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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. 

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. 

The paper considers the application of feedback control to orbital transfer maneuvers subject to constraints on the spacecraft thrust and on avoiding the collision with the primary body. Incremental reference governor (IRG) strategies are developed to complement the nominal Lyapunov controller, derived based on Gauss variational equations, and enforce the constraints. Simulation results are reported that demonstrate the successful constrained orbital transfer maneuvers with the proposed approach. A Lyapunov function based IRG and a prediction‐based IRG are compared. While both implementation successfully enforce the constraints, a prediction‐based IRG is shown to result in faster maneuvers. 

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. 

The use of Command governors (CGs) to enforce pointwise-in-time state and control constraints by minimally altering reference commands to closed-loop systems has been proposed for a range of aerospace applications. In this paper, we revisit the design of the CG and describe approaches to its implementation based directly on a bilevel (inner loop + outer loop) optimization problem in the formulation of CG. Such approaches do not require offline construction and storage of constraint admissible sets nor the use of online trajectory prediction, and hence can be beneficial in situations when the reference command is high-dimensional and constraints are nonlinear and change with time or are reconfigured online. In the case of linear systems with linear constraints, or in the case of nonlinear systems with linear constraints for which a quadratic Lyapunov function is available, the inner loop optimization problem is explicitly solvable and the bilevel optimization reduces to a single stage optimization. In other cases, a reformulation of the bilevel optimization problem into a mathematical programming problem with equilibrium constraints (MPEC) can be used to arrive at a single stage optimization problem. By applying the bilevel optimization-based CG to the classical low thrust orbital transfer problem, in which the dynamics are represented by Gauss-Variational Equations (GVEs) and the nominal controller is of Lyapunov type, we demonstrate that constraints, such as on the radius of periapsis to avoid planetary collision, on the osculating orbit eccentricity and on the thrust magnitude can be handled. Furthermore, in this case the parameters of the Lyapunov function can be simultaneously optimized online resulting in faster maneuvers. 

A parameter governor-based control scheme is developed to enforce various constraints, such as the Line of Sight (LoS) cone angle, the thrust limit, and the relative approach velocity during rendezvous missions in a near rectilinear halo orbit (NRHO) in the Earth-Moon system. The parameter governor is an add-on scheme to the nominal closed-loop system, which dynamically adjusts controller parameters in order to enforce the constraints. For the application to the rendezvous mission, we utilize the Time Shift Governor (TSG) which time shifts the target trajectory commanded to the Deputy spacecraft controller. The time shift is gradually reduced to zero so that the virtual target trajectory gradually converges to the Chief spacecraft trajectory as time evolves, and the rendezvous mission can be accomplished. Simulation results are reported that demonstrate the effectiveness of the proposed control scheme. 

Dosage schedule of the Proton Pump Inhibitors (PPIs) is critical for gastric acid disorder treatment. In this paper, we develop a constrained optimization based approach for scheduling the PPIs dosage. In particular, we exploit a mathematical prediction model describing the gastric acid secretion, and use it within the optimization algorithm to predict the acid level. The dosage of the PPIs which is used to enforce acid level constraints is computed by solving a constrained optimization problem. Simulation results show that the proposed approach can successfully suppress the gastric acid level with less PPIs intake compared with the conventional fixed PPIs dosage regimen, which may reduce the long-term side effects of the PPIs.