Self-optimizing control: Application to smart exercise machines

In a self-optimizing control problem, it is desired that the plant with a priori unknown parameters perform a task that optimizes a performance index. If the optimal task can be specified explicitly, an adaptive controller can often be designed to enable that task to be performed. However in many cases, the optimal task cannot be explicitly specified because it may depend on the unknown plant parameters, and must also be determined explicitly on-line. In the context of intelligent controllers for exercise machines, the resistive / assistive force on the machine is manipulated to cause the user of the machine to maximize his / her mechanical power output while exercising. The optimal manner in which the user exercises is represented by a velocity field which is a function of the individual's unknown biomechanic characteristics. The proposed self-optimizing control approach combines i) a continuous state adaptive controller which enables an arbitrary explicitly specified task to be performed; and ii) a finite state excitation supervisor which switches the desired task between a training task and the estimated optimal task based on current system parameter estimates. Depending on the switching scheme chosen, it is shown that the user will asymptotically either execute the true optimal exercise with probability one or operate close to it. Experimental results of the implementation verifies the efficacy of the design.