Robust Model Predictive Control of Linear Systems With Predictable Disturbance With Application to Multiobjective Adaptive Cruise Control

Abstract

This paper presents a novel robust model predictive control (RMPC) concept for linear time-invariant systems with a predictable additive disturbance and linear constraints on the state and the input. Major properties of the approach are that: 1) available knowledge of the disturbance is considered in the optimization and 2) the robustness and the performance are addressed separately. As a result, the control performance is optimized while a less conservative condition on constraint satisfaction and recursive feasibility compared to the existing RMPC schemes is obtained. Traditionally, the Lyapunov function is chosen as the optimum of the objective function which must usually be quadratic in terms of the state and the input and contain a terminal cost term. These standard assumptions for the stability may restrict the flexibility of the optimization problem formulation and, thus, limit the applicability of the related RMPC strategies. To overcome this limitation, this paper proposes an explicit Lyapunov function and ensures the input-to-state stability (ISS) with a quadratic constraint, allowing to use any arbitrary convex objective function. To evaluate the novel RMPC concept, a multiobjective adaptive cruise control (ACC) is proposed and a simulation study using measured velocity profiles for the leading vehicle on a highway is presented. In the evaluation, a less restrictive constraint tightening and a larger terminal constraint set compared to the classical RMPC policies could be found and multiple objectives including driving comfort, energy efficiency, stability, and robust recursive fulfillment of safety, velocity, and further physical constraints could be achieved with the novel RMPC concept.