Given a static plant described by a differentiable input-output function, which is completely unknown, but whose Jacobian takes values in a known polytope in the matrix space, we consider the problem of tuning the output (i.e., driving the output to a desired value), by suitably choosing the input. To this aim, we assume to have at our disposal a discrete sequence of trials only, as it happens, for instance, when we iteratively run a software, with new input data at each iteration, in order to achieve the desired output value. In this paper we prove that, if the polytope is robustly non-singular (or has full row rank, in the general non-square case), then a suitable discrete-time tuning law drives the output to the desired point. The computation of the tuning law is based on a convex-optimisation problem to be solved on-line. An application example is proposed to show the effectiveness of the approach.
Discrete-Time Trials for Tuning without a Model / Blanchini, Franco; Fenu, Gianfranco; Giordano, Giulia; Pellegrino, Felice Andrea. - 50:1(2017), pp. 1539-1544. (Intervento presentato al convegno 20th World Congress of the International Federation of Automatic Control (IFAC 2017 World Congress) tenutosi a Toulouse, France nel July 2017) [10.1016/j.ifacol.2017.08.306].
Discrete-Time Trials for Tuning without a Model
Giordano, Giulia;
2017-01-01
Abstract
Given a static plant described by a differentiable input-output function, which is completely unknown, but whose Jacobian takes values in a known polytope in the matrix space, we consider the problem of tuning the output (i.e., driving the output to a desired value), by suitably choosing the input. To this aim, we assume to have at our disposal a discrete sequence of trials only, as it happens, for instance, when we iteratively run a software, with new input data at each iteration, in order to achieve the desired output value. In this paper we prove that, if the polytope is robustly non-singular (or has full row rank, in the general non-square case), then a suitable discrete-time tuning law drives the output to the desired point. The computation of the tuning law is based on a convex-optimisation problem to be solved on-line. An application example is proposed to show the effectiveness of the approach.File | Dimensione | Formato | |
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