All posts under category "Mathematics / Math.OC"
In this paper, we propose a novel policy iteration method, called dynamic policy programming (DPP), to estimate the optimal policy in the infinite-horizon Markov decision processes. We prove the finite-iteration and asymptotic linfty-norm performance-loss bounds for DPP in the presence of approximat
The spaces D, S and E' over mathbb{R}^(n) are known to be flat modules over A=mathbb{C}[partial_{1},...,partial_{n}], whereas their duals D', S' and E are known to be injective modules over the same ring. Let A be a Noetherian k-algebra (k=mathbb{R} or mathbb{C}). The above observation leads us to s
The aim of this work is to design controllers through explicit minimization of the settling time of a closed-loop response, by using a class of methods adequate for this objective. To the best of our knowledge, all the methods available in the literature do not minimize directly the settling time bu
The projection algorithm is frequently used in adaptive control and this note presents a detailed analysis of its properties.
In this paper we consider the problem of minimizing a quadratic functional for a discrete-time linear stochastic system with multiplicative noise, on a standard probability space, in infinite time horizon. We show that the necessary and sufficient conditions for the existence of the optimal control
A new 'model-free' control methodology is applied for the first time to power systems included in microgrids networks. We evaluate its performances regarding output load and supply variations in different working configuration of the microgrid. Our approach, which utilizes 'intelligent' PI controlle
We study the asymptotic behavior of the Euler-Bernoulli beam which is clamped at one end and free at the other end. We apply a boundary control with memory at the free end of the beam and prove that the 'exponential decay' of the memory kernel is a necessary and sufficient condition for the exponent
This article considers a mean field game model inspired by crowd motion models in which agents aim at reaching a given target set and wish to minimize a cost consisting of an individual running cost, an individual cost depending on the arrival time at the target set, and an interaction running cost,
In this paper, we present a detailed convergence analysis of a recently developed approximate Newton-type fully distributed optimization method for smooth, strongly convex local loss functions, called Network-GIANT, which has been empirically illustrated to show faster linear convergence properties
The elements of a finite nonempty partially ordered set are exposed at independent uniform times in $[0,1]$ to a selector who, at any given time, can see the structure of the induced partial order on the exposed elements. The selector's task is to choose online a maximal element. This generalizes th
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