Suboptimal Adaptive Receding Horizon Control Using Simplified Nonlinear Programming

In this paper, an "Adaptive Receding Horizon Controller (ARHC)" is exemplified in the suboptimal control of a Furuta pendulum. A dynamic model of strongly overestimated inertia and friction parameters is used in an RHC controller to track the nominal trajectory under cost terms penalizing the control forces. The so obtained "optimized" trajectory is tracked by an adaptive controller that uses a realistic approximate dynamic model of the controlled system. Since the approximate and the actual model contain considerably smaller inertia and friction parameters than that used for optimization the cautiously optimized trajectory can be precisely tracked by the actual system without suffering from heavy force burdens. The adaptivity is guaranteed by a "Fixed Point Iteration"-based approach that in this manner easily can be combined with the mathematical framework of optimal controllers. Instead of using Lagrange multipliers, the optimization happens through explicitly applying the dynamic model in forward Euler integration. The operation of the method is exemplified via numerical simulations.