Hybrid control for tracking of invariant manifolds

Kathrin Flaßkamp*, Alex R. Ansari, Todd D. Murphey

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper presents a hybrid control method that controls to unstable equilibria of nonlinear systems by taking advantage of systems’ free dynamics. The approach uses a stable manifold tracking objective in a computationally efficient, optimization-based switching control design. Resulting nonlinear controllers are closed-loop and can be computed in real-time. Our method is validated for the cart–pendulum and the pendubot inversion problems. Results show the proposed approach conserves control effort compared to tracking the desired equilibrium directly. Moreover, the method avoids parameter tuning and reduces sensitivity to initial conditions. The resulting feedback map for the cart–pendulum has a switching structure similar to existing energy based swing-up strategies. We use the Lyapunov function from these prior works to numerically verify local stability for our feedback map. However, unlike the energy based swing-up strategies, our approach does not rely on pre-derived, system-specific switching controllers. We use hybrid optimization to automate switching control synthesis on-line for nonlinear systems.

Original languageEnglish (US)
Pages (from-to)298-311
Number of pages14
JournalNonlinear Analysis: Hybrid Systems
StatePublished - Aug 1 2017


  • Closed-loop control
  • Manifold tracking
  • Nonlinear control systems
  • Real-time algorithms
  • Stable manifolds
  • Switching control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Analysis
  • Computer Science Applications

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