Constrained Tracking Control of MIMO Nonlinear Systems With Discontinuous References and Unknown Dynamics

• Published in: IEEE transactions on automation science and engineering Vol. 22; pp. 15139 - 15149
• Main Authors: Zhang, Jin-Xi, Qi, Wei-Li, Chai, Tianyou
• Format: Journal Article
• Language: English
• Published: IEEE 2025
• Subjects: Discontinuous references; Hands; Jacobian matrices; Mathematical models; MIMO nonlinear systems; Neural networks; Nonlinear dynamical systems; output constraints; Safety; System dynamics; tracking control; Trajectory; unknown dynamics; Vectors; Vehicle dynamics
• ISSN: 1545-5955; 1558-3783
• DOI: 10.1109/TASE.2025.3566443

This paper is dealt with the tracking control problem for the multi-input multi-output (MIMO) block-triangular nonlinear systems with output constraints under discontinuous references. It is focused on the case where the system exhibits inherent nonlinearities, e.g., radically unbounded nonlinearities, and totally unknown dynamics. This renders the existing solutions infeasible. To surmount this challenge, a novel hybrid tracking control strategy composed of a robust decoupling constrained controller and a proportional controller is devised in this paper. It guarantees that the system outputs evolve within the prescribed constraint bands and track the discontinuous references with the tunable settling time and accuracy. Moreover, the controller shows a significant simplicity. No attempt is made for parameter identification, function approximation, disturbance estimation, derivative calculation or command filtering, despite the unknown system dynamics and the recursive control design. The theoretical findings are validated by a comparative experiment on a 2-DOF serial flexible link (2DSFL) robot. Note to Practitioners-MIMO nonlinear systems are widely present in practice, e.g., robotic manipulators, ground vehicles and aircrafts. For operational specifications and safety considerations, they are always subject to output constraints. On the other hand, building an exact mathematical model for a practical system is unfulfillable. The existing constrained control methods for uncertain MIMO nonlinear systems work for the case where the control distribution matrix is norm-bounded or the control distribution matrix, additive nonlinearity, Jacobian matrix or disturbance bound is known. Moreover, the control algorithms are complex due to the dependence on parameter identification, function approximation and disturbance estimation. Additionally, they fail to be applied to discontinuous references, which are common in vehicle guidance, industrial electronics and robotic applications. The related tracking control approaches are effective for the regular discontinuity of the reference, the bounded nonlinearities of the system, the known system dynamics, or the known bounding functions of the nonlinearities. To overcome the above challenges, a low-complexity hybrid tracking control strategy composed of a robust decoupling constrained controller and a proportional controller is developed in this paper. It steers the system outputs to track the discontinuous references without constraint violation. The result of a comparative experiment on a 2DSFL robot show the effectiveness and advantage of the proposed approach.