Unified Performance Control for Non-Square Nonlinear Systems with Relaxed Controllability

TL;DR

This paper develops a unified control approach for non-square nonlinear systems with relaxed controllability, enabling flexible performance specifications and fault tolerance even under actuator faults and unknown control gains.

Contribution

It introduces a generalized controllability condition and a backstepping design that handles non-square systems with faults and uncertainties without structural modifications.

Findings

The proposed controller achieves prescribed performance under relaxed controllability.

The method is effective for systems with actuator faults and unknown control gains.

Numerical simulations validate the theoretical results.

Abstract

In this paper, we investigate the problem of unified prescribed performance tracking for a class of non-square strict-feedback nonlinear systems under relaxed controllability conditions. By using a skillful matrix decomposition and introducing some feasible auxiliary matrices, a more generalized controllability condition than the current state of the art is constructed, which can be applied to both square and non-square nonlinear systems subject to actuator faults and unknown yet time-varying control gain. Incorporating the relaxed controllability conditions and the uniform performance specifications into the backstepping design procedure, a prescribed performance fault-tolerant controller is developed that can achieve different performance demands without modifying the controller structure, which is more flexible and practical.In addition, the destruction of the system stability by unknown controllability auxiliary matrices and unknown nonlinearities is circumvented by embedding the available core information of the state-dependent uncertainties into the design procedure. Both theoretical analysis and numerical simulation demonstrate the effectiveness and benefits of the proposed method.