A nullcline-based control strategy for PWL-shaped oscillators

• Published in: Nonlinear dynamics Vol. 97; no. 2; pp. 1011 - 1033
• Main Authors: Arena, Paolo, Patané, Luca, Spinosa, Angelo Giuseppe
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01-07-2019; Springer Nature B.V
• Subjects: Automotive Engineering; Classical Mechanics; Control; Dynamical Systems; Engineering; Locomotion; Mechanical Engineering; Original Paper; Oscillators; Robot control; Robot dynamics; Strategy; Topology; Vibration; Central Pattern Generator; Nonlinear oscillator; FitzHugh-Nagumo neuron; Synchronisation
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-019-05028-z

Starting from the piecewise-linear framework applied to networked FitzHugh-Nagumo oscillators, this paper aims at presenting a control strategy relying on phase portrait reshaping through the manipulation of their nullclines in order to fulfil both phase and time requirements. This has been achieved by relating the slopes of piecewise linearly approximated model’s nullclines in its limit cycle to its oscillation period. Additionally, the targeted issue addressed by this paper has been assessed by combining the former framework with an event-driven control strategy aimed at reducing its effects to specific time instants instead of continuous, instantaneous phases, which is much more computationally expensive. The strategy is therefore motivated by its simplicity and is supported by key applications to bioinspired locomotion control in legged robots, which suggest how a dynamics-preserving approximation of the phase portrait combined with a sampled control action can produce pre-defined phase topologies in directed, non-diffusive tree graphs.