Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Robust Steady-State-Aware Model Predictive Control for Systems with Limited Computational Resources and External Disturbances

Hassan Jafari Ozoumchelooei, Mehdi Hosseinzadeh

TL;DR

This work tackles robust steady-state tracking for constrained, resource-limited systems by extending steady-state-aware MPC with a tube-based framework. By decoupling nominal trajectory optimization from robust control synthesis and employing offline computations of an invariant tube, RSSA-MPC maintains the same online complexity as SSA-MPC while guaranteeing constraint satisfaction under external disturbances. Theoretical results establish recursive feasibility and closed-loop stability, with the best admissible steady-state recovered when the exact target is infeasible. Simulation and experimental validation on a Parrot Bebop 2 drone demonstrate robust performance under disturbances, confirming the method's practical viability for real-world, constrained systems.

Abstract

Model Predictive Control (MPC) is a powerful control strategy; however, its reliance on online optimization poses significant challenges for implementation on systems with limited computational resources. One possible approach to address this issue is to shorten the prediction horizon and adjust the conventional MPC formulation to enlarge the region of attraction. However, these methods typically introduce additional computational load. Recently, steady-state-aware MPC has been introduced to ensure output tracking and convergence to a given desired steady-state configuration while maintaining constraint satisfaction at all times without adding extra computational load. Despite its promising performance, steady-state-aware MPC does not account for external disturbances, which can significantly limit its applicability to real-world systems. This paper aims to advance the method further by enhancing its robustness against external disturbances. To achieve this, we adopt the tube-based design framework, which decouples nominal trajectory optimization from robust control synthesis, thereby requiring no additional online computational resources. Theoretical guarantees of the proposed methodology are shown analytically, and its effectiveness is assessed through simulations and experimental studies on a Parrot Bebop 2 drone.

Robust Steady-State-Aware Model Predictive Control for Systems with Limited Computational Resources and External Disturbances

TL;DR

This work tackles robust steady-state tracking for constrained, resource-limited systems by extending steady-state-aware MPC with a tube-based framework. By decoupling nominal trajectory optimization from robust control synthesis and employing offline computations of an invariant tube, RSSA-MPC maintains the same online complexity as SSA-MPC while guaranteeing constraint satisfaction under external disturbances. Theoretical results establish recursive feasibility and closed-loop stability, with the best admissible steady-state recovered when the exact target is infeasible. Simulation and experimental validation on a Parrot Bebop 2 drone demonstrate robust performance under disturbances, confirming the method's practical viability for real-world, constrained systems.

Abstract

Model Predictive Control (MPC) is a powerful control strategy; however, its reliance on online optimization poses significant challenges for implementation on systems with limited computational resources. One possible approach to address this issue is to shorten the prediction horizon and adjust the conventional MPC formulation to enlarge the region of attraction. However, these methods typically introduce additional computational load. Recently, steady-state-aware MPC has been introduced to ensure output tracking and convergence to a given desired steady-state configuration while maintaining constraint satisfaction at all times without adding extra computational load. Despite its promising performance, steady-state-aware MPC does not account for external disturbances, which can significantly limit its applicability to real-world systems. This paper aims to advance the method further by enhancing its robustness against external disturbances. To achieve this, we adopt the tube-based design framework, which decouples nominal trajectory optimization from robust control synthesis, thereby requiring no additional online computational resources. Theoretical guarantees of the proposed methodology are shown analytically, and its effectiveness is assessed through simulations and experimental studies on a Parrot Bebop 2 drone.

Paper Structure

This paper contains 8 sections, 2 theorems, 28 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Statement
  3. Robust Steady-State-Aware Model Predictive Control
  4. Robust Terminal Constraint Set $\Omega$
  5. Theoretical Properties of the Proposed RSSA-MPC
  6. Simulation Studies
  7. Experimental Results
  8. Conclusion

Key Result

Theorem IV.1

Consider the system described by eq1 and subject to the constraints specified in eq2. Assume that the optimization problem eq:OptimizitonProblem is feasible at the time instant $t$. Then, it remains feasible for all $t\in\mathbb{Z}_{\geq0}$.

Figures (6)

  • Figure 1: Time profile of $p_y$ at different disturbance magnitudes. The solid lines show the average response, the shaded regions represent the standard deviation, and the red and black dashed lines show the constraint and reference Y position, respectively.
  • Figure 2: Performance Index (PI) as a function of disturbance magnitude $\beta$.
  • Figure 3: Region of Attraction for RSSA-MPC and the convectional robust MPC mayne2005robust with $N=10$. The red dashed line represents the constraint.
  • Figure 4: Overview of the experimental setup utilized to experimentally validate the proposed RSSA-MPC.
  • Figure 5: Time profiles of the drone's X, Y, and Z positions and control inputs for $\beta = 0.015$, with red dashed lines indicating constraints and black dashed lines representing reference positions.
  • ...and 1 more figures

Theorems & Definitions (8)

  • Definition II.2
  • Remark II.3
  • Remark III.1
  • Theorem IV.1
  • proof
  • Theorem IV.2
  • proof
  • Remark IV.3