Equivalence between Neighboring-Extremal Control and Self-Optimizing Control for the Steady-State Optimization of Dynamical Systems

The problem of steering a dynamical system toward optimal steady-state performance is considered. For this purpose, a static optimization problem can be formulated and solved. However, because of uncertainty, the optimal steady-state inputs can rarely be applied directly in an open-loop manner. Instead, plant measurements are typically used to help reach the plant optimum. This paper investigates the use of optimizing control techniques for input adaptation. Two apparently different techniques of enforcing steady-state optimality are discussed, namely, neighboring-extremal control and self-optimizing control based on the null-space method. These two techniques are compared for the case of unconstrained real-time optimization in the presence of parametric variations. It is shown that, in the noise-free scenario, the two methods can be made equivalent through appropriate tuning. Note that both approaches can use measurements that are taken either at successive steady-state operating points or during the transient behavior of the plant. Implementation of optimizing control is illustrated through a simulated CSTR example.