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Peter Bakaráč and Michal Kvasnica

Abstract

This paper presents a fast way of implementing nonlinear model predictive control (NMPC) using the random shooting approach. Instead of calculating the optimal control sequence by solving the NMPC problem as a nonlinear programming (NLP) problem, which is time consuming, a sub-optimal, but feasible, sequence of control inputs is determined randomly. To minimize the induced sub-optimality, numerous random control sequences are selected and the one that yields the smallest cost is selected. By means of a motivating case study we demonstrate that the random shooting-based approach is superior, from a computational point of view, to state-of-the-art NLP solvers, and features a low level of sub-optimality. The case study involves a continuous stirred tank reactor where a fast multi-component chemical reaction takes place.

Open access

Martin Klaučo, Slavomír Blažek and Michal Kvasnica

Abstract

A path planning problem for a heterogeneous vehicle is considered. Such a vehicle consists of two parts which have the ability to move individually, but one of them has a shorter range and is therefore required to keep in a close distance to the main vehicle. The objective is to devise an optimal path of minimal length under the condition that at least one part of the heterogeneous system visits all desired waypoints exactly once. Two versions of the problem are considered. One assumes that the order in which the waypoints are visited is known a priori. In such a case we show that the optimal path can be found by solving a mixed-integer second-order cone problem. The second version assumes that the order in which the waypoints are visited is not known a priori, but can be optimized so as to shorten the length of the path. Two approaches to solve this problem are presented and evaluated with respect to computational complexity.

Open access

Juraj Števek, Alexander Szűcs, Michal Kvasnica, Miroslav Fikar and Štefan Kozák

Given a set of input-output measurements, the paper proposes a method for approximation of a nonlinear system by a piecewise affine model (PWA). First step of the two-stage procedure is identification from input-output data, in order to obtain an appropriate nonlinear function in analytic form. The analytic expression of the model can be represented either by a static nonlinear function or by a dynamic system and can be obtained using a basis function expansion modeling approach. Subsequently we employ nonlinear programming to derive optimal PWA approximation of the identified model such that the approximation error is minimized. Moreover, we show that approximation of multivariate systems can be transformed into a series of one-dimensional approximations, which can be solved efficiently using standard optimization techniques.