Towards Integrated Design of Plant/Controller With Application in Mechatronics Systems

2011 ◽  
Author(s):  
Roozbeh Kianfar ◽  
Jonas Fredriksson
Keyword(s):  
Optimization Problem ◽  
Integrated Design ◽  
Affine Function ◽  
Dimensional Problem ◽  
Convex Optimization Problem ◽  
Vertex Enumeration ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Structural Variables ◽  
Dimensional Optimization

In this paper, a method is proposed for integrated design of mechatronics systems. The integrated design problem is formulated as a semi-definite programming optimization problem. However, this is an infinite dimensional convex optimization problem, which is hard to solve. In this paper, it is shown that a vertex enumeration method can be used to transform the infinite dimensional optimization problem into a finite dimensional problem, which under the assumptions that the state space matrices are affine function of structural variables and that the structural variables belong to a polytope, can be solved efficiently. To show the effectiveness of the method, the method is applied to a mechatronics system.

scholarly journals Sensitivity functionals in convex optimization problem

Filomat ◽  
2016 ◽  
Vol 30 (14) ◽  
pp. 3681-3687
Author(s):  
Robert Namm ◽  
Gyungsoo Woo
Keyword(s):  
Variational Inequality ◽  
Convex Optimization ◽  
Lagrange Multiplier ◽  
Optimization Problem ◽  
Lagrange Multiplier Method ◽  
Multiplier Method ◽  
Convex Optimization Problem ◽  
Infinite Dimensional ◽  
Finite Dimensional

We consider sensitivity functionals and Lagrange multiplier method for solving finite dimensional convex optimization problem.An analysis based on this property is also applied for semicoercive infinite dimensional variational inequality in mechanics.

scholarly journals An FDA-Based Approach for Clustering Elicited Expert Knowledge

Stats ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 184-204
Author(s):  
Carlos Barrera-Causil ◽  
Juan Carlos Correa ◽  
Andrew Zamecnik ◽  
Francisco Torres-Avilés ◽  
Fernando Marmolejo-Ramos
Keyword(s):  
Functional Data ◽  
Expert Knowledge ◽  
Probability Distributions ◽  
Knowledge Elicitation ◽  
Parallel Analysis ◽  
Data Sets ◽  
Dimensional Problem ◽  
Prior Distributions ◽  
Infinite Dimensional ◽  
Finite Dimensional

Expert knowledge elicitation (EKE) aims at obtaining individual representations of experts’ beliefs and render them in the form of probability distributions or functions. In many cases the elicited distributions differ and the challenge in Bayesian inference is then to find ways to reconcile discrepant elicited prior distributions. This paper proposes the parallel analysis of clusters of prior distributions through a hierarchical method for clustering distributions and that can be readily extended to functional data. The proposed method consists of (i) transforming the infinite-dimensional problem into a finite-dimensional one, (ii) using the Hellinger distance to compute the distances between curves and thus (iii) obtaining a hierarchical clustering structure. In a simulation study the proposed method was compared to k-means and agglomerative nesting algorithms and the results showed that the proposed method outperformed those algorithms. Finally, the proposed method is illustrated through an EKE experiment and other functional data sets.

A variational approach to nonlinear stochastic differential equations with linear multiplicative noise

2019 ◽  
Vol 25 ◽  
pp. 71
Author(s):  
Viorel Barbu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Parabolic Equations ◽  
Optimization Problem ◽  
Multiplicative Noise ◽  
Generalized Solution ◽  
Convex Optimization Problem ◽  
Nonlinear Stochastic Differential Equations ◽  
Infinite Dimensional ◽  
Wiener Processes

One introduces a new concept of generalized solution for nonlinear infinite dimensional stochastic differential equations of subgradient type driven by linear multiplicative Wiener processes. This is defined as solution of a stochastic convex optimization problem derived from the Brezis-Ekeland variational principle. Under specific conditions on nonlinearity, one proves the existence and uniqueness of a variational solution which is also a strong solution in some significant situations. Applications to the existence of stochastic total variational flow and to stochastic parabolic equations with mild nonlinearity are given.

scholarly journals Real-time Bidding for Time Constrained Impression Contracts in First and Second Price Auctions - Theory and Algorithms

2021 ◽  
Vol 5 (3) ◽  
pp. 1-37
Author(s):  
Ryan J. Kinnear ◽  
Ravi R. Mazumdar ◽  
Peter Marbach
Keyword(s):  
Real Time ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Piecewise Constant Function ◽  
Convex Optimization Problem ◽  
Piecewise Constant ◽  
Infinite Dimensional ◽  
Optimal Behavior ◽  
Price Auction ◽  
Second Price Auctions

We study the optimal bids and allocations in a real-time auction for heterogeneous items subject to the requirement that specified collections of items of given types be acquired within given time constraints. The problem is cast as a continuous time optimization problem that can, under certain weak assumptions, be reduced to a convex optimization problem. Focusing on the standard first and second price auctions, we first show, using convex duality, that the optimal (infinite dimensional) bidding policy can be represented by a single finite vector of so-called ''pseudo-bids''. Using this result we are able to show that the optimal solution in the second price case turns out to be a very simple piecewise constant function of time. This contrasts with the first price case that is more complicated. Despite the fact that the optimal solution for the first price auction is genuinely dynamic, we show that there remains a close connection between the two cases and that, empirically, there is almost no difference between optimal behavior in either setting. This suggests that it is adequate to bid in a first price auction as if it were in fact second price. Finally, we detail methods for implementing our bidding policies in practice with further numerical simulations illustrating the performance.

Minimum-Time Control of Crane With Simultaneous Traverse and Hoist

1999 ◽  
Author(s):  
C. J. Ong ◽  
G. S. Hu ◽  
C. L. Teo
Keyword(s):  
Basis Function ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Minimum Time ◽  
Numerical Examples ◽  
Control Parameterization ◽  
Time Control ◽  
Finite Dimensional ◽  
Endpoint Constraints ◽  
Dimensional Optimization

Abstract The problem of minimum-time control of crane having simultaneous traverse and hoisting motions is considered. We propose an approach that converts this problem into a finite dimensional optimization problem via control parameterization with an appropriate basis function. Such an approach simplifies the treatment of the constraints and allows for the easy satisfaction of the endpoint constraints. This optimization problem is solved using a novel two-stage optimization process. Under additional conditions, the solution obtained from this process can be shown to be the optimum. When these conditions are not met, a near optimal solution is obtained. Several numerical examples are provided, including the case where there is unequal cable length at the endpoints.

scholarly journals Inverse reinforcement learning in contextual MDPs

2021 ◽  
Author(s):  
Stav Belogolovsky ◽  
Philip Korsunsky ◽  
Shie Mannor ◽  
Chen Tessler ◽  
Tom Zahavy
Keyword(s):  
Reinforcement Learning ◽  
Optimization Problem ◽  
Decision Processes ◽  
Inverse Reinforcement Learning ◽  
Convex Optimization Problem ◽  
Reward Function ◽  
Dynamic Treatment Regime ◽  
Markov Decision ◽  
Dynamic Treatment ◽  
Recorded Data

AbstractWe consider the task of Inverse Reinforcement Learning in Contextual Markov Decision Processes (MDPs). In this setting, contexts, which define the reward and transition kernel, are sampled from a distribution. In addition, although the reward is a function of the context, it is not provided to the agent. Instead, the agent observes demonstrations from an optimal policy. The goal is to learn the reward mapping, such that the agent will act optimally even when encountering previously unseen contexts, also known as zero-shot transfer. We formulate this problem as a non-differential convex optimization problem and propose a novel algorithm to compute its subgradients. Based on this scheme, we analyze several methods both theoretically, where we compare the sample complexity and scalability, and empirically. Most importantly, we show both theoretically and empirically that our algorithms perform zero-shot transfer (generalize to new and unseen contexts). Specifically, we present empirical experiments in a dynamic treatment regime, where the goal is to learn a reward function which explains the behavior of expert physicians based on recorded data of them treating patients diagnosed with sepsis.

scholarly journals The Farkas lemma of Shimizu, Aiyoshi and Katayama

1985 ◽  
Vol 31 (3) ◽  
pp. 445-450 ◽  
Author(s):  
Charles Swartz
Keyword(s):  
Convex Programming ◽  
Infinite Dimensional ◽  
Farkas Lemma ◽  
Finite Dimensional

Shimizu, Aiyoshi and Katayama have recently given a finite dimensional generalization of the classical Farkas Lemma. In this note we show that a result of Pshenichnyi on convex programming can be used to give a generalization of the result of Shimizu, Aiyoshi and Katayama to infinite dimensional spaces. A generalized Farkas Lemma of Glover is also obtained.

DUAL FORMULATION OF OPTIMAL PROBLEM FOR CONTINUOUS-TIME SYSTEMS

2005 ◽  
Vol 02 (03) ◽  
pp. 251-258
Author(s):  
HANLIN HE ◽  
QIAN WANG ◽  
XIAOXIN LIAO
Keyword(s):  
Objective Function ◽  
Continuous Time ◽  
Dimensional Space ◽  
Finite Dimensional Space ◽  
Error Response ◽  
Infinite Dimensional ◽  
Dual Formulation ◽  
Finite Dimensional ◽  
Continuous Time Systems ◽  
Time Systems

The dual formulation of the maximal-minimal problem for an objective function of the error response to a fixed input in the continuous-time systems is given by a result of Fenchel dual. This formulation probably changes the original problem in the infinite dimensional space into the maximal problem with some restrained conditions in the finite dimensional space, which can be researched by finite dimensional space theory. When the objective function is given by the norm of the error response, the maximum of the error response or minimum of the error response, the dual formulation for the problems of L1-optimal control, the minimum of maximal error response, and the minimal overshoot etc. can be obtained, which gives a method for studying these problems.

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