Linear MPC with optimal prioritized infeasibility handling: application, computational issues and stability

The day-ahead problem of finding optimal dispatch and prices for the Brazilian power system is modeled as a mixed-integer problem, with nonconvexities related to fixed costs and minimal generation requirements for some thermal power plants. The computational tool DESSEM is currently run by the independent system operator, to define the dispatch for the next day in the whole country. DESSEM also computes marginal costs of operation that CCEE, the trading chamber, uses to determine the hourly prices for energy commercialization. The respective models sometimes produce an infeasible output. This work analyzes theoretically those infeasibilities, and proposes a prioritization to progressively resolve the constraint violation, in a manner that is sound from the practical point of view. Pros and cons of different mathematical formulations are analyzed. Special attention is put on robustness of the model, when the optimality requirements for the unit-commitment problem vary.

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“…Moreover, there are different approaches based on Model Predictive Control. The paper [7] uses ideas from Optimal Weight Design.…”

Section: A2 Using Irreducibly Inconsistent Sets (Iis) and "Conflict Refiner" Algorithmsmentioning

confidence: 99%

Analysis of infeasible unit-commitment solutions arising in energy optimization

Secchin

Ramalho

Sagastizábal

et al. 2022

Preprint

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“…Additionally, we introduce an algorithm to formulate the lexicographic problem as a single linear program using the theoretical properties of Lagrangian duality and assess its computational performance. As our approach is based on the exact penalty method which works well for nonlinear programs as well, it has the potential to be generalized to solve prioritized optimal control or MPC problems more efficiently [16] than the existing sequential methods.…”

Section: B Approach and Contributionsmentioning

confidence: 99%

A Weighted Method for Fast Resolution of Strictly Hierarchical Robot Task Specifications Using Exact Penalty Functions

Sathya

Pipeleers

Decré

et al. 2021

IEEE Robot. Autom. Lett.

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Extensive work has been done on efficiently resolving hierarchical robot task specifications that minimize the -2 norm of linear constraint violations, but not for -1 norm, in which there has recently been growing interest for sparse control. Both approaches require solving a cascade of quadratic programs (QP) or linear programs (LP). In this letter, we introduce alternate and more efficient approaches to hierarchical -1 norm minimization by formulating it as a single LP that can be solved by any off-the-shelf solver. The first approach is a recursive method that transforms the lexicographic LP (LLP) into a single objective problem using Lagrangian duality. The second approach, which forms the main focus of this letter, is a weighted method based on the exact penalty method, that is equivalent to the original LLP for a well chosen set of weights.We propose methods to compute and adapt these weights. The algorithms were applied on an interesting dual arm robot task. We discuss and benchmark the computational efficiency of these methods. Simplicity of the weighted method makes it a promising approach for tackling challenging prioritized robot control problems involving a control horizon or nonlinear constraints. Within this letter, we take the first step towards that goal by demonstrating the efficacy of the weighted method on a simpler instantaneous robot control problem with linear constraints.

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“…However, it does not provide an algorithm to compute numerically reasonable weights. A parametric programming algorithm was proposed in [17] for computing optimally small equivalent weights for linear MPC, but this computation can take several minutes and is unsuitable for controlling nonlinear systems like a robot, where the linearization of the system changes at every control instance. Therefore, it is worth exploring whether it is possible to tune weights such that they remain sufficiently high for all the MPC control instances of a task, even if the weights are not optimally small.…”

Section: Introductionmentioning

confidence: 99%

A Simple Formulation for Fast Prioritized Optimal Control of Robots using Weighted Exact Penalty Functions

Sathya

Decré

Pipeleers

et al. 2022

2022 International Conference on Robotics and Automation (ICRA)

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Prioritization of tasks is a common approach to resolve conflicts in instantaneous control of redundant robots. However, the idea of prioritization has not yet been satisfactorily extended to model predictive control (MPC) to allow for realtime robot control. The standard sequential approach for prioritization is unsuitable because of the computational burden involved in solving a nonlinear problem (NLP) at every priority level. We introduce an alternate promising approach of using weighted exact penalties for the MPC stage costs, where a correctly tuned set of weights can introduce strict prioritization. We prove the existence of a set of equivalent weights that provides the same solution as the sequential approach for a local convex approximation of the original NLP and use this insight to design an algorithm to adaptively tune the weights. The weighted method is validated on a dual arm robot task in simulations and also implemented on a physical robot. We report computational times that are fast enough for prioritized MPC of robot manipulators for the first time, to the best of our knowledge.*The authors gratefully acknowledge support from Flanders Make through the Flanders Make SBO project -MULTIROB and from the Research Foundation Flanders (FWO) through the project G.0C45.15. Flanders Make is the Flemish strategic research centre for the manufacturing industry.1 The authors are with the Division of Robotics, Automation and Mechatronics in the Department of Mechanical Engineering, KU Leuven, C300 BE-3001, Belgium and DMMS-

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Linear MPC with optimal prioritized infeasibility handling: application, computational issues and stability

Cited by 37 publications

References 12 publications

Analysis of infeasible unit-commitment solutions arising in energy optimization

Analysis of infeasible unit-commitment solutions arising in energy optimization

A Weighted Method for Fast Resolution of Strictly Hierarchical Robot Task Specifications Using Exact Penalty Functions

A Simple Formulation for Fast Prioritized Optimal Control of Robots using Weighted Exact Penalty Functions

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