Attention as a Design Criterion and Analysis Tool in Control Problems

author: Roger W. Brockett, Harvard School of Engineering and Applied Sciences, Harvard University
published: Oct. 16, 2012,   recorded: September 2012,   views: 221


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We may reasonably why optimal control theory has not been more useful in understanding the control mechanisms found in biology. The questions there range from understanding control of the operation of an individual cell to the motor control of the complete organism. Given that evolution has had as long as it has to optimize brain and muscle/skeletal structures, why is that we don't find optimal control theory to be more effective in explaining these structures? Looking more critically at optimal control theory in an engineering setting, one observes that there are a great many applications in which the payoff for implementing an "optimal" relationship between sensed signals and control variables does not justify the cost of the equipment needed to achieve it. For example, in high volume consumer goods, such as dish washers and clothes dryers, it is inexpensive to sense the temperature of the water or air but the benefits associated with implementing a linear relationship between the temperature of the mixed water and the flow from the hot and cold water lines do not justify the cost. Acceptable performance is obtainable using a simple on-off control. Even in the case of audio equipment, where there is a payoff for building systems that are very close to linear, the benefits of linearity are confined to finite range of amplitudes and a subset of frequencies. At the heart of the problem is the fact that standard optimal control theory provides no mechanisms to incorporate implementation costs. In this talk we describe a formulation of control problems based on the Liouville equation that allows the designers to balance implementation costs with the quality of the resulting trajectories.

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