Neighborhood estimation in sensitivity-based update rules for real-time optimal control

Specht, Caroline; Gerdts, Matthias; Lampariello, Roberto

doi:10.23919/ecc51009.2020.9143701

Cited by 2 publications

(3 citation statements)

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“…The estimation of the neighborhoods in the theorem is difficult in general. A numerical approach can be found in [20]. For linear-quadratic problems it is known, see [21], that the solution depends piecewise linearly on the initial state.…”

Section: Sensitivity Analysis and Sensitivity Updates Docp(p N Nmentioning

confidence: 99%

Sensitivity updates for linear-quadratic optimization problems in multi-step model predictive control

Emam

Gerdts

2023

J. Phys.: Conf. Ser.

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The paper discusses how parametric sensitivity analysis can be used in certain model predictive control (MPC) schemes. The sensitivity analysis will be performed with regard to the initial state measurement and update schemes will be derived that speed-up the computations. Throughout we restrict the discussion to linear-quadratic optimal control problems in discrete time, which frequently arise in tracking tasks with MPC. The derived tools from sensitivity analysis can be embedded into MPC schemes with a prediction step and multi-step MPC schemes with re-optimization and prediction step. Numerical experiments illustrating the sensitivity analysis are presented.

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Section: Sensitivity Analysis and Sensitivity Updates Docp(p N Nmentioning

confidence: 99%

Sensitivity updates for linear-quadratic optimization problems in multi-step model predictive control

Emam

Gerdts

2023

J. Phys.: Conf. Ser.

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“…For large deviations to the nominal parameter, smoothness of the solution map in general is not given and Taylor expansion is not justified anymore. An attempt to overcome this difficulty can be found in [23], where the neighborhoods are estimated and databases of solutions and sensitivities are used to obtain a real-time capable approximation method.…”

Section: Introductionmentioning

confidence: 99%

“…Here, the use of radial basis functions, first introduced in a cartography application in [13], is a successful technique. The approach in [23] follows this spirit, too, but uses sensitivity updates instead of interpolation.…”

Section: Introductionmentioning

confidence: 99%

A Function Approximation Approach for Parametric Optimization

Marchi

Dreves

Gerdts

et al. 2022

J Optim Theory Appl

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We present a novel approach for approximating the primal and dual parameter-dependent solution functions of parametric optimization problems. We start with an equation reformulation of the first-order necessary optimality conditions. Then, we replace the primal and dual solutions with some approximating functions and find for some test parameters optimal coefficients as solution of a single nonlinear least-squares problem. Under mild assumptions it can be shown that stationary points are global minima and that the function approximations interpolate the solution functions at all test parameters. Further, we have a cheap function evaluation criterion to estimate the approximation error. Finally, we present some preliminary numerical results showing the viability of our approach.

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Neighborhood estimation in sensitivity-based update rules for real-time optimal control

Cited by 2 publications

References 0 publications

Sensitivity updates for linear-quadratic optimization problems in multi-step model predictive control

Sensitivity updates for linear-quadratic optimization problems in multi-step model predictive control

A Function Approximation Approach for Parametric Optimization

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