(522g) Contingency Planning for Fault Tolerance in Robust Nonlinear MPC

Faults can occur in any real-world system, and while in some cases it is possible to identify faults that are likely to occur or that have severe consequences, the time at which they occur is generally not predictable. If a fault occurs, a standard controller may not be able to maintain stability, much less performance. This has led to the development of controllers that are robust, or tolerant, to faults while ensuring stability and acceptable performance (Zhang and Jiang, 2008).

In this work, we present a novel approach to guaranteeing fault tolerance for multiple fault models in robust MPC for nonlinear systems subject to additive disturbances. The approach is based on designing a set of feasible contingency trajectories, which a nonlinear robust MPC can track online to ensure the uncertain system reaches a safe state in the event of a fault. Our formulation relies on the concept of M-step robust fault tolerance, originally introduced for robust control of linear systems with a single fault model (Shekhar and Maciejowski, 2011). M-step robust fault tolerance enables guaranteeing that the fault-free contingency paths are chosen such that there always exists a feasible state and control trajectory to a predefined point (or region) in the state space if the fault occurs at any time as the state moves toward its desired equilibrium. The proposed approach allows specifying a generic safety region for multiple nonlinear fault models, without requiring a long prediction horizon for each fault model.

There are several approaches to robust MPC that guarantee robust stability and constraint satisfaction by design. Tube-based approaches provide a compromise between the computational expense of min-max robust MPC and the limited inherent robustness of nominal MPC by incorporating a (possibly) conservative constraint tightening into the MPC optimization problem. We here incorporate the proposed M-step robust fault tolerance into the invariant set tube-based approach of Mayne et al. (2011). This results in an online optimization problem with computational complexity that is independent of the number of fault models. The approach achieves this independence through separating the design of the controller into an offline determination of feasible reference trajectories for all models versus online tracking of the reference corresponding to the current model (Paulson et al., 2019). We demonstrate the advantages of the proposed method for fault-tolerant control of several nonlinear example problems.

Mayne, D.Q., Kerrigan, E.C., van Wyk, E.J., and Falugi, P. “Tube-based robust nonlinear model predictive control.” International Journal of Robust and Nonlinear Control, 21:1341–1353, 2011.

Paulson, J.A., Heirung, T.A.N., and Mesbah, A. “Fault-tolerant tube- based robust nonlinear model predictive control.” In Proceedings of the American Control Conference. Philadelphia, PA, 2019.

Shekhar, R.C. and Maciejowski, J.M. “Robust predictive control with feasible contingencies for fault tolerance.” In Proceedings of the IFAC World Congress, pages 4666–4671. Milan, Italy, 2011.

Zhang, Y. and Jiang, J. “Bibliographical review on reconfigurable fault- tolerant control systems.” Annual Reviews in Control, 32(2):229–252, 2008.