Control of smart exercise machines-part II: Self-optimizing control

Perry Y. Li, Roberto Horowitz

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


This is the second part of a two-part paper on the design of an intelligent controller for a class of exercise machines. The control objective is to cause the user to exercise in a manner that optimizes a criterion related to the user's mechanical power. The optimal exercise strategy is determined by an a priori unknown biomechanical behavior, called the Hill surface, of the individual user. Consequently, the control scheme must simultaneously: 1) identify the user's biomechanical behavior; 2) optimize the controller; and 3) stabilize the system to the estimated optimal states. In Part I of this paper, a dynamic damping controller was proposed which satisfies the safety requirement and is capable of causing the user to execute an arbitrary exercise strategy if the user's biomechanical behavior is known. In this second part of the paper, we address the selfoptimization problem in which both the determination and the eventual execution of the optimal exercise strategy are accomplished, when the user's biomechanical behavior is unknown. This is achieved by a combination of an adaptive controller and a reference generator. The latter switches the desired exercise strategy between a training strategy and the estimated optimal strategy. Depending on the switching scheme chosen, it is shown that, asymptotically, the user will either execute the optimal exercise with probability one or operate close to it. Experimental results of the overall system verify the efficacy of the design.

Original languageEnglish (US)
Pages (from-to)248-258
Number of pages11
JournalIEEE/ASME Transactions on Mechatronics
Issue number4
StatePublished - 1997


  • Adaptive control
  • Biomechanics
  • Hybrid systems
  • Intelligent control
  • Passivity
  • Robotics
  • Self optimization
  • Velocity field control


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