Control systems theory is widely used to help ensure that aerial vehicles operate within their safety envelopes while meeting tracking objectives, such as for the emergency landing on unequipped runways. Important challenges in aerospace applications of control theory include (a) delayed or uncertain measurements of the states of the dynamics, which can arise from image processing in vision based landing, (b) sign or magnitude constraints on controls such as constraints on the allowable thrusts for a vehicle, and (c) the inadequacy of standard linearizations for designing feedback controls for aerial vehicles due to the significant coupling between the lateral and longitudinal dynamics. One approach to addressing these challenges uses interval observers, which provide componentwise upper and lower bounds for trajectories of uncertain dynamics, using limited information about the dynamics that is available from the measurements. Observers are dynamic systems that are constructed such that the observation error (measuring the difference between states of the observers and states of the corresponding components of the uncertain system) converges to zero over time. While standard observers yield asymptotic convergence of the observation error to zero, recent advances led to finite time observers, where the observation error reaches zero in a finite time. These include fixed time observers, whose convergence time is independent of the initial state of the dynamics.
An alternative approach to applying mathematical control to aerospace problems is based on reference governors, which are add-on control mechanisms that provide real-time modifications of trajectories of dynamical systems that prevent violations of input or state constraints. Advantages of reference governors include their ability to maintain the performance features of existing controls such as robustness to actuator noise or other uncertainties, while also certifying that the constraints are always satisfied. Reference governors entail constructing the maximum output admissible set (or MOAS) for aerial dynamics. Recent advances in control theory for reference governors include methods for computing the MOAS, and state augmentations that can reduce the study of systems with nonlinear constraints to the study of systems with linear constraints on augmented state spaces. This motivated studying applications of interval observers and reference governors to help land aerial vehicles on windy ship decks, and for formation control for aerial vehicles.
This research has been sponsored in part by a research grant from the US National Science Foundation and a contract from the US Office of Naval Research, which are collaborative with Laurent Burlion from Rutgers University. Below are additional references on applications of feedback control to aerospace systems. Click on the titles to see the presentation or paper. The people whose names are underlined were students when the paper was written.
- Burlion, L., V. Gibert, M. Malisoff, and F. Mazenc, "Controls for a nonlinear system arising in vision based landing of airliners," International Journal of Robust and Nonlinear Control, Volume 31, Issue 4, March 2021, pp. 1227-1244.
- Burlion, L., M. Malisoff, and F. Mazenc, "Stabilization for a chain of saturating integrators arising in the visual landing of aircraft with sampling," Systems & Control Letters, Volume 135, Issue 104574, January 2020, pp. 1-11.
- Gruszka, A., M. Malisoff, and F. Mazenc, "Tracking control and robustness analysis for PVTOL aircraft under bounded feedbacks," International Journal of Robust and Nonlinear Control, Volume 22, Issue 17, November 2012, pp. 1899-1920.
- Gruszka, A., M. Malisoff, and F. Mazenc, "Bounded tracking controllers and robustness analysis for UAVs," IEEE Transactions on Automatic Control, Volume 58, Issue 1, January 2013, pp. 180-187.
- LSU Department of Mathematics LinkedIn Research Announcement about Prof. Malisoff's Office of Naval Research Project, January 2022.
- Mazenc, F., L. Burlion, and M. Malisoff, "Stabilization and robustness analysis for a chain of saturating integrators with imprecise measurements," IEEE Control Systems Letters, Volume 3, Issue 2, April 2019, pp. 428-433.
- Mazenc, F., M. Malisoff, and L. Burlion, "Almost fixed time observers for parameters and for state variables of nonlinear systems,'' IEEE Control Systems Letters, Volume 7, 2023, pp. 667-672.
- Schieni, R., C. Zhao, J. Barreira, M. Malisoff, and L. Burlion, "Quadrotor flight envelope protection while following high-speed trajectories: a reference governor approach," in Proceedings of the AIAA SCITECH Forum (National Harbor MD, 23–27 January 2023), Paper AIAA 2023-1442, 14pp.