Adaptive System Design

Origin. Soviet control theory (Feldbaum, Tsypkin, Fomin); self-adjusting and self-organizing systems research (1960s-1980s).

Mechanism. An adaptive system tunes its own parameters in response to persistent error. The controller has two loops: an inner loop that performs control using current parameters, and an outer loop that adjusts those parameters when performance degrades. The outer loop is slower than the inner loop by at least an order of magnitude, so the inner loop reaches quasi-equilibrium before the outer loop acts.

Procedure. Identify the control parameters and their nominal values. Implement the nominal controller. Monitor performance: are the controlled variables staying within bounds? If persistent deviation occurs, infer that the environment has changed and adjust the parameters in the direction that reduces error. The adjustment must be slow (high inertia) to avoid chasing noise; use a long averaging window. Include a forgetting mechanism: if the adjustment moves parameters far from nominal, check whether the environment has changed or whether the model is wrong.

Applies to. Systems operating in non-stationary environments, where the optimal control changes over time but changes slowly relative to the control action frequency.

Limitations. Adaptation is stabilizing only if the environment changes slowly relative to the adaptation rate; if the environment changes faster, adaptation chases a moving target and produces oscillation. Also: adaptation can mask system degradation; if a component is failing gradually, the adaptive layer compensates, and the failure is not detected until the component fails completely and suddenly. Adaptation must not fully compensate; retain some error signal to indicate that something is wrong.