The Bernstein Polynomials Based Globally Optimal Nonlinear Model Predictive Control

  • Bhagyesh V. Patil
  • Ashok KrishnanEmail author
  • Foo Y. S. Eddy
  • Ahmed Zidna
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 991)


Nonlinear model predictive control (NMPC) has shown considerable success in the control of a nonlinear systems due to its ability to deal directly with nonlinear models. However, the inclusion of a nonlinear model in the NMPC framework potentially results in a highly nonlinear (usually ‘nonconvex’) optimization problem. This paper proposes a solution technique for such optimization problems. Specifically, this paper proposes an improved Bernstein global optimization algorithm. The proposed algorithm contains a Newton-based box trim operator which extends the classical Newton method using the geometrical properties associated with the Bernstein polynomial. This operator accelerates the convergence of the Bernstein global optimization algorithm by discarding those regions of the solution search space which do not contain any solution. The utility of this improved Bernstein algorithm is demonstrated by simulating an NMPC problem for tracking multiple setpoint changes in the reactor temperature of a continuous stirred-tank reactor (CSTR) system. Furthermore, the performance of the proposed algorithm is compared with those of the previously reported Bernstein global optimization algorithm and a conventional sequential-quadratic programming based sub-optimal NMPC scheme implemented in MATLAB.


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Bhagyesh V. Patil
    • 1
  • Ashok Krishnan
    • 1
    • 2
    Email author
  • Foo Y. S. Eddy
    • 2
  • Ahmed Zidna
    • 3
  1. 1.Cambridge Centre for Advanced Research and Education in SingaporeSingaporeSingapore
  2. 2.School of Electrical and Electronic EngineeringNanyang Technological UniversityNanyangSingapore
  3. 3.LGIPMUniversité de LorrainLorrainFrance

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