arXiv daily

Optimization and Control (math.OC)

Fri, 14 Apr 2023

Other arXiv digests in this category:Thu, 14 Sep 2023; Wed, 13 Sep 2023; Tue, 12 Sep 2023; Mon, 11 Sep 2023; Fri, 08 Sep 2023; Tue, 05 Sep 2023; Fri, 01 Sep 2023; Thu, 31 Aug 2023; Wed, 30 Aug 2023; Tue, 29 Aug 2023; Mon, 28 Aug 2023; Fri, 25 Aug 2023; Thu, 24 Aug 2023; Wed, 23 Aug 2023; Tue, 22 Aug 2023; Mon, 21 Aug 2023; Fri, 18 Aug 2023; Thu, 17 Aug 2023; Wed, 16 Aug 2023; Tue, 15 Aug 2023; Mon, 14 Aug 2023; Fri, 11 Aug 2023; Thu, 10 Aug 2023; Wed, 09 Aug 2023; Tue, 08 Aug 2023; Mon, 07 Aug 2023; Fri, 04 Aug 2023; Thu, 03 Aug 2023; Wed, 02 Aug 2023; Tue, 01 Aug 2023; Mon, 31 Jul 2023; Fri, 28 Jul 2023; Thu, 27 Jul 2023; Wed, 26 Jul 2023; Tue, 25 Jul 2023; Mon, 24 Jul 2023; Fri, 21 Jul 2023; Thu, 20 Jul 2023; Wed, 19 Jul 2023; Tue, 18 Jul 2023; Mon, 17 Jul 2023; Fri, 14 Jul 2023; Thu, 13 Jul 2023; Wed, 12 Jul 2023; Tue, 11 Jul 2023; Mon, 10 Jul 2023; Fri, 07 Jul 2023; Thu, 06 Jul 2023; Wed, 05 Jul 2023; Tue, 04 Jul 2023; Mon, 03 Jul 2023; Fri, 30 Jun 2023; Thu, 29 Jun 2023; Wed, 28 Jun 2023; Tue, 27 Jun 2023; Mon, 26 Jun 2023; Fri, 23 Jun 2023; Thu, 22 Jun 2023; Wed, 21 Jun 2023; Tue, 20 Jun 2023; Fri, 16 Jun 2023; Thu, 15 Jun 2023; Tue, 13 Jun 2023; Mon, 12 Jun 2023; Fri, 09 Jun 2023; Thu, 08 Jun 2023; Wed, 07 Jun 2023; Tue, 06 Jun 2023; Mon, 05 Jun 2023; Fri, 02 Jun 2023; Thu, 01 Jun 2023; Wed, 31 May 2023; Tue, 30 May 2023; Mon, 29 May 2023; Fri, 26 May 2023; Thu, 25 May 2023; Wed, 24 May 2023; Tue, 23 May 2023; Mon, 22 May 2023; Fri, 19 May 2023; Thu, 18 May 2023; Wed, 17 May 2023; Tue, 16 May 2023; Mon, 15 May 2023; Fri, 12 May 2023; Thu, 11 May 2023; Wed, 10 May 2023; Tue, 09 May 2023; Mon, 08 May 2023; Fri, 05 May 2023; Thu, 04 May 2023; Wed, 03 May 2023; Tue, 02 May 2023; Mon, 01 May 2023; Fri, 28 Apr 2023; Thu, 27 Apr 2023; Wed, 26 Apr 2023; Tue, 25 Apr 2023; Mon, 24 Apr 2023; Fri, 21 Apr 2023; Thu, 20 Apr 2023; Wed, 19 Apr 2023; Tue, 18 Apr 2023; Mon, 17 Apr 2023; Thu, 13 Apr 2023; Wed, 12 Apr 2023; Tue, 11 Apr 2023; Mon, 10 Apr 2023
1.Fixed non-stockout-probability policies for the single-item lost-sales model

Authors:Ton de Kok

Abstract: We consider the classical discrete time lost-sales model under stationary continuous demand and linear holding and penalty costs and positive constant lead time. To date the optimal policy structure is only known implicitly by solving numerically the Bellman equations. In this paper we derive the first optimality equation for the lost-sales model. We propose a fixed non-stockout-probability (FP3) policy, implying that each period the order size ensures that P3, the probability of no-stockout at the end of the period of arrival of this order, equals some target value. The FP3-policy can be computed efficiently and accurately from an exact recursive expression and two-moment fits to the emerging random variables. We use the lost-sales optimality equation to compute the optimal FP3-policy. Comparison against the optimal policy for discrete demand suggests that the fixed P3-policy is close-to-optimal. An extensive numerical experiment shows that the FP3-policy outperforms other policies proposed in literature in 97% of all cases. Under the FP3-policy, the volatility of the replenishment process is much lower than the volatility of the demand process. This cv-reduction holds a promise for substantial cost reduction at upstream stages in the supply chain of the end-item under consideration, compared to the situation with backlogging.

2.Stochastic maximum principle for recursive optimal control problems with varying terminal time

Authors:Jiaqi Wang, Shuzhen Yang

Abstract: This paper introduces a new recursive stochastic optimal control problem driven by a forward-backward stochastic differential equations (FBSDEs), where the ter?minal time varies according to the constraints of the state of the forward equation. This new optimal control problem can be used to describe the investment portfolio problems with the varying investment period. Based on novel \r{ho}-moving variational and adjoint equations, we establish the stochastic maximum principle for this optimal control problem including the classical optimal control problem as a particular case. Furthermore, we propose an example to verify our main results.

3.Extremum Seeking Regulator for Nonlinear Systems with Unknown Control Directions and an Uncertain Exosystem

Authors:Shimin Wang, Martin Guay, Dabo Xu

Abstract: This paper proposes a solution to the practical robust output regulation problem for a class of nonlinear systems with unknown control directions and uncertain exosystem dynamics. The concurrence of the unknown control directions and uncertain parameters in both the system dynamics and the exosystem pose a significant challenge to solve this problem. Moreover, in light of the nonlinear internal model approach, this paper converts the robust, practical output regulation problem into a robust non-adaptive stabilization problem for the augmented system with integral Input-to-State Stable (iISS) inverse dynamics. By employing an extremum-seeking control approach, the construction of the control laws avoids the use of Nussbaumtype gain techniques to handle the practical robust output regulation problem subject to time-varying control directions. The stability of the non-adaptive output regulation design is proven via a Lie bracket averaging technique where uniform ultimate boundedness of the closed-loop signals is guaranteed. As a result, the estimation and tracking errors converge to zero exponentially, provided that the frequency of the dither signal goes to infinity. Finally, a numerical example with unknown coefficients is provided to illustrate the validity of the theoretical results.

4.On the local everywhere bounndedness of the minima of a class of integral functionals of the Calculus of the Variations with q between 1 and 2

Authors:Tiziano Granucci

Abstract: In this paper we study the regularity and the boundedness of the minima of two classes of functionals of the calculus of variations

5.Using a one-dimensional finite-element approximation of Webster's horn equation to estimate individual ear canal acoustic transfer from input impedances

Authors:Nick Wulbusch, Reinhild Roden, Alexey Chernov, Matthias Blau

Abstract: In many applications, knowledge of the sound pressure transfer to the eardrum is important. The transfer is highly influenced by the shape of the ear canal and its acoustic properties, such as the acoustic impedance at the eardrum. Invasive procedures to measure the sound pressure at the eardrum are usually elaborate or costly. In this work, we propose a numerical method to estimate the transfer impedance at the eardrum given only input impedance measurements at the ear canal entrance by using one-dimensional first-order finite elements and Nelder-Mead optimization algorithm. Estimations on the area function of the ear canal and the acoustic impedance at the eardrum are achieved. Results are validated through numerical simulations on ten different ear canal geometries and three different acoustic impedances at the eardrum using synthetically generated data from three-dimensional finite element simulations.

6.Human preference and asset performance systems design integration

Authors:Harold van Heukelum, Ruud Binnekamp, Rogier Wolfert

Abstract: Current systems design optimisation methodologies are one-sided as these ignore the dynamic interplay between people's preferences (demand) and engineering assets' physical performance (supply). Moreover, classical multi-objective optimisation methods contain fundamental (aggregation) modelling errors. Also, the classical multi-objective optimisation Pareto front will not offer a best-fit design point but rather a set of design performance alternatives. This leaves designers without a unique solution to their problems. Finally, current multi-objective optimisation processes are rather disconnected from design and management practices since these lack deep involvement of decision-makers for expressing their interests in one common preference domain. Therefore, a new open design systems methodology and a novel integrative optimisation method based on maximising the aggregated group preference are introduced in this paper. Their added value and use are demonstrated in two real-life infrastructure design exemplars, showing how to arrive at a true best fit for common-purpose design points.

7.Towards Learning and Verifying Maximal Neural Lyapunov Functions

Authors:Jun Liu, Yiming Meng, Maxwell Fitzsimmons, Ruikun Zhou

Abstract: The search for Lyapunov functions is a crucial task in the analysis of nonlinear systems. In this paper, we present a physics-informed neural network (PINN) approach to learning a Lyapunov function that is nearly maximal for a given stable set. A Lyapunov function is considered nearly maximal if its sub-level sets can be made arbitrarily close to the boundary of the domain of attraction. We use Zubov's equation to train a maximal Lyapunov function defined on the domain of attraction. Additionally, we propose conditions that can be readily verified by satisfiability modulo theories (SMT) solvers for both local and global stability. We provide theoretical guarantees on the existence of maximal Lyapunov functions and demonstrate the effectiveness of our computational approach through numerical examples.

8.Learning-Assisted Optimization for Transmission Switching

Authors:Salvador Pineda, Juan Miguel Morales, Asunción Jiménez-Cordero

Abstract: The design of new strategies that exploit methods from Machine Learning to facilitate the resolution of challenging and large-scale mathematical optimization problems has recently become an avenue of prolific and promising research. In this paper, we propose a novel learning procedure to assist in the solution of a well-known computationally difficult optimization problem in power systems: The Direct Current Optimal Transmission Switching (DC-OTS). This model consists in finding the configuration of the power network that results in the cheapest dispatch of the power generating units. For this, the model includes a set of binaries that determine the on/off status of the switchable transmission lines. Therefore, the DC-OTS problem takes the form of a mixed-integer program, which is NP-hard in general. Its solution has been approached by way of exact and heuristic methods. The former employ techniques from mixed-integer programming to solve the problem to certified global optimality, while the latter seek to identify good solutions quickly. While the heuristic methods tend to be comparatively much faster, they may suggest suboptimal or even infeasible networks topologies. The proposed approach in this paper leverages known solutions to past instances of the DC-OTS problem to speed up the mixed-integer optimization of a new unseen model. Although it does not offer optimality guarantees, a series of numerical experiments run on a real-life power system dataset show that it features a very high success rate in identifying the optimal grid topology (especially when compared to alternative competing heuristics), while rendering remarkable speed-up factors.