Non Parametric System Identification Essay

System identification is a branch of systems theory that characterizes behavior of a system through its interactions with the environment described as inputs and outputs. The relationship between the input and the output can be quantitatively described in form of a mathematical model. This description could be outlined through a parametric model which uses a group of parameters usually incorporated in a few differential equations governing the physics of the system or a non-parametric model through measurements of the system at a large number of points [35]. Parametric approach often requires an in depth knowledge of the system and uses more assumptions in modeling. Because of this, parametric system identification may result in unreliable prediction for complex systems where our understanding of the physics of the system is insufficient. Here we used a non-parametric approach as control of walking in humans is a complex task involving many degrees of freedom. We chose to perturb the system using visual perturbations as the input since the optic flow has a profound effect on the perception of speed. We measured muscle activations and kinematics as the output of the system. In linear time invariant (LTI) systems the relationship between the input and the output could be described in the frequency domain through frequency response functions (FRFs). In these systems an input with the frequency of f1 creates an output at frequency f2. The gain function of FRFs describes the relationship between input and output amplitudes and the phase function describes the timing information (i.e. lead or lag). Periodic systems like locomotion however are not LTI. Close to their point of operation these …show more content…
Figure 4 shows phase dependent IRFs for the soleus muscle which is a plantarflexor from the group of calf