A synthesis approach of fast robust MPC with RBF-ARX model to nonlinear system with uncertain steady status information
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A synthesis approach of fast robust MPC with RBF-ARX model to nonlinear system with uncertain steady status information Xiaoying Tian 1 & Hui Peng 1
&
Feng Zhou 2 & Xiaoyan Peng 3
# Springer Science+Business Media, LLC, part of Springer Nature 2019
Abstract The mechanical model of a plant in real industry is usually difficult to obtain. This paper integrates the data-driven RBF-ARX modeling method and a fast Robust Model Predictive Control (RMPC) approach to achieving output-tracking control of a nonlinear system with unknown steady status information. Considering the large online computational burden of online RMPC, this paper proposes a RBF-ARX model-based efficient robust predictive control (RBF-ARX-ERPC) approach. First, based on the RBF-ARX model, a polytopic uncertain linear parameter varying (LPV) state-space model is built to represent the dynamic behavior of the system; next, two convex polytopic sets are constructed to wrap the globally nonlinear behavior of the system. Then, an optimization problem including several linear matrix inequalities (LMIs) is formulated, which is solved offline to synthesize a sequence of explicit control laws corresponding to a sequence of asymptotically stable invariant ellipsoids in the state space, of which all the optimization results are stored in a look-up table. For the real-time control online, it only involves simple state-vector computation and bisection search. Two simulation examples, i.e. the modeling and control of a widely used continuously stirred tank reactor (CSTR) and a linear one-stage inverted pendulum (LOSIP) system, and the real-time control experiments on an actual LOSIP plant are provided to demonstrate the effectiveness of the proposed RBF-ARX model-based efficient RPC approach. Keywords RBF-ARX model . Predictive control . Offline computation . Robustness and stability . CSTR process . LOSIP system . Real-time control
1 Introduction Model predictive control (MPC) has been widely used in real industry, since it can handle systematic constraints explicitly when optimizing system performance. As we all know, the plants in real industry are usually nonlinear, simultaneously, the operation conditions often undergo significant changes, which may make control performance of MPC deteriorate drastically. Mayne [1] said that the presence of uncertainty
* Hui Peng [email protected] 1
School of Automation, Central South University, Changsha 410083, Hunan, China
2
College of Electronic Information and Electrical Engineering, Changsha University, Changsha 410003, Hunan, China
3
College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, Hunan, China
in MPC, whether in the form of additive disturbances, state estimation error or model error, is still a major challenge. In the past few decades, many researchers have devoted their attentions to robust MPC researches, and they have acquired many effective achievements. For RMPC algorithms online, Kothare, Balakrishnan and Morari [2] proposed a RMPC algorithm that uses LMIs to solve f
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