Data‐Driven Inversion of Linear MIMO Systems by Piecewise‐Constant Inputs

ABSTRACT

This paper investigates a data‐driven inversion method for linear square MIMO systems employing piecewise‐constant inputs. The goal is to compute an input function that enforces, in minimum time, output interpolation at prescribed time instants, subject to a bound on the control effort, without explicit knowledge of the system model. Using only step‐response data, the inversion problem is formulated as the solution of a block Toeplitz linear equation whose blocks are the Markov parameters of the system. A bisection algorithm is then used to compute the minimum feasible control time. The analytical results show that, for sufficiently small switching time, the inverse Toeplitz operator norm scales inversely with the switching time. Moreover, local convergence of the bisection algorithm is established by proving local monotonicity of the actual control norm. The impact of measurement noise on the computed control is quantified, and a data‐smoothing procedure is suggested to mitigate noise effects. The effectiveness of the method is investigated on the linearized four‐tankbenchmark system, including both noise‐free and noisy scenarios.