Weak-duality in worst-case adaptive control

The worst-case dual control problem under bounded disturbances and modelling errors is formulated and approximate solutions derived in some simple cases. Comparison with worst-case time-domain design illustrates the potential advantage of dual schemes over traditional self-tuning control. Synergetic interaction between identification and control can give performance guarantees by giving bounds on overshoot and tracking error in a deterministic description of the problem. To enforce the synergic interaction between identification and control for more complicated models, a combined criterion is introduced which involves a worst-case loss-function of identification and predicted tracking performance. A simulation example illustrates the potential performance of the method.