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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. 

This paper introduces a computationally efficient approach for solving Model Predictive Control (MPC) reference tracking problems with state and control constraints. The approach consists of three key components: First, a log-domain interior-point quadratic programming method that forms the basis of the overall approach; second, a method of warm-starting this optimizer by using the MPC solution from the previous timestep; and third, a computational governor that bounds the suboptimality of the warm-start by altering the reference command provided to the MPC problem. As a result, the closed-loop system is altered in a manner so that MPC solutions can be computed using fewer optimizer iterations per timestep. In a numerical experiment, the computational governor reduces the worst-case computation time of a standard MPC implementation by 90%, while maintaining good closed-loop performance.