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Academic literature on the topic 'Linear quadratic theory'
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Dissertations / Theses on the topic "Linear quadratic theory"
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Mouadeb, Abdu-Nasser R. "Extension of linear quadratic regulator theory and its applications." Thesis, University of Ottawa (Canada), 1992. http://hdl.handle.net/10393/7535.
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Linear Quadratic Regulatory theory (L.Q.R.) has received widespread application due to its simplicity and also due to the fact that the control provided this by theory is linear in form. These features make the implication of feedback control and easy task. In contrast, nonlinear regulation lack those attractive features enjoyed by the linear regulator. Moreover, in order to obtain the feedback control, one has to solve Hamilton-Jacobi-Bellman equation which is not an easy task. Also, if solution can be obtained, implementation is not always practical. In this work, we extend the Linear Quadratic Regulatory theory to the following; (I) LQR theory is modified for the case when there is no control contribution to the cost functional. (II) LQR is used to regulate or fine-tune a nonlinear system around a nominal trajectory through linearization of nonlinear systems. (III) Applying the LQR theory for the regulation of angular velocities of a three-axes satellite around a nominal point. (IV) Applying the LQR for the regulation of the movement of a robot around a time-optional trajectory. (V) The limitation of the control obtained through linearization is indicated.
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Shen, Dan. "Nash strategies for dynamic noncooperative linear quadratic sequential games." Columbus, Ohio : Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1156434869.
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Fry, Jedediah Micah. "On Integral Quadratic Constraint Theory and Robust Control of Unmanned Aircraft Systems." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/102615.
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This dissertation advances tools for the certification of unmanned aircraft system (UAS) flight controllers. We develop two thrusts to this goal: (1) the validation and improvement of an uncertain UAS framework based on integral quadratic constraint (IQC) theory and (2) the development of novel IQC theorems which allow the analysis of uncertain systems having time-varying characteristics.
Pertaining to the first thrust, this work improves and implements an IQC-based robustness analysis framework for UAS. The approach models the UAS using a linear fractional transformation on uncertainties and conducts robustness analysis on the uncertain system via IQC theory. By expressing the set of desired UAS flight paths with an uncertainty, the framework enables analysis of the uncertain UAS flying about any level path whose radius of curvature is bounded. To demonstrate the versatility of this technique, we use IQC analysis to tune trajectory-tracking and path-following controllers designed via H2 or H-infinity synthesis methods. IQC analysis is also used to tune path-following PID controllers. By employing a non-deterministic simulation environment and conducting numerous flight tests, we demonstrate the capability of the framework in predicting loss of control, comparing the robustness of different controllers, and tuning controllers. Finally, this work demonstrates that signal IQCs have an important role in obtaining IQC analysis results which are less conservative and more consistent with observations from flight test data.
With regards to the second thrust, we prove a novel theorem which enables robustness analysis of uncertain systems where the nominal plant and the IQC multiplier are linear time-varying systems and the nominal plant may have a non-zero initial condition. When the nominal plant and the IQC multiplier are eventually periodic, robustness analysis can be accomplished by solving a finite-dimensional semidefinite program. Time-varying IQC multipliers are beneficial in analysis because they provide the possibility of reducing conservatism and are capable of expressing uncertainties that have unique time-domain characteristics. A number of time-varying IQC multipliers are introduced to better describe such uncertainties. The utility of this theorem is demonstrated with various examples, including one which produces bounds on the UAS position after an aggressive Split-S maneuver.<br>Doctor of Philosophy
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Wahl, Eric J. "The effect of damping on an optimally tuned dwell-rise-dwell cam designed by linear quadratic optimal control theory." Ohio : Ohio University, 1993. http://www.ohiolink.edu/etd/view.cgi?ohiou1176312992.
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Doruk, Resat Ozgur. "Missile Autopilot Design By Projective Control Theory." Master's thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/4/1089929/index.pdf.
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In this thesis, autopilots are developed for missiles with moderate dynamics and
stationary targets. The aim is to use the designs in real applications. Since the real
missile model is nonlinear, a linearization process is required to get use of systematic
linear controller design techniques. In the scope of this thesis, the linear quadratic
full state feedback approach is applied for developing missile autopilots. However,
the limitations of measurement systems on the missiles restrict the availability of all
the states required for feedback. Because of this fact, the linear quadratic design will
be approximated by the use of projective control theory. This method enables the
designer to use preferably static feedback or if necessary a controller plus a low
order compensator combination to approximate the full state feedback reference.
Autopilots are checked for the validity of linearization, robust stability against
aerodynamic, mechanical and measurement uncertainties.
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Wild, Marcel Wolfgang. "Dreieckverbande : lineare und quadratische darstellungstheorie." Thesis, University of Zurich, 1987. http://hdl.handle.net/10019.1/70322.
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Prof. Marcel Wild completed his PhD with Zurick University and this is a copy of the original works<br>The original works can be found at http://www.hbz.uzh.ch/<br>ABSTRACT: A linear representation of a modular lattice L is a homomorphism from L into the lattice Sub(V) of all subspaces of a vector space V. The representation theory of lattices was initiated by the Darmstadt school (Wille, Herrmann, Poguntke, et al), to large extent triggered by the linear representations of posets (Gabriel, Gelfand-Ponomarev, Nazarova, Roiter, Brenner, et al). Even though posets are more general than lattices, none of the two theories encompasses the other. In my thesis a natural type of finite lattice is identified, i.e. triangle lattices, and their linear representation theory is advanced. All of this was triggered by a more intricate setting of quadratic spaces (as opposed to mere vector spaces) and the question of how Witt’s Theorem on the congruence of finite-dimensional quadratic spaces lifts to spaces of uncountable dimensions. That issue is dealt with in the second half of the thesis.
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Flores, Callisaya Hector 1980. "Empacotamento em quadráticas." [s.n.], 2012. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307468.
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Orientador: José Mario Martínez Pérez<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica<br>Made available in DSpace on 2018-08-20T05:08:42Z (GMT). No. of bitstreams: 1
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Previous issue date: 2012<br>Resumo: Neste trabalho, serão propostos modelos matemáticos para problemas de empacotamento não reticulado de esferas em regiões limitadas por quadráticas no plano e no espaço. Uma técnica para construir representações ou parametrizações será introduzida, mediante a qual será possível encontrar um sistema de desigualdades que determinam o empacotamento de um número fixo de esferas. Desta forma, resolvemos o problema de empacotamento de esferas através de uma sequência de sistemas de desigualdades. Finalmente, para obter resultados eficientes, minimizaremos a função de sobreposição, usando o método do Lagrangiano Aumentado<br>Abstract: In this work, we will propose mathematical models for not latticed packing of spheres problems in regions bounded by quadratic in the plane and in the space. A technique to construct representations or parameterizations will be introduced, by which it will be possible to find a system of inequalities which determine the packing of a fixed number of spheres. Thus, we solve the problem of packing spheres through a sequence of systems of inequalities. Finally, to obtain effective results, we will minimize the overlay function using the Augmented Lagrangian Method<br>Doutorado<br>Matematica Aplicada<br>Doutor em Matemática Aplicada
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Troschke, Sven-Oliver. "Enhanced approaches to the combination of forecasts : univariate linear plus quadratic and multivariate linear methods /." Lohmar [u. a.] : Eul, 2002. http://www.gbv.de/dms/zbw/358295025.pdf.
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Mörhed, Joakim, and Filip Östman. "Automatic Parking and Path Following Control for a Heavy-Duty Vehicle." Thesis, Linköpings universitet, Reglerteknik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-144496.
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The interest in autonomous vehicles has never been higher and there are several components that need to function for a vehicle to be fully autonomous; one of which is the ability to perform a parking at the end of a mission. The objective of this thesis work is to develop and implement an automatic parking system (APS) for a heavy-duty vehicle (HDV). A delimitation in this thesis work is that the parking lot has a known structure and the HDV is a truck without any trailer and access to more computational power and sensors than today's commercial trucks. An automatic system for searching the parking lot has been developed which updates an occupancy grid map (OGM) based on measurements from GPS and LIDAR sensors mounted on the truck. Based on the OGM and the known structure of the parking lot, the state of the parking spots is determined and a path can be computed between the current and desired position. Based on a kinematic model of the HDV, a gain-scheduled linear quadratic (LQ) controller with feedforward action is developed. The controller's objective is to stabilize the lateral error dynamics of the system around a precomputed path. The LQ controller explicitly takes into account that there exist an input delay in the system. Due to minor complications with the precomputed path the LQ controller causes the steering wheel turn too rapidly which makes the backup driver nervous. To limit these rapid changes of the steering wheel a controller based on model predictive control (MPC) is developed with the goal of making the steering wheel behave more human-like. A constraint for maximum allowed changes of the controller output is added to the MPC formulation as well as physical restrictions and the resulting MPC controller is smoother and more human-like, but due to computational limitations the controller turns out less effective than desired. Development and testing of the two controllers are evaluated in three different environments of varying complexity; the simplest simulation environment contains a basic vehicle model and serves as a proof of concept environment, the second simulation environment uses a more realistic vehicle model and finally the controllers are evaluated on a full-scale HDV. Finally, system tests of the APS are performed and the HDV successfully parks with the LQ controller as well as the MPC controller. The concept of a self-parking HDV has been demonstrated even though more tuning and development needs to be done before the proposed APS can be used in a commercial HDV.
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SANTOS, Watson Robert Macedo. "Metodos para Solução da Equação HJB-Riccati via Famíla de Estimadores Parametricos RLS Simplificados e Dependentes de Modelo." Universidade Federal do Maranhão, 2014. http://tedebc.ufma.br:8080/jspui/handle/tede/1892.
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Previous issue date: 2014-08-21<br>Due to the demand for high-performance equipments and the rising cost of energy,
the industrial sector is developing equipments to attend minimization of the theirs
operational costs. The implementation of these requirements generate a demand
for projects and implementations of high-performance control systems. The optimal
control theory is an alternative to solve this problem, because in its design considers
the normative specifications of the system design, as well as those that are related
to the operational costs. Motivated by these perspectives, it is presented the study
of methods and the development of algorithms to the approximated solution of the
Equation Hamilton-Jacobi-Bellman, in the form of discrete Riccati equation, model
free and dependent of the dynamic system. The proposed solutions are developed
in the context of adaptive dynamic programming that are based on the methods for
online design of optimal control systems, Discrete Linear Quadratic Regulator type.
The proposed approach is evaluated in multivariable models of the dynamic systems
to evaluate the perspectives of the optimal control law for online implementations.<br>Devido a demanda por equipamentos de alto desempenho e o custo crescente da
energia, o setor industrial desenvolve equipamentos que atendem a minimização dos
seus custos operacionais. A implantação destas exigências geram uma demanda por
projetos e implementações de sistemas de controle de alto desempenho. A teoria de
controle ótimo é uma alternativa para solucionar este problema, porque considera
no seu projeto as especificações normativas de projeto do sistema, como também as
relativas aos seus custos operacionais. Motivado por estas perspectivas, apresenta-se
o estudo de métodos e o desenvolvimento de algoritmos para solução aproximada
da Equação Hamilton-Jacobi-Bellman, do tipo Equação Discreta de Riccati, livre
e dependente de modelo do sistema dinâmico. As soluções propostas são desenvolvidas no contexto de programação dinâmica adaptativa (ADP) que baseiam-se nos
métodos para o projeto on-line de Controladores Ótimos, do tipo Regulador Linear
Quadrático Discreto. A abordagem proposta é avaliada em modelos de sistemas
dinâmicos multivariáveis, tendo em vista a implementação on-line de leis de controle
ótimo.