Akademik Veri Yönetim Sistemi
CoDIT 2024, Valletta, Malta, 1 - 04 Temmuz 2024, ss.31-36, (Tam Metin Bildiri)
In this article, we investigate the application of Lagrange polynomials for compressing data vectors within the context of constrained model predictive control (MPC). Lagrange polynomials, traditionally used for interpolating among n data points, are leveraged in a novel manner to facilitate efficient representation and computation of control signals in MPC systems. The study demonstrates that Lagrange polynomials of degree n, designed to pass through n specified data points, can be utilized to compress input signal vectors in SISO/MIMO state-space models employed in MPC. By selectively choosing a subset of the original data vector sampled at a constant rate and constructing a Lagrange polynomial to interpolate through this subset, the remaining data points can be accurately estimated through interpolation. The application of Lagrange polynomials in this context enables significant reduction in computational complexity, crucial for real-time implementation of MPC algorithms particularly with longer prediction horizons. Moreover, by representing control signals within the prediction horizon using a fixed-size subset and exploiting Lagrange interpolation for the rest, the computational demands of solving the constrained quadratic optimization problem inherent in MPC become independent of the prediction horizon length. This innovation holds promise for enhancing the feasibility and efficiency of MPC controllers in controlling fast dynamical systems, where rapid decision-making is paramount.