Low-Complexity Control for a Class of Uncertain MIMO Nonlinear Systems under Generalized Time-Varying Output Constraints (extended version)
This addresses control challenges for uncertain nonlinear systems with complex constraints, such as in robotics, but is incremental as it builds on existing constraint-handling methods.
The paper tackles the problem of satisfying multiple time-varying output constraints in uncertain MIMO nonlinear systems, even when constraints are coupled or infeasible, by introducing a control framework that ensures convergence to the constrained set within finite time and includes an online mechanism for handling infeasibilities, validated through mobile robot simulations.
This paper introduces a novel control framework to address the satisfaction of multiple time-varying output constraints in uncertain high-order MIMO nonlinear control systems. Unlike existing methods, which often assume that the constraints are always decoupled and feasible, our approach can handle coupled time-varying constraints even in the presence of potential infeasibilities. First, it is shown that satisfying multiple constraints essentially boils down to ensuring the positivity of a scalar variable, representing the signed distance from the boundary of the time-varying output-constrained set. To achieve this, a single consolidating constraint is designed that, when satisfied, guarantees convergence to and invariance of the time-varying output-constrained set within a user-defined finite time. Next, a novel robust and low-complexity feedback controller is proposed to ensure the satisfaction of the consolidating constraint. Additionally, we provide a mechanism for online modification of the consolidating constraint to find a least violating solution when the constraints become mutually infeasible for some time. Finally, simulation examples of trajectory and region tracking for a mobile robot validate the proposed approach.