Preliminary Design of a Receding Horizon Controller Supported by Adaptive Feedback

Abstract

Receding horizon controllers are special approximations of optimal controllers in which the continuous time variable is discretized over a horizon of optimization. The cost function is defined as the sum of contributions calculated in the grid points and it is minimized under the constraint that expresses the dynamic model of the controlled system. The control force calculated only for one step of the horizon is exerted, and the next horizon is redesigned from the measured initial state to avoid the accumulation of the effects of modeling errors. In the suggested solution, the dynamic model is directly used without any gradient reduction by using a transition between the gradient descent and the Newton–Raphson methods to achieve possibly fast operation. The optimization is carried out for an "overestimated" dynamic model, and instead of using the optimized force components the optimized trajectory is adaptively tracked by an available approximate dynamic model of the controlled system. For speeding up the operation of the system, various cost functions have been considered in the past. The operation of the method is exemplified by simulations made for new cost functions and the dynamic control of a 4-degrees-of-freedom SCARA robot using the simple sequential Julia language code realizing Euler integration.