A Unified Approach for Tracking Control of MIMO Nonlinear Systems Under Unknown Control Directions and Irregular Constraints

In this work, a unified state feedback control scheme is proposed for Multi-Input Multi-Output (MIMO) nonlinear systems subject to irregular output constraints and unknown control directions. In contrast to most existing state-of-the-art works, the constraints considered in this work can not only be asymmetric but can also appear in stages, sometimes being positive or negative. The designed controller can be applied to scenarios with or without constraints, without the need to modify or switch its structure. Moreover, it does not rely on the minimum-maximum values (MMVs) of the constraints, making it easier to implement. In addition, the issue of continuously increasing parameters in the Nussbaum function is addressed by integrating the designed bounding functions with the proposed barrier functions. This integration ensures the effectiveness of our approach regardless of the presence or absence of constraints. The effectiveness and benefits of the proposed method are verified by simulations on a planar two-link robotic manipulator.
Note to Practitioners
—In the majority of existing works, only scenarios with consistently present or consistently absent constraints on the system output or states are typically considered. As a result, the control methods proposed in those works are limited to either one of these scenarios, but not both. The objective of this paper is to provide a practical control solution that is suitable for both cases without the need for any switching. Moreover, in most existing works, it is necessary to possess the minimum-maximum values (MMVs) of the constraint functions. However, acquiring this information in practice entails a substantial computational burden. In this work, this restriction has been removed, thereby reducing the application conditions and increasing practicality. In addition, this work is applicable even when the control direction is unknown. This approach has been shown to be feasible through preliminary simulation experiments. In future research, the physical reality and its application to the collision avoidance control of multi-agent systems will be tried.