Continuous-Time Nonlinear Model Predictive Tracking Control with Input Constraints Using Feedback Linearization

Abstract

This paper presents a tracking control scheme for nonlinear systems with input constraints by combining the continuous-time model predictive control and the feedback linearization. Although there are some similar combinations for nonlinear systems presented in literature, their formulations are complex and massive computations are unavoidable. This study aims to simplify the formulations and reduce the computational loads by imposing the Laguerre functions to approximate the control signals. Since the Laguerre functions have the property of orthogonality, the tracking control problem, by applying the combination, leads to a constrained quadratic optimization problem in terms of the coefficients associated with the Laguerre functions, where the input constraints are converted so as to be state-dependent, based on feedback linearization. The Hildreth’s quadratic programming algorithm is used to solve the optimization problem, so as to determine the coefficients. Moreover, this study also summarizes some common linearization schemes and shows their pros and cons. Furthermore, the proposed approach is applied to two illustrative examples, and the control performances are compared with those by linear control strategies combined with those linearization schemes.

Editorial of the Special Issue “Advanced Robotics Applications in Industry”

“…In the first paper, presented by Kuo and Pongpanyaporn [1] a tracking control strategy is proposed for nonlinear systems based on the utilization of a combination of continuoustime model predictive control and feedback linearization. While similar combinations have been presented in the literature, they often involve complex formulations and significant computations.…”

“…Despite the publication of the above-mentioned manuscripts, the corresponding works will be subject to further development, so that open challenges derived from the field can be adequately addressed. Following the literature investigation performed by the authors in [7] as well as from the rest of the research works [1][2][3][4][5][6], the recent Industry 4.0 technological advances have facilitated engineers to solve complex problems. however, new challenges are also emerging.…”

Trajectory Tracking of a Data-Based Model of a Two-Link Robotic Manipulator Using Model Predictive Controller

“…However, economic robots need sophisticated control to ensure precise position tracking. Many works of literature have extensively examined model-based control of robotic arms, including control in joint and task space [4][5][6][7][8][9][10][11][12]. Due to their potential to improve control performance in comparison to conventional control approaches and potentially allow the use of affordable hardware or compliant robots in tasks where highprecision trajectory tracking is required, data-driven models for controller design applied to robotic manipulation have attracted increasing interest in recent years.…”