An FAS-ARMAX Approach to Minimum Variance Control for Nonlinear MIMO Manipulators

This paper investigates the optimal regulation problem of nonlinear multi-input multi-output (MIMO) manipulators subject to process and measurement stochastic noises. Achieving regulation is challenging due to the highly coupled nonlinear dynamics and the infinite historical data sequences generated by stochastic disturbances. Although the fully actuated system (FAS) approach can transform the nonlinear dynamics into a linear double-integrator structure, this transformation by itself is insufficient to ensure the optimal regulation performance, as it cannot directly handle unmeasurable states and random white noises. To address this issue, we propose a systematic control framework that transforms the linearized FAS model into a fixeddimension Auto-Regressive Moving Average with eXogenous inputs (ARMAX) formulation for Minimum Variance Control (MVC). First, to jointly address the stochastic noises and infinite historical sequences, we construct a discrete-time input-output model by integrating a steady-state Kalman filter and the Cayley-Hamilton theorem into the system transformation. Besides, a rigorous Z-domain analysis based on the Maximum Modulus Principle is carried out to establish the structural identifiability of the Moving Average (MA) term. Finally, simulation results demonstrate that the proposed method effectively suppresses random disturbances.