Stability Properties of the Adaptive Horizon Multi-Stage MPC

This paper presents an adaptive horizon multi-stage model-predictive control (MPC) algorithm. It establishes appropriate criteria for recursive feasibility and robust stability using the theory of input-to-state practical stability (ISpS). The proposed algorithm employs parametric nonlinear programming (NLP) sensitivity and terminal ingredients to determine the minimum stabilizing prediction horizon for all the scenarios considered in the subsequent iterations of the multi-stage MPC. This technique notably decreases the computational cost in nonlinear model-predictive control systems with uncertainty, as they involve solving large and complex optimization problems. The efficacy of the controller is illustrated using three numerical examples that illustrate a reduction in computational delay in multi-stage MPC.Comment: Accepted for publication in Elsevier's Journal of Process Contro

An Evolutionary Algorithm Using Duality-Base-Enumerating Scheme for Interval Linear Bilevel Programming Problems

Interval bilevel programming problem is hard to solve due to its hierarchical structure as well as the uncertainty of coefficients. This paper is focused on a class of interval linear bilevel programming problems, and an evolutionary algorithm based on duality bases is proposed. Firstly, the objective coefficients of the lower level and the right-hand-side vector are uniformly encoded as individuals, and the relative intervals are taken as the search space. Secondly, for each encoded individual, based on the duality theorem, the original problem is transformed into a single level program simply involving one nonlinear equality constraint. Further, by enumerating duality bases, this nonlinear equality is deleted, and the single level program is converted into several linear programs. Finally, each individual can be evaluated by solving these linear programs. The computational results of 7 examples show that the algorithm is feasible and robust

pfm-cracks: A parallel-adaptive framework for phase-field fracture propagation

This paper describes the main features of our parallel-adaptive open-source framework for solving phase-field fracture problems called pfm-cracks. Our program allows for dimension-independent programming in two- and three-dimensional settings. A quasi-monolithic formulation for the coupled two-component system of displacements and a phase-field indicator variable is used. The nonlinear problem is solved with a robust, efficient semi-smooth Newton algorithm. A highlight is adaptive predictor–corrector mesh refinement. The code is fully parallelized and scales to 1000 and more MPI ranks. Illustrative tests demonstrate the current capabilities, from which some are parts of benchmark collections

SOCP relaxation bounds for the optimal subset selection problem applied to robust linear regression

This paper deals with the problem of finding the globally optimal subset of h elements from a larger set of n elements in d space dimensions so as to minimize a quadratic criterion, with an special emphasis on applications to computing the Least Trimmed Squares Estimator (LTSE) for robust regression. The computation of the LTSE is a challenging subset selection problem involving a nonlinear program with continuous and binary variables, linked in a highly nonlinear fashion. The selection of a globally optimal subset using the branch and bound (BB) algorithm is limited to problems in very low dimension, tipically d<5, as the complexity of the problem increases exponentially with d. We introduce a bold pruning strategy in the BB algorithm that results in a significant reduction in computing time, at the price of a negligeable accuracy lost. The novelty of our algorithm is that the bounds at nodes of the BB tree come from pseudo-convexifications derived using a linearization technique with approximate bounds for the nonlinear terms. The approximate bounds are computed solving an auxiliary semidefinite optimization problem. We show through a computational study that our algorithm performs well in a wide set of the most difficult instances of the LTSE problem.Comment: 12 pages, 3 figures, 2 table

Adjoint-based predictor-corrector sequential convex programming for parametric nonlinear optimization

This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that guarantees the tracking performance of the algorithm. Two variants of this algorithm are investigated. The first one can be used to solve nonlinear programming problems while the second variant is aimed to treat online parametric nonlinear programming problems. The local convergence of these variants is proved. An application to a large-scale benchmark problem that originates from nonlinear model predictive control of a hydro power plant is implemented to examine the performance of the algorithms.Comment: This manuscript consists of 25 pages and 7 figure