Fast Self-Triggered MPC for Constrained Linear Systems With Additive Disturbances

Abstract

This paper proposes a robust self-triggered model predictive control (MPC) algorithm for a class of constrained linear systems subject to bounded additive disturbances, in which the inter-sampling time is determined by a fast convergence self-triggered mechanism. The main idea of the self-triggered mechanism is to select a sampling interval so that a rapid decrease in the predicted costs associated with optimal predicted control inputs is guaranteed. This allows for a reduction in the required computation without compromising performance. By using a constraint tightening technique and exploring the nature of the open-loop control between sampling instants, a set of minimally conservative constraints is imposed on nominal states to ensure robust constraint satisfaction. A multi-step openloop MPC optimization problem is formulated, which ensures recursive feasibility for all possible realisations of the disturbance. The closed-loop system is guaranteed to satisfy a mean-square stability condition. To further reduce the computational load, when states reach a predetermined neighbourhood of the origin, the control law of the robust self-triggered MPC algorithm switches to a self-triggered local controller. A compact set in the state space is shown to be robustly asymptotically stabilized. Numerical comparisons are provided to demonstrate the effectiveness of the proposed strategies.

Robust Resource-Aware Self-triggered Model Predictive Control

“…Remark 2 If the sampling time is fixed, the proposed robust controller will coincide with the discrete-time ellipsoidal robust MPC method by discretizing the continuous time dynamics (7) explicitly. To see this, recall that the first component in (9), E(q k (t), Q f b,k (t)) is derived from the discrete-time explicit solution (12). Meanwhile, the second component in (9), E(0, Q op,k (t, λ k (t))) coincides with the ellipsoidal additive process noise generated by explicit discretization [21,Theorem 5.1 and Remark 5.2].…”

“…To see this, recall that the first component in (9), E(q k (t), Q f b,k (t)) is derived from the discrete-time explicit solution (12). Meanwhile, the second component in (9), E(0, Q op,k (t, λ k (t))) coincides with the ellipsoidal additive process noise generated by explicit discretization [21,Theorem 5.1 and Remark 5.2]. Hence, the proposed robust controller will not introduce extra conservativeness in comparison with the state-of-art discrete-time ellipsoidal robust MPC.…”

“…For example, a tube-based method [6], [7] and a Lipschitz constant based method [8] have been applied to quantify the uncertainty evolution. In discrete-time systems, the triggering time sequence has been chosen to maximize the duration of openloop operation [7] or by monitoring the discrepancy between nominal performance and actual performance [9]. Similar strategies have been applied to continuous time systems, This work has received support from the Swiss National Science Foundation under the RISK project (Risk Aware Data-Driven Demand Response), grant number 200021 175627, and under the NCCR Automation project, grant agreement 51NF40 180545.…”

Dual‐mode event‐triggered predictive control for nonlinear systems with bounded disturbances

“…Model predictive control (MPC), also called receding horizon predictive control, is a control strategy which uses explicit linear or nonlinear dynamics to predict the future state response of the system. [1][2][3][4] During each control period, the MPC algorithm obtains a series of operational variables by solving an optimal control problem to optimize the future state response of the system. [5][6][7] Owning to its great potential applications, MPC has been continuously developed and improved in practical applications and has been widely used in electrical power systems, chemical industries, aerospace field, and other industrial fields.…”

“…Model predictive control (MPC), also called receding horizon predictive control, is a control strategy which uses explicit linear or nonlinear dynamics to predict the future state response of the system 1‐4 . During each control period, the MPC algorithm obtains a series of operational variables by solving an optimal control problem to optimize the future state response of the system 5‐7 .…”