(239d) Output Feedback Mixed H2/H∞ Model Predictive Control: Observer Based Approach

The issue of robustness in Model Predictive Control (MPC) is of prime importance since it was developed. Although there are different schemes introduced by the control community to address this issue, it still remains a challenge in the face of control engineers. In the present work, a newer kind of robust observer based MPC has been developed, by extending the Nash game based mixed H₂/H_∞ MPC, introduced earlier by the same authors (Aadaleesan and Saha, 2008b), for state feedback case.

It has been shown that the overall closed-loop stability cannot be ensured for systems with individually stable observer and controller for constrained systems. To address this issue the immediate solution was given as tube-based MPC design (Mayne et al. 2006). As an alternative approach to deal with such a problem, incorporating the closed-loop robustness to disturbance rejection/model uncertainty is addressed in the present paper, as a mixed H₂/H_∞ observer based MPC. Solving a robust control problem in a game theoretic approach is already well known in the control community (Basar and Olsder, 1999) and to achieve both robust performance and robust stability in a single setting is possible with mixed H₂/H_∞ control. To get a better advantage of these both in controller design is attempted for the first time in (Aadaleesan and Saha, 2008b) for state feedback case. This is extended in the present work for output feedback case. The resulting control problem reduces to solving simultaneously three coupled Riccati equations, thereby the closed-loop stability is ensured if there exists a stabilizing solution to these coupled Riccati equations. The Lyapunov candidate matrix solutions are bounded to lie in ellipsoidal sets. The closed-loop robustness with the present robust MPC is exemplified using the parametric change in a nonlinear process viz. bioreactor. The process is well identified with a Wiener-type Laguerre-Wavelet Network model (Aadaleesan and Saha, 2008a). This model is then used along with the developed observer-based mixed H₂/H_∞ MPC. The closed-loop performance shows that the controller is robust to the plant-model mismatch that yields due to unexpected changes in the plant.

References

1)Aadaleesan, P and Saha, P, Nonlinear system identification using Wiener type Laguerre?Wavelet network model, Chemical Engineering Science, Volume 63, Issue 15, pp. 3932-3941, 2008a.

2)Aadaleesan, P and Saha, P, Mixed H₂/H_∞ Model Predictive Control for Unstable and Non-Minimum Constrained Processes, AIChE Annual Meeting, Nov. 16-20, Philadelphia, USA, 2008b.

3)Basar, T and Olsder, G. J. Dynamic Noncorporative Game Theory, SIAM, Philadelphia, 1999.

4)Mayne, D.Q, Rakovic, S.V, Findeisen. R and Allgower. F, Robust output feedback model predictive control of constrained linear systems, Automatica, 42, pp. 1217-1222, 2006.