Adaptive Receding Horizon Control For Nonlinear Systems Exemplified by Two Coupled van der Pol Oscillators

A heuristic “Adaptive Receding Horizon Controller” (ARHC) approach was recently suggested in which tracking the “nominal trajectory” was formulated as minimizing a cost term by the use of a “heavy dynamic model”, and the so obtained “optimized path“ was adaptively tracked by the use of a “less heavy” engine for which only an approximate model was available. For tracking this optimized trajectory a Fixed Point Iteration-based solution was suggested on the basis of Banach's Fixed Point Theorem. For reducing the computational burden of optimization the heavy dynamic model was not taken into account as a constraint (as usually it used to be), but it was directly used in building up the horizon with forward differences. As a consequence the number of the free variables of optimization was drastically decreased, and the computational burden of gradient reduction was spared, too. In this paper this method is further investigated by the use of two nonlinearly coupled van der Pol oscillators as a paradigm of nonlinear dynamical system. Furthermore, the usual quadratic cost functions were substituted by much simpler ones. In the paper simulation results exemplify the operation of the method that seems to be promising for breaking out of the realm of the traditional quadratic cost functions, and linear time-invariant dynamic models.