On Complexity Certification of Active-Set QP Methods with Applications to Linear MPC

Released on by Daniel Arnström
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  • On Complexity Certification of Active-Set QP Methods with Applications to Linear MPC Book Detail

  • Author : Daniel Arnström
  • Release Date : 2021-03-03
  • Publisher : Linköping University Electronic Press
  • Genre :
  • Pages : 45
  • ISBN 13 : 9179296920
  • File Size : 52,52 MB
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On Complexity Certification of Active-Set QP Methods with Applications to Linear MPC by Daniel Arnström PDF Summary

Book Description: In model predictive control (MPC) an optimization problem has to be solved at each time step, which in real-time applications makes it important to solve these efficiently and to have good upper bounds on worst-case solution time. Often for linear MPC problems, the optimization problem in question is a quadratic program (QP) that depends on parameters such as system states and reference signals. A popular class of methods for solving such QPs is active-set methods, where a sequence of linear systems of equations is solved. The primary contribution of this thesis is a method which determines which sequence of subproblems a popular class of such active-set algorithms need to solve, for every possible QP instance that might arise from a given linear MPC problem (i.e, for every possible state and reference signal). By knowing these sequences, worst-case bounds on how many iterations, floating-point operations and, ultimately, the maximum solution time, these active-set algorithms require to compute a solution can be determined, which is of importance when, e.g, linear MPC is used in safety-critical applications. After establishing this complexity certification method, its applicability is extended by showing how it can be used indirectly to certify the complexity of another, efficient, type of active-set QP algorithm which reformulates the QP as a nonnegative least-squares method. Finally, the proposed complexity certification method is extended further to situations when enhancements to the active-set algorithms are used, namely, when they are terminated early (to save computations) and when outer proximal-point iterations are performed (to improve numerical stability).

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Nonlinear Model Predictive Control

Nonlinear Model Predictive Control

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During the past decade model predictive control (MPC), also referred to as receding horizon control or moving horizon control, has become the preferred control