) Model Predictive Control for Unstable and Non-Minimum Constrained Processes, 2008; Aadaleesan in Nash Game based Mixed \(\mathcal {H}_{2}/\mathcal {H}_{\infty }\) Model Predictive Control applied with Laguerre-Wavelet Network Model, 2011) for linear state feedback systems addressed in Part 1 (Aadaleesan and Saha in Int J Dyn Control, 2016) of this series. The mixed \({\mathcal {H}}_{2}/{\mathcal {H}}_{\infty }\) MPC proposed in Part 1 (Aadaleesan and Saha in Int J Dyn Control, 2016) and that developed by Orukpe et al. (Model predictive control based on mixed \(\mathcal {H}_2/\mathcal {H}_{\infty }\) control approach, 2007) are compared in this Part 2. The issues of stability and robustness of the multi-criterion optimal control are dealt in this paper using set theoretic concepts.