# Application of Heavy and Underestimated Dynamic Models in Adaptive Receding Horizon Control Without Constraints

## DOI:

https://doi.org/10.52846/stccj.2022.2.2.36## Keywords:

Newton-Raphson Algorithm, Gradient Descent Algorithm, Reduced Gradient Algorithm, Receding Horizon Control, Fixed Point Iteration-based Adaptive Control## Abstract

In the heuristic “Adaptive Receding Horizon Controller” (ARHC) the available dynamic model of the controlled system usually is placed in the role of a constraint under which various cost functions can be minimized over a horizon. A possible secure design can be making calculations for a “heavy dynamic model” that may produce high dynamical burden that is efficiently penalized by the cost functions and instead of the original nominal trajectory results a “deformed” one that can be realized by the controlled system of “less heavy dynamics”. In the lack of accurate system model a fixed point iterationbased adaptive approach is suggested for the precise realization of this deformed trajectory. To reduce the computational burden of the control the usual approach in which the dynamic model is considered as constraint and Lagrange-multipliers are introduced as co-state variables is evaded. The heavy dynamic model is directly built in the cost and the computationally greedy Reduced Gradient Algorithm is replaced by a transition between the simple and fast Newton-Raphson and the slower Gradient Descent algorithms (GDA). In the paper simulation examples are presented for two dynamically coupled van der Pol oscillators as a strongly nonlinear system. The comparative use of simple nondifferentiable and differentiable cost functions is considered, too.

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*Syst. Theor. Control Comput. J.*, vol. 2, no. 2, pp. 1–8, Dec. 2022, doi: 10.52846/stccj.2022.2.2.36.