Quasi - Steady Approximation and Adaptive Nonlinear Controls ∗

Accurate and realistic mathematical modeling is always essential for conventional computer simulations such as CFD calculations of reacting flow systems. However, if the goal is not merely to make passive “what if” predictions but rather to use the available “actuators” in the system to exert active control over the dynamical behaviors of certain measured output variables, then the problem becomes a control problem. The present paper shows that (for finite dimensional dynamical systems only) it it possible to find “control laws” to accomplish the desired control objectives without having detailed knowledge of the mathematical model— provided reliable and accurate sensor measurements of the output variables are available.