Recursive parameter identification of constrained systems: an application to electrically stimulated muscle.

In the application of real-time identification methods for diagnosis or adaptive control of biomedical systems, there is often known model information that is ignored. Constraints on the allowable values of parameters, which may be based on physical considerations, are often neglected because the information does "fit" easily into commonly used parameter-identification algorithms. In this paper a method of incorporating constraints on model parameters is developed. This method is applicable to most recursive parameter-identification algorithms. It enforces linear equality constraints on identified parameters. The use of this method for the real-time identification of autoregressive moving-average-type time series models, subject to parameter constraints, is described in detail. These constraints may be time varying. At each time step, the parameter estimate obtained by a recursive least squares estimator is orthogonally projected onto the constraint surface. This simple idea, when appropriately executed, enhances the output prediction accuracy of estimated parameters. Using constraint information in this way is important when we do not wish to destroy a "natural" parameterization of the model (by an initial projection to incorporate equality constraints), or when we cannot use a single initial model simplification (because the constraints are time varying or involve inputs and outputs). Because it improves output prediction at future times, this method is advantageous for use in predictive adaptive controllers. The use of this algorithm is demonstrated in the identification of electrically stimulated quadriceps muscles in paraplegic human subjects, using percutaneous intramuscular electrodes. The nonlinear steady-state force versus pulsewidth recruitment characteristic of the electrode-muscle system is identified simultaneously with the input-output muscle response dynamics, using a Hammerstein-type model. Knowledge of the recruitment curve's shape is translated into constraints on the identified parameters. This information improves the experimental predictive quality of the identified model.