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Optimization and pole assignment in control system design

Eric Chu (2001)

International Journal of Applied Mathematics and Computer Science

Some elementary optimization techniques, together with some not so well-known robustness measures and condition numbers, will be utilized in pole assignment. In particular, ''Method 0'' by Kautsky et al. (1985) for optimal selection of vectors is shown to be convergent to a local minimum, with respect to the condition number . This contrasts with the misconception by Kautsky et al. that the method diverges, or the recent discovery by Yang and Tits (1995) that the method converges to stationary points....

Optimization of Discrete-Time, Stochastic Systems

Papageorgiou, Nikolaos (1995)

Serdica Mathematical Journal

* This research was supported by a grant from the Greek Ministry of Industry and Technology.In this paper we study discrete-time, finite horizon stochastic systems with multivalued dynamics and obtain a necessary and sufficient condition for optimality using the dynamic programming method. Then we examine a nonlinear stochastic discrete-time system with feedback control constraints and for it, we derive a necessary and sufficient condition for optimality which we then use to establish the existence...

Optimization of the shape and the location of the actuators in an internal control problem

Antoine Henrot, Hervé Maillot (2001)

Bollettino dell'Unione Matematica Italiana

Consideriamo un corpo Ω sottomesso ad una forza esterna data e del quale vogliamo controllare lo spostamento. Cerchiamo un rinforzo per minimizzare un funzionale che dipende dallo spostamento del corpo. L'insieme delle configurazioni ammissibili è un insieme di funzioni caratteristiche di sottodomini (un rinforzo ammissibile è un sottodominio con una rigidezza uguale ad uno) di volume prescritto. In tal caso, si ha bisogno di una versione rilassata del problema di ottimizzazione e si cerca una densità...

Optimization of thrust allocation in the propulsion system of an underwater vehicle

Jerzy Garus (2004)

International Journal of Applied Mathematics and Computer Science

The paper addresses methods of thrust distribution in a propulsion system for an unmanned underwater vehicle. It concentrates on finding an optimal thrust allocation for desired values of forces and moments acting on the vehicle. Special attention is paid to the unconstrained thrust allocation. The proposed methods are developed using a configuration matrix describing the layout of thrusters in the propulsion system. The paper includes algorithms of thrust distribution for both faultless work of...

Optimization problems for structural acoustic models with thermoelasticity and smart materials

Irena Lasiecka (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Optimization problem for a structural acoustic model with controls governed by unbounded operators on the state space is considered. This type of controls arises naturally in the context of "smart material technology". The main result of the paper provides an optimal synthesis and solvability of associated nonstandard Riccati equations. It is shown that in spite of the unboundedness of control operators, the resulting gain operators (feedbacks) are bounded on the state space. This allows to provide...

Optimization schemes for wireless sensor network localization

Ewa Niewiadomska-Szynkiewicz, Michał Marks (2009)

International Journal of Applied Mathematics and Computer Science

Many applications of wireless sensor networks (WSN) require information about the geographical location of each sensor node. Self-organization and localization capabilities are one of the most important requirements in sensor networks. This paper provides an overview of centralized distance-based algorithms for estimating the positions of nodes in a sensor network. We discuss and compare three approaches: semidefinite programming, simulated annealing and two-phase stochastic optimization-a hybrid...

Optimization-based approach to path planning for closed chain robot systems

Wojciech Szynkiewicz, Jacek Błaszczyk (2011)

International Journal of Applied Mathematics and Computer Science

An application of advanced optimization techniques to solve the path planning problem for closed chain robot systems is proposed. The approach to path planning is formulated as a “quasi-dynamic” NonLinear Programming (NLP) problem with equality and inequality constraints in terms of the joint variables. The essence of the method is to find joint paths which satisfy the given constraints and minimize the proposed performance index. For numerical solution of the NLP problem, the IPOPT solver is used,...

Optimized state estimation for nonlinear dynamical networks subject to fading measurements and stochastic coupling strength: An event-triggered communication mechanism

Chaoqing Jia, Jun Hu, Chongyang Lv, Yujing Shi (2020)

Kybernetika

This paper is concerned with the design of event-based state estimation algorithm for nonlinear complex networks with fading measurements and stochastic coupling strength. The event-based communication protocol is employed to save energy and enhance the network transmission efficiency, where the changeable event-triggered threshold is adopted to adjust the data transmission frequency. The phenomenon of fading measurements is described by a series of random variables obeying certain probability distribution....

Optimizing the linear quadratic minimum-time problem for discrete distributed systems

Mostafa Rachik, Ahmed Abdelhak (2002)

International Journal of Applied Mathematics and Computer Science

With reference to the work of Verriest and Lewis (1991) on continuous finite-dimensional systems, the linear quadratic minimum-time problem is considered for discrete distributed systems and discrete distributed time delay systems. We treat the problem in two variants, with fixed and free end points. We consider a cost functional J which includes time, energy and precision terms, and then we investigate the optimal pair (N, u) which minimizes J.

Option pricing in a CEV model with liquidity costs

Krzysztof Turek (2016)

Applicationes Mathematicae

The goal of this paper is to make an attempt to generalise the model of pricing European options with an illiquid underlying asset considered by Rogers and Singh (2010). We assume that an investor's decisions have only a temporary effect on the price, which is proportional to the square of the change of the number of asset units in the investor's portfolio. We also assume that the underlying asset price follows a CEV model. To prove existence and uniqueness of the solution, we use techniques similar...

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