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Stabilization of a linear system under control constraints is approached by combining the classical variation of parameters method for solving ODEs and a straightforward construction of a feedback law for the variational system based on a quadratic Lyapunov function. Sufficient conditions for global closed-loop stability under control constraints with zero in the interior and zero on the boundary of the control set are derived, and several examples are reported. The extension of the method to nonlinear systems with control constraints is described. 

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. 

Understanding the intention of vehicles in the surrounding traffic is crucial for an autonomous vehicle to successfully accomplish its driving tasks in complex traffic scenarios such as highway forced merging. In this paper, we consider a behavioral model that incorporates both social behaviors and personal objectives of the interacting drivers. Leveraging this model, we develop a receding-horizon control-based decision-making strategy, that estimates online the other drivers' intentions using Bayesian filtering and incorporates predictions of nearby vehicles' behaviors under uncertain intentions. The effectiveness of the proposed decision-making strategy is demonstrated and evaluated based on simulation studies in comparison with a game theoretic controller and a real-world traffic dataset. 

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. 

The problem of transforming a locally asymptotically stabilizing time-varying control law to a globally stabilizing one with accelerated finite/fixed-time convergence is studied. The solution is based on an extension of the theory of homogeneous systems to the setting where the symmetry and stability properties only hold with respect to a part of the state variables. The proposed control design advances the kind of approaches first studied in [1], and relies on the implicit Lyapunov function framework. Examples of finite-time and nearly fixed-time stabilization of a nonholonomic integrator are reported. 

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.