Fig 1. Graphical Representation of the Response Surface Identification.

The relationship x(p) between a controller parameter p (in this work, step-frequency) and the physiological objective x (in this work, metabolic energetic cost) was replicated by a response surface $\bar{x}(p,\mathbf{\lambda })$ defined by a set of shape parameters λ. The shape parameters were identified to minimize the error between predicted respiratory response $\bar{y}$ (based on a model of the measurement dynamics [20]) and actual measures $\hat{y}$. This dynamic estimation process enabled us to use non-steady-state breath-by-breath measures to approximate the relationship between the control parameter p and energetic cost x. Optimization was performed with respect to the response surface, $\bar{x}(p,\mathbf{\lambda })$, that approximates the energy-parameter relationship.