Models and theories of speech motor control generally fall into one of two camps: models based on optimizing motor trajectories, and models based on dynamical systems theory. In a new paper, Adam Lammert and I show one way we can bridge this divide. frontiersin.org/articles/10.33…
In optimal control theories of movement, movements are planned to minimize some cost function. Often, the terms of this function are things like effort, accuracy, jerk, torque, path curvature, etc.
In speech models, these cost functions are usually evaluated prior to movement onset, to plan a desired movement trajectory (which can be either in terms of articulator position/velocity or muscle length).
Optimal control models of speech include GEPPETO and its variants. DIVA can also be seen as an optimal control model, based on approximating a desired trajectory in sensory space.
Although optimal feedback control models exist in other motor domains that eliminate the need to pre-plan trajectories, calculating the optimal cost functions needed to control movement is complex, especially for the nonlinear and high-degree-of-freedom speech system.
Alternatively, speech has been modeled using dynamical systems theory in Task Dynamics (and in our FACTS model). Here, trajectories are not pre-planned, but instead emerge from the interaction of the state of the speech production system and high-level dynamical control laws.
Both optimal trajectory control and dynamical systems models have been used to explain a wide variety of speech phenomena. However, the two approaches are currently incompatible, as there is no way to incorporate optimization into the Task Dynamics Framework.
Adam and I bridge this divide through the use of Dynamic Movement Primitives (europepmc.org/abstract/MED/2…). This approach provides a method to optimize dynamical control systems through the addition of a forcing function to the dynamical control laws that govern movement.
These forcing functions allow the dynamical control laws to produce movements that deviate from their normal trajectories. Using a highly simplified jaw model, we show that DMPs can be used to replicate learning of a velocity-dependent force-field applied to the jaw. 
After repeated exposure to these forcefields that pull the jaw in an anterior direction, participants are able to return to producing relatively straight-line jaw trajectories. We show that both trajectory-and effort-based optimization approaches replicate this behavior.
We also show that the structure needed for DMPs (specifically, a planning system that replaces explicit time dependency) can serve as an analogue of the planning oscillator system of Task Dynamics, and allows us to replicate things like the c-center effect in complex onsets.
We think this work has exciting implications for bridging the two dominant approaches to speech motor control, and moves closer towards an optimal feedback control model of speech.
This work also has implications for development, changes in speech register (i.e., H&H theory), effects of lexical neighborhood and frequency on productions, among others.
