Real-time optimization of dynamic systems using multiple units

Model-free, unconstrained, real-time optimization of the operating point of a dynamic system involves forcing the gradient of the cost function to zero. In these methods, gradient estimation is a key issue, for which methods that perturb the input over time are used. Tile main limitation of these methods is that they require tile dynamics of the adaptation to be two orders of magnitude slower than tile system dynamics. To circumvent this limitation, a novel, simple, yet effective way of estimating the gradient is presented in this paper. Multiple identical units with non-identical inputs are used and the gradient is computed via finite difference. Thus, the perturbation is along the 'unit dimension', thereby allowing a faster adaptation. Tile convergence of the scheme is rigorously established via Lyapunov analysis. An illustrative example is provided where the proposed scheme resulted in an 100-fold improvement in tile time needed for convergence. Copyright (C) 2007 John Wiley & Sons, Ltd.