Information projections in learning
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This thesis is aimed at discussing the relevance of the theory of reference frames in mathematical psychology in understanding the differences between biological and engineering control systems. As an example, the problem of human posture control is discussed via the use of a simplified model. The head, upper torso, and the upper legs are represented as straight lines with point masses attached to their mid points. The fact that as a child first learns to balance head with his mother's help, then the hip while sitting, and then the knee is taken into account in this representation. If the problem of the control of the head is P1, the head and the upper torso is P2 and everything above the knee is P3, it is contended that the solution of P2 is a natural extension of the solution of P1 and the solution of P3 is a natural extension of the solution of P2. Subsequently each problem is considered individually. At each stage, control laws for torque are written in terms of position, velocity and acceleration variables. Our theory leads to a natural solution which is consistent with everyday observations of how a child masters posture control.