A holistic optimization approach for inverted cart-pendulum control tuning

  • Maude J. BlondinEmail author
  • Panos M. Pardalos
Methodologies and Application


The inverted cart-pendulum (ICP) is a nonlinear underactuated system, which dynamics are representative of many applications. Therefore, the development of ICP control laws is important since these laws are suitable to other systems. Indeed, many nonlinear control strategies have emerged from the control of the ICP. For these reasons, the ICP remains a canonical and fundamental benchmark problem in control theory and robotics that is of interest to the scientific community. Till now, the trial-and-error method is still widely applied for ICP controller tuning as well as the sequential tuning referring to tune the swing-up controller and thereafter, the stabilization controller. Therefore, the aim of this paper is to automate and facilitate the ICP control in one step. Thus, this paper proposes to holistically optimize ICP controllers. The holistic optimization is performed by a simplified Ant Colony Optimization method with a constrained Nelder–Mead algorithm (ACO-NM). Holistic optimization refers to a simultaneous tuning of the swing-up, stabilization and switching mode parameters. A new cost function is designed to minimize swing-up time, achieve high stabilization performance and consider system constraints. The holistic approach optimizes four controller structures, which include controllers that have never been tuned by a specific method besides by the trial-and-error method. Simulation results on a ICP nonlinear model show that ACO-NM in the holistic approach is effective compared to other algorithms. In addition, contrary to the majority of work on the subject, all the optimized controllers are validated experimentally. The simulation and experimental results obtained confirm that the holistic approach is an efficient optimization tool and specifically responds to the need of optimization technique for the potential-well controller structure and for the Q [diagonal of the matrix and the full matrix] in the linear–quadratic regulator (LQR) technique. Moreover, ICP experimental response analysis demonstrates that using the full Q provides greater experimental stabilization performance than using its diagonal terms in the LQR technique.


Inverted cart-pendulum system Nonlinear control Optimization Holistic approach Swing-up Stabilization 



This work was supported by the Vanier Canada Graduate Scholarship, the Michael Smith Foreign Study Supplements Program from the Natural Sciences. It was also supported by the Bourse Mobilité Étudiante from Ministère de l’Éducation du Québec and the CEMF Claudette MacKay-Lassonde Graduate Engineering Ambassador Award. This work was partially supported by Postdoctoral research scholarship from Fonds de recherche nature et Technologies du Québec and by the Paul and Heidi Brown preeminent professorship of ISE, University of Florida.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Human and animal rights

This article does not contain any studies with human participants or animals performed by any of the authors.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.University of FloridaGainesvilleUSA
  2. 2.University of FloridaGainesvilleUSA

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