Admissibility-Preserving Control for Multi-Input Systems with Joint Capacity Constraints

2026-09-30

AI Summary

This study addresses the limitation of conventional per-channel bounding methods for multi-input nonlinear systems under joint capacity constraints, which tend to suppress feasible control directions. To overcome this, we propose an Anisotropic Joint Feasibility-Preserving Invariant Reachability (AJ-APIR) framework that explicitly exploits the geometry of joint constraints to decouple normal and tangential components. By integrating backstepping with spectral decomposition of state-dependent gain matrices, the method redistributes control effort without sacrificing tracking performance. Theoretical analysis guarantees forward invariance of the jointly feasible set and exponential convergence of the tracking error to zero. Simulation results further validate the effectiveness of the proposed approach under power budget constraints.

Abstract

This paper addresses the control of multi-input strict-feedback nonlinear systems subject to a joint capacity constraint, in which the admissible input set is a coupled subset of the individual actuator limits. Unlike existing constraint-handling methods that enforce actuator bounds channel by channel and may unnecessarily suppress admissible control directions, we develop an Anisotropic Joint-Admissibility-Preserving Input Realization (AJ-APIR) framework that explicitly exploits the geometry of the joint constraint. The proposed realization constructs a state-dependent gain matrix whose spectral decomposition separates the commanded input into normal and tangential directions relative to the constraint boundary. The normal component is attenuated as the boundary is approached, while the tangential component is preserved, which allows the admissible control effort to be redistributed without loss of tracking authority. Integrated with a backstepping controller, the AJ-APIR framework guarantees forward invariance of the joint admissible set for all time. We establish exponential convergence of the tracking error to zero together with uniform boundedness of all closed-loop signals, and characterize the resulting command-demand behavior under the joint constraint. Simulation results for a representative second-order, two-input nonlinear system subject to a power-budget constraint demonstrate the efficacy of the proposed method to enforce the joint input constraint.

Problem

• multi-input nonlinear systems
• joint capacity constraints
• strict-feedback systems
• admissibility-preserving control
• actuator limits

Innovation

• Joint capacity constraint
• Anisotropic input realization
• Spectral decomposition
• Strict-feedback nonlinear systems
• Backstepping control