Model reference safety‐critical adaptive control for a class of nonlinearly parameterized systems

Abstract

AbstractSafety is the most fundamental problem of safety‐critical systems. Safety control addresses the problem whether a given unsafe region of the state space can be avoided by a specific control‐input. Moreover, linearly parameterized dynamical system is a general assumption in most safety‐critical adaptive control literature; however, unknown parameters in real systems are usually nonlinear. The control problem of nonlinearly parameterized systems is really difficult without linear‐in‐the‐parameters (LIP) assumptions, which tends to be complicated and computationally intensive. In this paper, a novel model reference safety‐critical adaptive control (MRAC) approach is proposed for a class of nonlinearly parameterized systems. The proposed approach involves a novel controller architecture with a modified update law, which specifically filters out the unsafe behavior (the system is in a state which the system cannot operate normally, i.e., the given unsafe region), while preserving favorable tracking capability and robustness. The novelty of this paper is that the nonlinearly parameterized systems can be enforced safety, without LIP assumptions and complex calculations. Most importantly, this approach is effective for nonlinearly parameterized systems as well as linearly parameterized systems. Finally, three illustrative numerical examples are presented to demonstrate the effectiveness of the proposed design approach.