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Reduced precision solution criteria for nonlinear model predictive control with the feasibility-perturbed sequential quadratic programming algorithm

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Abstract

We propose a novel kind of termination criteria, reduced precision solution (RPS) criteria, for solving optimal control problems (OCPs) in nonlinear model predictive control (NMPC), which should be solved quickly for new inputs to be applied in time. Computational delay, which may destroy the closed-loop stability, usually arises while non-convex and nonlinear OCPs are solved with differential equations as the constraints. Traditional termination criteria of optimization algorithms usually involve slow convergence in the solution procedure and waste computing resources. Considering the practical demand of solution precision, RPS criteria are developed to obtain good approximate solutions with less computational cost. These include some indices to judge the degree of convergence during the optimization procedure and can stop iterating in a timely way when there is no apparent improvement of the solution. To guarantee the feasibility of iterate for the solution procedure to be terminated early, the feasibility-perturbed sequential quadratic programming (FP-SQP) algorithm is used. Simulations on the reference tracking performance of a continuously stirred tank reactor (CSTR) show that the RPS criteria efficiently reduce computation time and the adverse effect of computational delay on closed-loop stability.

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Authors and Affiliations

  1. State Key Lab of Industrial Control Technology, Institute of Industrial Control, Department of Control Science and Engineering, Zhejiang University, Hangzhou, 310027, China

    Jiao-na Wan, Zhi-jiang Shao, Ke-xin Wang, Xue-yi Fang, Zhi-qiang Wang & Ji-xin Qian

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  1. Jiao-na Wan
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  2. Zhi-jiang Shao
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  3. Ke-xin Wang
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  4. Xue-yi Fang
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  5. Zhi-qiang Wang
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Correspondence to Zhi-jiang Shao.

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Project supported by the National Natural Science Foundation of China (Nos. 60934007 and 60974007) and the National Basic Research Program (973) of China (No. 2009CB320603)

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Wan, Jn., Shao, Zj., Wang, Kx. et al. Reduced precision solution criteria for nonlinear model predictive control with the feasibility-perturbed sequential quadratic programming algorithm. J. Zhejiang Univ. - Sci. C 12, 919–931 (2011). https://doi.org/10.1631/jzus.C10a0512

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