


We also evaluate the skill exhibited in human control strategy and corresponding models through several defined taskdependent as well as taskindependent performance criteria, including generalizability, longterm consistency, and robustness. Using specific performance criteria, we then optimize performance in initially stable HCS models through adaptive SPSA parameter refinement. One formulation of the performance criteria allows us to simplify a model's structure after training. Finally, we propose to use HCS models as virtual teachers in
A cascade neural network grows in complexity as is required by the training data.

Similarity analysis & model validation 
The main strength of modeling by learning, as required for human control strategies, is that no explicit physical model is required; this also represents its biggest weakness, however, especially when the unmodeled process is (1) dynamic and (2) stochastic in nature, as is the case for human control strategy. For such processes, model errors can feed back on themselves to produce trajectories which are not characteristic of the source process or are even potentially unstable. Yet, most learning approaches today, including feedforward neural networks, utilize some static error measure as a test of convergence for the learning algorithm. While this measure is very useful during training, it offers no guarantees, theoretical or otherwise, about the dynamic behavior of the resulting learned model. Thus, we have developed a similarity measure, based on Hidden Markov Model analysis, as a means of validating learned models of human control strategy.  


We are primarily interested in generating a probabilistic similarity measure between the dynamic system trajectories generated by the human and those generated by the learned HCS models (i.e. the cascade network models). The diagram below illustrates the overall approach. We generate normalized probabilities P1 and P2 for the HMM trained on the human control data. The relationsip between these normalized probabilites defines the similarity measure. As an example, we have applied this validation procedure to the learning of human driving.  

(a) (b)
Stan's stability profile (a), and Oliver's stability profile (b), where orange and yellow colors indicate a successful maneuver through the scurve, the red indicates a marginally successful maneuver, and the brown indicates an unsuccessful maneuver.
[1]  M. Nechyba and Y. Xu, Stochastic Similarity for Validating Human Control Strategy Models, Proc. IEEE Conf. on Robotics and Automation, vol. 1, pp. 27883, 1997.  
[2]  M. Nechyba and Y. Xu, Human Control Strategy: Abstraction, Verification and Replication, to appear in IEEE Control Systems Magazine, 1997.  
[3]  M. Nechyba and Y. Xu, On the Fidelity of Human Skill Models, Proc. IEEE Int. Conference on Robotics and Automation, vol. 3, pp. 268893, 1996.  
[4]  M. Nechyba and Y. Xu, Human Skill Transfer: Neural Networks as Learners and Teachers, Proc. IEEE Int. Conference on Intelligent Robots and Systems, vol. 3, pp. 3149, 1995.  
[5]  M. Nechyba and Y. Xu, Neural Network Approach to Control System Identification with Variable Activation Functions, Proc. IEEE Int. Symp. on Intelligent Control, vol. 1, pp. 35863, 1994.  
[6]  M. Nechyba and Y. Xu, Stochastic Similarity for Validating Human Control Strategy Models, Technical Report, CMURITR9629, Carnegie Mellon University, 1996.  
[7]  M. Nechyba and Y. Xu, Towards Human Control Strategy Learning: Neural Network Approach with Variable Activation Functions, Technical Report, CMURITR9509, Carnegie Mellon University, 1995. 