Linear robust adaptive model predictive control: Computational complexity and conservatism

Abstract

In this paper, we present a robust adaptive model predictive control (MPC) scheme for linear systems subject to parametric uncertainty and additive disturbances. The proposed approach provides a computationally efficient formulation with theoretical guarantees (constraint satisfaction and stability), while allowing for reduced conservatism and improved performance due to online parameter adaptation. A moving window parameter set identification is used to compute a fixed complexity parameter set based on past data. Robust constraint satisfaction is achieved by using a computationally efficient tube based robust MPC method. The predicted cost function is based on a least mean squares point estimate, which ensures finite-gain L2 stability of the closed loop. The overall algorithm has a fixed (user specified) computational complexity. We illustrate the applicability of the approach and the trade-off between conservatism and computational complexity using a numerical example.

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

“…Furthermore, we show that by designing the objective function based on an additional mean squared point estimateθ, we can guarantee finite gain L 2 stability w.r.t. disturbances, extending the stability results in [6], [8] to nonlinear systems.…”

“…In general, RAMPC schemes [5], [6], [7], [8], [9], [10], [11], [12] use set membership estimation to provide a set of non falsified parameters, which is utilized in a robust tubebased MPC approach to provide robustness w.r.t. uncertain parameters and disturbances.…”

“…Approaches for general linear uncertain systems with polytopic tubes can be found in [6], [7], [8]. The special case of finite impulse response (FIR) systems and unknown constant/time-varying offsets are discussed in [5] and [19], respectively.…”

“…2 A possible exception to this statement may be the RAMPC scheme in the thesis [9], that addresses similar challenges as the proposed approach, but is limited to continuous time feedback linearizable systems. [7], [8], [9], [11], [25], [26], we consider the general problem of providing conditions on the robust MPC tube propagation and set updates. In particular, we provide general conditions regarding overapproximation of the uncertainty, nonincreasingness of the parameter set, and monotonicity properties of the tube propagation, that ensure robust recursive feasibility and robust constraint satisfaction.…”

“…This has motivated an increasing amount of research focused on online model adaptation/learning in MPC, spanning the last two This work was supported by the German Research Foundation under Grants GRK 2198/1, AL 316/12-2, and MU 3929/1-2, and by the International Max Planck Research School for Intelligent Systems (IMPRS-IS). 1 decades [2], [3], [4], with current research focused on robust adaptive formulations [5], [6], [7], [8], [9], [10], [11], [12], dual/learning formulations [13], [14] and machine learning based approaches [15], [16], [17], [18]. However, all of these approaches suffer from at least one of the following shortcomings: a) limitation to restrictive system classes, such as linear systems [5], [6], [7], [8] or feedback linearizable systems [9], b) failure to provide theoretical guarantees regarding recursive feasibility, closed-loop stability and constraint satisfaction [14], [15], [16], [18], c) significant increase in the computational complexity [11,Chap.…”