State Constrained Model Reference Adaptive Control with Input Amplitude and Rate Limits
Poulomee Ghosh, Shubhendu Bhasin
TL;DR
The paper tackles safe tracking of an uncertain MIMO LTI plant by enforcing bounds on the state $x$, the input $u$, and the input rate $\dot{u}$ within user-defined sets. It introduces a two-layer barrier Lyapunov function (BLF)-based MRAC, treating $u$ and $\dot{u}$ as constrained states and employing three BLFs to guarantee constraint satisfaction. Projection-based adaptive laws for $\hat{K}_x$ and $K_u$ are provided along with verifiable feasibility conditions $C1$-$C2$, ensuring all closed-loop signals remain bounded. A simulation on aircraft lateral dynamics shows constraint satisfaction and smoother control relative to robust MRAC, highlighting practical value for safety-critical applications.
Abstract
This paper proposes a robust model reference adaptive controller (MRAC) for uncertain multi-input multi-output (MIMO) linear time-invariant (LTI) plants with user-defined constraints on the plant states, input amplitude, and input rate. The proposed two-layer barrier Lyapunov function (BLF)-based control design considers the input and the input rate as states that are constrained using two BLFs in the first layer, while another BLF in the second layer constrains the plant states. The adaptive control law ensures that the plant states, input amplitude, and input rate remain within the user-defined safe sets despite unmatched bounded disturbances. Sufficient conditions for the existence of a feasible control policy are also provided. To the best of the authors' knowledge, this is the first optimization-free method that imposes user-defined constraints on the state, input, and input rate and also provides verifiable feasibility conditions in the presence of parametric uncertainties and disturbances. Simulation results demonstrate the effectiveness of the proposed algorithm.