Studying various cost functions by nonlinear programming for the control of an underactuated mechanical system

Abstract

The traditional “Receding Horizon Controller (RHC)” is a heuristic approach based on the concept of “Nonlinear Programming (NP)” that in the most general cases applies Lagrange’s “Reduced Gradient (RG)” method. Since its realization requires a huge amount of numerical calculations, in the practice it is often restricted to quadratic cost functions and “Linear Time Invariant (LTI)” approximation of the dynamic model of the controlled system as “Linear Quadratic Regulator (LQR)”. To release these restrictions a novel approach was recently invented that directly drives the gradient of the “auxiliary function” near zero by replacing the RG with a fixed point-based iteration. It was also shown that the same iteration technique allows the introduction of an “Adaptive Receding Horizon Controller (ARHC)”. Since the convergence of the ARHC strongly depends on the structure of the cost contributions in this paper the operation of the classic RG-based RHC is investigated in the control of the “TORA” system that is a popular paradigm for benchmarking purposes. Conclusions are drawn for the allowable or recommended parameter settings for the cost contributions.