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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.