IEEE Access (Jan 2024)

RBF-ARX Model-Based Robust Predictive Control Strategy With One Degree-of-Freedom

  • Xiaoying Tian,
  • Pengfei Gao,
  • Jingjing Yan,
  • Yuqing Zheng

DOI
https://doi.org/10.1109/ACCESS.2024.3466907
Journal volume & issue
Vol. 12
pp. 141179 – 141189

Abstract

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To make a trade-off between computation burden and control performance of the existing robust MPC algorithms, this paper proposed an improved robust MPC strategy considering one degree-of-freedom for control variable(s), which makes a trade-off between computation burden and control performance. Firstly, based on RBF-ARX (state-dependent Auto-Regressive model with eXogenous input and Radial Basis Function network type coefficients) model, a polytopic uncertain linear parameter varying (LPV) model can be built, and two convex polytopic sets can be constructed to wrap the globally nonlinear behavior of the system. Then, a quasi-min-max MPC problem was formulated as a complex linear matrix inequalities (LMIs) optimization problem, which can be solved through a fast computation strategy that contains an online algorithm and an offline algorithm. To reduce its conservatism, this paper introduced one free variable(s) to control variable(s) and designed a new online algorithm, which means that a simple online optimization problem was formulated to solve for the introduced free variable(s). During online control process, the new algorithm only needs to execute simple state-vector computation and bisection search, and then solves a simple LMI optimization problem to obtain free variable(s). In addition, the stability of the closed-loop system was studied. Finally, two examples, i.e. a widely used continuously stirred tank reactor and a linear one-stage inverted pendulum, are provided to test the effectiveness of the proposed RBF-ARX model-based efficient robust predictive control approach with one degree-of-freedom for control variable(s).

Keywords