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1. A Computational Governor for Maintaining Feasibility and Low Computational Cost in Model Predictive Control

   https://doi.org/10.1109/TAC.2023.3292980  

   Leung, Jordan; Permenter, Frank; Kolmanovsky, Ilya V (May 2024, IEEE Transactions on Automatic Control)

   This paper introduces an approach for reducing the computational cost of implementing Linear Quadratic Model Predictive Control (MPC) for set-point tracking subject to pointwise-in-time state and control constraints. The approach consists of three key components: First, a log-domain interior-point method used to solve the receding horizon optimal control problems; second, a method of warm-starting this optimizer by using the MPC solution from the previous timestep; and third, a computational governor that maintains feasibility and bounds the suboptimality of the warm-start by altering the reference command provided to the MPC problem. Theoretical guarantees regarding the recursive feasibility of the MPC problem, asymptotic stability of the target equilibrium, and finite-time convergence of the reference signal are provided for the resulting closed-loop system. In a numerical experiment on a lateral vehicle dynamics model, the worst-case execution time of a standard MPC implementation is reduced by over a factor of 10 when the computational governor is added to the closed-loop system. 

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2. Feasibility Governor for Linear Model Predictive Control

   https://doi.org/10.23919/ACC50511.2021.9483054  

   Skibik, Terrence; Liao-McPherson, Dominic; Cunis, Torbjorn; Kolmanovsky, Ilya; Nicotra, Marco M. (May 2021, Proceedings of 2021 American Control Conference, New Orleans, USA)

   This paper introduces the Feasibility Governor (FG): an add-on unit that enlarges the region of attraction of Model Predictive Control by manipulating the reference to ensure that the underlying optimal control problem remains feasible. The FG is developed for linear systems subject to polyhedral state and input constraints. Offline computations using polyhedral projection algorithms are used to construct the feasibility set. Online implementation relies on the solution of a convex quadratic program that guarantees recursive feasibility. The closed-loop system is shown to satisfy constraints, achieve asymptotic stability, and exhibit zero-offset tracking. 

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3. A stability governor for constrained linear–quadratic MPC without terminal constraints

   https://doi.org/10.1016/j.automatica.2024.111650  

   Leung, Jordan; Permenter, Frank; Kolmanovsky, Ilya V (June 2024, Automatica)

   This paper introduces a supervisory unit, called the stability governor (SG), that provides improved guarantees of stability for constrained linear systems under Model Predictive Control (MPC) without terminal constraints. At each time step, the SG alters the setpoint command supplied to the MPC problem so that the current state is guaranteed to be inside of the region of attraction for an auxiliary equilibrium point. The proposed strategy is shown to be recursively feasible and asymptotically stabilizing for all initial states sufficiently close to any equilibrium of the system. Thus, asymptotic stability of the target equilibrium can be guaranteed for a large set of initial states even when a short prediction horizon is used. A numerical example demonstrates that the stability governed MPC strategy can recover closed-loop stability in a scenario where a standard MPC implementation without terminal constraints leads to divergent trajectories. 

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4. Learning to Satisfy Constraints in Spacecraft Rendezvous and Proximity Maneuvering: A Learning Reference Governor Approach

   https://doi.org/10.2514/6.2022-2514  

   Ikeya, Kosuke; Liu, Kaiwen; Girard, Anouck; Kolmanovsky, Ilya V. (January 2022, Proceedings of AIAA SCITECH 2022 Forum January 3-7, 2022 San Diego, CA & Virtua)

   This paper illustrates an approach to integrate learning into spacecraft automated rendezvous, proximity maneuvering, and docking (ARPOD) operations. Spacecraft rendezvous plays a significant role in many spacecraft missions including orbital transfers, ISS re-supply, on-orbit refueling and servicing, and debris removal. On one hand, precise modeling and prediction of spacecraft dynamics can be challenging due to the uncertainties and perturbation forces in the spacecraft operating environment and due to multi-layered structure of its nominal control system. On the other hand, spacecraft maneuvers need to satisfy required constraints (thrust limits, line of sight cone constraints, relative velocity of approach, etc.) to ensure safety and achieve ARPOD objectives. This paper considers an application of a learning-based reference governor (LRG) to enforce constraints without relying on a dynamic model of the spacecraft during the mission. Similar to the conventional Reference Governor (RG), the LRG is an add-on supervisor to a closed-loop control system, serving as a pre-filter on the command generated by the ARPOD planner. As the RG, LRG modifies, if it becomes necessary, the command to a constraint-admissible reference to enforce specified constraints. The LRG is distinguished, however, by the ability to rely on learning instead of an explicit model of the system, and guarantees constraints satisfaction during and after the learning. Simulations of spacecraft constrained relative motion maneuvers on a low Earth orbit are reported that demonstrate the effectiveness of the proposed approach. 

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5. Time Shift Governor for Spacecraft Proximity Operation in Elliptic Orbits

   https://doi.org/10.2514/6.2024-2452  

   Kim, Taehyeun; Kolmanovsky, Ilya; Girard, Anouck (January 2024, American Institute of Aeronautics and Astronautics)

   This paper presents a parameter governor-based control approach to constrained spacecraft rendezvous and docking (RVD) in the setting of the Two-Body problem with gravitational perturbations. An add-on to the nominal closed-loop system, the Time Shift Governor (TSG) is developed, which provides a time-shifted Chief spacecraft trajectory as a target reference for the Deputy spacecraft, and enforces various constraints during RVD missions, such as Line of Sight cone constraints, total magnitude of thrust limit, relative velocity constraint, and exponential convergence to the target during RVD missions. As the time shift diminishes to zero, the virtual target incrementally aligns with the Chief spacecraft over time. The RVD mission is completed when the Deputy spacecraft achieves the virtual target with zero time shift, which corresponds to the Chief spacecraft. Simulation results for the RVD mission in an elliptic orbit around the Earth are presented to validate the proposed control strategy. 

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