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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
111

Dinâmica não linear e projeto de controle em sistemas de transporte vertical: comportamentos periódicos e caóticos / Nonlinear dynamic and control design in vertical transportation systems: periodic and chaotic behaviors

Santo, Douglas Roca [UNESP] 24 February 2015 (has links) (PDF)
Made available in DSpace on 2015-08-20T17:09:47Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-02-24. Added 1 bitstream(s) on 2015-08-20T17:26:24Z : No. of bitstreams: 1 000835540.pdf: 3471317 bytes, checksum: 69659432ad7f54405aa8a0a2a2a7a99f (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O crescimento acelerado dos grandes centros urbanos aliado a recursos financeiros limitados e à pressão pelo aumento da demanda forçaram as cidades a desenvolverem-se predominantemente na direção vertical, com a construção de edifícios altos (arranha-céus). Para atender à demanda destas construções, o desenvolvimento de elevadores de alta velocidade tornou-se uma necessidade. Nesses elevadores, é necessário preocupar-se com o conforto e segurança dos passageiros. Pesquisas atuais têm dado atenção aos níveis de vibrações verticais e horizontais dentro da cabina e variações das acelerações do elevador. A vibração horizontal é causada normalmente por deformações e desalinhamento dos trilhos de guia e distúrbios devido ao fluxo de ar ao redor da cabina. Para melhorar a qualidade de viagem dos passageiros, os elevadores devem possuir um bom sistema de controle e monitoramento, com o objetivo de aumentar a precisão em seu posicionamento e fazer com que o limite de velocidade não cause desconforto nos passageiros, diminuindo as vibrações horizontais e verticais da cabina do elevador. Este trabalho tem como objetivo estudar e controlar o comportamento dinâmico horizontal de um modelo com três graus de liberdade de um sistema de transporte vertical, excitando através de deformações dos trilhos de guia. A rigidez da mola translacional equivale ao movimento pendular da cabina é modelada como uma mola do tipo Duffing. Motivado pela necessidade de aumentar o nível de conforto dos passageiros, o método equação de Ricatti Dependente de Estados é utilizado como estratégia para controlar as vibrações e acelerações horizontais. Por fim, foram realizados extensivos estudos sobre o comportamento dinâmico do modelo matemática adotado por meio de simulações numéricas / The explosive growth of large urban centers allied to financial limited resources and pressure from increased demand, has forced the cities to develop prodominantly in the vertical direction with the construction of tall buildings (skyscrapers). To supply the demand of these constructions, the development of high speed elevators became a necessity. For high speed passenger's elevators, it is important to considerer passenger's safety and confort. Current research has focused attention on the horizontal and vertical vibration levels inside the cabin and oscillations of the elevator acceleration is usually caused by deformations and misalignments of the guide rails and disturbances caused by the air flow around the cabin. To improve passengers' travel quality, elevators should feature a good feature a good monitoring and control system in order to increase the positioning accuracy and set speed limits not to cause passengers discomfort, decreasing vertical and horizontal vibrations of the elevator cabin. This research aims on studuing and controlling the dynamic horizontal behavior of a three degree of freedom model of a vertical transportation system excited through guide rail deformations. The stiffness of the translational spring equivalent to the tilting motion of the cabin is modeled as a Duffing-type spring. Motivated by the necessity to improve passengers' comfort level, the State-Deéndent Ricatti Equation method is used as a strategy to control the horizontal vibrations and accelerations. Next, we perform extensive numerical simulations studied of the nonlinear behavior of the adopted mathematical model
112

Modélisation et contrôle du moteur à allumage commandé pour Euro 6 / Modeling and control for Euro VI Spark Ignited (SI) engine

Rivas Caicedo, Maria Adelina 10 October 2012 (has links)
Cette thèse a été développé grâce à une Conventions Industrielles de Formation par la Recherche (CIFRE). Cette convention fait partie d’un programme de l’Association nationale de la recherche et de la technologie (ANRT), coordonné par le Centre nationale de la recherche scientifique (CNRS). L’accord CIFRE subventionne les entreprises françaises qui engagent un thésard pour conduire un projet scientifique dans l’entreprise, en partenariat avec un laboratoire publique de recherche. Pour cette thèse, l’accord CIFRE a été signé par Renault et les laboratoires GIPSA Lab de Grenoble et PRISME d’Orléans.Cette thèse se focalise sur la modélisation 0D, en particulier sur une description plus détaillé du processus de la combustion et l’estimation des masses enfermées dans la chambre de combustion d’un moteur à allumage commandé (Spark Ignited (SI) engine). Les principaux développements comportent des points suivants :- L’impact flamme parois pendant la combustion : un nouveau modèle pour prendre en compte ce phénomène dans le cadre d’un modèle de combustion 0D à deux zones a été développé. Ce modèle permet de prendre en compte la géométrie de la chambre de combustion et la proportion de flamme que brûle proche des parois du cylindre. Plusieurs études ont montré qu’une grand proportion (20% au 30%) du mélange frais brûle dans ce mode de combustion ce qui montre l’importance de prendre en compte ce phénomène. - L’estimation de la mass totale enfermée dans la chambre de combustion après la fermeture des soupapes est un phénomène très intéressant qui présente un Challenger pour les chercheurs motoristes. Une estimation plus précise de la mass enfermée dans la chambre de combustion permet d’avoir un meilleur contrôle de l’injection du carburant et une amélioration dans le traitement des polluants.- Le dernier point à traiter dans cette thèse est la commande d’un système d’injection “common rail”. Ce point a pour but de compléter la modélisation de la combustion en ajoutant une thématique liée à l’injection, lequel est un paramètre crucial dans le processus de la combustion. L’objectif d’un système d’injection common rail est de contrôler l’avance de l’injection, la durée et la pression, de façon indépendante dans chaque cylindre, pour avoir un meilleur contrôle de la combustion, en dépendant des conditions d’opération. Cette injection permet de réguler le carburant en quantités très petites, ce qu’aide à réduire la consommation, les émissions polluantes, et aussi à améliorer la performance du moteur. / This thesis has been developed thanks to a Conventions Industrielles de Formation par la Recherche (CIFRE)1 agreement, that is a program of the french agency Association nationale de la recherche et de la Technologie(ANRT), coordinated by the Centre nationale de la recherche scientifique (CNRS). The CIFRE program grants the Franch companies who engage a PhD student to carry out a research project of the company within a public research lab. For this thesis, a CIFRE agreement has been accorded between the automobile company Renault France and the scientific laboratories Gipsa Lab in Grenoble and PRISME in Orléans.This thesis is focused on the modeling of a detailed description of the 0D combustion process and the estimation of the enclosed mass in the combustion chamber for a Spark Ignited (SI) engine. The main developments are summarized as follows:- The combustion process is frequently modeled as growing flame inside of the combustion chamber. Many 0D thermodynamical Engine models mostly focus on the laminar characteristics of such a free developing ame, but they lack of a suitable approximation of the combustion when the ame reaches the cylinder walls. In this thesis, a flame-wall interaction model is proposed as a complement of a 0D two zones thermodynamical model.- The estimation of the total mass enclosed in the combustion chamber is an interesting and challenging task for the engine control community. In this thesis, two nonlinear observers are synthesized for the enclosed mass estimation: a classical nonlinear high gain observer and an extended linear parameter varying (LPV) high gain observer.- A controller for a common rail injection system is developed in this thesis. First, an input state linearization of a common rail model is performed, in order to overcome the strong nonlinearities and build a virtual linear model. Using the virtual model, two linear control strategies are implemented to regulate the common rail pressure: an optimal linear quadratic regulator LQR with integral action and an optimal LQR tracking (feedforward) with integral action strategy.
113

Caracterização experimental de sistemas mecânicos com comportamento não-linear /

Hansen, Cristian. January 2015 (has links)
Orientador: Samuel da Silva / Banca: João Antonio Pereira / Banca: Americo Barbosa da Cunha Junior / Resumo: Grande parte dos projetos estruturais atuais buscam por concepções mais econômicas, o que leva à estruturas mais leves e flexíveis. Estruturas assim podem apresentar comporta- mento não-linear devido às grandes deformações. Se faz então necessário o uso de modelos que incluam o comportamento não-linear, a maioria destes modelos buscam incluir uma função matemática que represente os mecanismos não-lineares presentes. Estruturas vi- brando em regime não-linear de movimento podem ter efeitos diversos como saltos, ciclos limites, interação modal, existência de múltiplas harmônicas etc. As séries de Volterra são apresentadas e utilizadas como ferramenta na identificação de sistemas não-lineares. Posteriormente, os modelos de Volterra são empregados na detecção de variação estrutu- ral em sistemas mecânicos que apresentam comportamento não-linear inerente (no estado saudável). Esta técnica baseia-se na identificação dos núcleos de Volterra expandidos na uma base ortonormal de Kautz. Os núcleos de Volterra são usados para filtrar as contri- buições lineares e não-lineares. Para ilustrar a aplicabilidade da técnica diversos testes experimentais são realizados em três bancadas experimentais que simulam estruturas com não-linearidades do tipo hardening e softening. Os sinais de excitação são aplicados com diferentes níveis de amplitude para observar o comportamento de vibração não-linear. Variações estruturais são simuladas nas estruturas, a partir de cargas ou alteração do acoplamento magnético. Os resultados obtidos permitem-nos mostrar a eficácia das séries de Volterra para a detecção de variação estrutural e quantificação de comportamento não-linear em sistemas mecânicos não-lineares / Abstract: A large number of structural engineering designs are seeking for more economic concepts, which leads to lightweight and flexible structures. These structures have nonlinear beha- vior caused by large deformations. In that case, it is need to use models that include a mathematical function to represent the possible nonlinear behavior. The first step to find a model to describe the nonlinearities is to identify the presence of some nonlinear mechanisms, as for instance, jump, multi-harmonics, modal interactions etc. The Vol- terra series are introduced and used as tool on identification of nonlinear systems. After that, Volterra models are used on detection of structural changes on mechanical systems with inherent nonlinear behavior (in the healthy condition). This technique is based on identification of the Volterra kernels expanded in an orthonormal Kautz basis. The Volterra kernels are used to filter the linear and nonlinear contributions. To illustrate the results, several experimental tests are performed in three test rigs which simulate nonlinear behavior, both, hardening and softening. The excitations signals are applied with different amplitude levels to observe the non-linear vibration behavior. Structural changes are simulated in the systems by loads or magnetic coupling. The results obtained allow us to show the effectiveness of Volterra series for detection of structural changes and quantification of nonlinear behavior on nonlinear mechanical systems / Mestre
114

Investigation of artificial neural networks for modeling, identification and control of nonlinear plant

Muga, Julius N'gon'ga January 2009 (has links)
Thesis (MTech (Electrical Engineering))--Cape Peninsula University of Technology, 2009 / In real world systems such as the waste water treatment plants, the nonlinearities, uncertainty and complexity playa major role in their daily operations. Effective control of such systems variables requires robust control methods to accommodate the uncertainties and harsh environments. It has been shown that intelligent control systems have the ability to accommodate the system uncertain parameters. Techniques such as fuzzy logic, neural networks and genetic algorithms have had many successes in the field of control because they contain essential characteristics needed for the design of identifiers and controllers for complex systems where nonlinearities, complexity and uncertainties exist. Approaches based on neural networks have proven to be powerful tools for solvinq nonlinear control and optimisation problems. This is because neural networks have the ability to learn and approximate nonlinear functions arbitrarily wei!. The approximation capabilities of such networks can be used for the design of both identifiers and controllers. Basically, an artificial neural network is a computing architecture that consists of massively parallel interconnections of simple computing elements that provide insights into the kind of highly parallel computation that is carried out by biological nervous system. A large number of networks have been proposed and investigated with various topological structures. functionality and training algorithms for the purposes of identification and control of practical systems. For the purpose of this research thesis an approach for the investigation of the use of neural networks in identification, modelling and control of non-linear systems has been carried out. In particular, neural network identifiers and controllers have been designed for the control of the dissolved oxygen (DO) concentration of the activated sludge process in waste water treatment plants. These plants, being complex processes With several variables (states) and also affected by disturbances require some form of control in order to maintain the standards of effluent. DO concentration control in the aeration tank is the most widely used controlled variable. Nonlinearity is a feature that describes the dynamics of the dissolved oxygen process and therefore the DO estimation and control may not be sufficiently achieved with a conventional linear controller. Neural networks structures are proposed, trained and utilized for purposes of identification. modelling and design of NN controllers for nonlinear DO control. Algorithms and programs are developed using Matlab environment and are deployed on a hardware PLC platform. The research is limited to the feedforward multilayer perceptron and the recurrent neural networks for the identification and control. Control models considered are the direct inverse mode! control, internal mode! contra! and feedback linearizing control. Real-time implementation is limited to the lab-scale wastewater treatment plant.
115

Dinâmica não linear e projeto de controle em sistemas de transporte vertical : comportamentos periódicos e caóticos /

Santo, Douglas Roca. January 2015 (has links)
Orientador: José Manoel Balthazar / Banca: Paulo Batista Gonçalves / Banca: Átila Madureira Bueno / Resumo: O crescimento acelerado dos grandes centros urbanos aliado a recursos financeiros limitados e à pressão pelo aumento da demanda forçaram as cidades a desenvolverem-se predominantemente na direção vertical, com a construção de edifícios altos (arranha-céus). Para atender à demanda destas construções, o desenvolvimento de elevadores de alta velocidade tornou-se uma necessidade. Nesses elevadores, é necessário preocupar-se com o conforto e segurança dos passageiros. Pesquisas atuais têm dado atenção aos níveis de vibrações verticais e horizontais dentro da cabina e variações das acelerações do elevador. A vibração horizontal é causada normalmente por deformações e desalinhamento dos trilhos de guia e distúrbios devido ao fluxo de ar ao redor da cabina. Para melhorar a qualidade de viagem dos passageiros, os elevadores devem possuir um bom sistema de controle e monitoramento, com o objetivo de aumentar a precisão em seu posicionamento e fazer com que o limite de velocidade não cause desconforto nos passageiros, diminuindo as vibrações horizontais e verticais da cabina do elevador. Este trabalho tem como objetivo estudar e controlar o comportamento dinâmico horizontal de um modelo com três graus de liberdade de um sistema de transporte vertical, excitando através de deformações dos trilhos de guia. A rigidez da mola translacional equivale ao movimento pendular da cabina é modelada como uma mola do tipo Duffing. Motivado pela necessidade de aumentar o nível de conforto dos passageiros, o método equação de Ricatti Dependente de Estados é utilizado como estratégia para controlar as vibrações e acelerações horizontais. Por fim, foram realizados extensivos estudos sobre o comportamento dinâmico do modelo matemática adotado por meio de simulações numéricas / Abstract: The explosive growth of large urban centers allied to financial limited resources and pressure from increased demand, has forced the cities to develop prodominantly in the vertical direction with the construction of tall buildings (skyscrapers). To supply the demand of these constructions, the development of high speed elevators became a necessity. For high speed passenger's elevators, it is important to considerer passenger's safety and confort. Current research has focused attention on the horizontal and vertical vibration levels inside the cabin and oscillations of the elevator acceleration is usually caused by deformations and misalignments of the guide rails and disturbances caused by the air flow around the cabin. To improve passengers' travel quality, elevators should feature a good feature a good monitoring and control system in order to increase the positioning accuracy and set speed limits not to cause passengers discomfort, decreasing vertical and horizontal vibrations of the elevator cabin. This research aims on studuing and controlling the dynamic horizontal behavior of a three degree of freedom model of a vertical transportation system excited through guide rail deformations. The stiffness of the translational spring equivalent to the tilting motion of the cabin is modeled as a Duffing-type spring. Motivated by the necessity to improve passengers' comfort level, the State-Deéndent Ricatti Equation method is used as a strategy to control the horizontal vibrations and accelerations. Next, we perform extensive numerical simulations studied of the nonlinear behavior of the adopted mathematical model / Mestre
116

Metodologia de projeto de automação industrial visando a conversão automática de redes de petri interpretadas em códigos implementáveis

Silva, Hugo Vinicius Dias 08 April 2013 (has links)
CAPES / O objetivo deste trabalho é apresentar uma proposta de metodologia para o desenvolvimento de projetos de automação industrial com vistas a agregar as vantagens da utilização dos formalismos para representação dos Sistemas a Eventos Discretos com a necessidade de implementar os algoritmos utilizados em equipamentos de controle industrial. Tal metodologia propõe um conjunto de etapas para a construção do algoritmo de controle, baseando-se na Rede de Petri Interpretada utilizada para representação da planta controlada e da lógica de controle. Através desta metodologia é possível realizar o controle de um sistema de automação industrial garantindo que a lógica de controle não possua erros quando for executada. A utilização da metodologia foi exemplificada aplicado-a ao projeto de automação de dois casos práticos, onde o primeiro caso é utilizado para detalhar as etapas contidas na metodologia, já o segundo projeto prático possui uma especificação de funcionamento mais complexa, corroborando a utilização dos métodos formais para garantir a corretude lógica do processo. Buscando evidenciar a independência da metodologia frente à tecnologia utilizada para controlar tais processos, os algoritmos resultantes da execução da metodologia foram implementados em CLP e FPGA, sendo que a utilização de equipamentos de controle com características paralelas aponta uma tendência dos projetos de automação industrial. / The objective of this work is to present a proposed methodology for the development of industrial automation projects by aggregating the advantages of using formalisms for representing Discrete Event Systems with the need to implement algorithms considered in industrial control equipment. This methodology proposes a set of steps for the construction of the control algorithm, based on Interpreted Petri Net used to represent the plant to be controlled and the control logic. Through this method it is possible to control an industrial automation system ensuring that the control logic contains no errors when executed. The use of the methodology was exemplified by automating two study cases, where the former is used to detail the steps in the methodology, and the second presents a practical function with more complex specification, corroborating the use of formal methods to ensure the correctness of the process logic. In order to demonstrate the independence of the methodology regarding to the technology used to control such processes, algorithms resulting from the application of the methodology were implemented in PLC and FPGA, and the use of control equipment with parallel features shows a trend of industrial automation projects.
117

Metodologia de projeto de automação industrial visando a conversão automática de redes de petri interpretadas em códigos implementáveis

Silva, Hugo Vinicius Dias 08 April 2013 (has links)
CAPES / O objetivo deste trabalho é apresentar uma proposta de metodologia para o desenvolvimento de projetos de automação industrial com vistas a agregar as vantagens da utilização dos formalismos para representação dos Sistemas a Eventos Discretos com a necessidade de implementar os algoritmos utilizados em equipamentos de controle industrial. Tal metodologia propõe um conjunto de etapas para a construção do algoritmo de controle, baseando-se na Rede de Petri Interpretada utilizada para representação da planta controlada e da lógica de controle. Através desta metodologia é possível realizar o controle de um sistema de automação industrial garantindo que a lógica de controle não possua erros quando for executada. A utilização da metodologia foi exemplificada aplicado-a ao projeto de automação de dois casos práticos, onde o primeiro caso é utilizado para detalhar as etapas contidas na metodologia, já o segundo projeto prático possui uma especificação de funcionamento mais complexa, corroborando a utilização dos métodos formais para garantir a corretude lógica do processo. Buscando evidenciar a independência da metodologia frente à tecnologia utilizada para controlar tais processos, os algoritmos resultantes da execução da metodologia foram implementados em CLP e FPGA, sendo que a utilização de equipamentos de controle com características paralelas aponta uma tendência dos projetos de automação industrial. / The objective of this work is to present a proposed methodology for the development of industrial automation projects by aggregating the advantages of using formalisms for representing Discrete Event Systems with the need to implement algorithms considered in industrial control equipment. This methodology proposes a set of steps for the construction of the control algorithm, based on Interpreted Petri Net used to represent the plant to be controlled and the control logic. Through this method it is possible to control an industrial automation system ensuring that the control logic contains no errors when executed. The use of the methodology was exemplified by automating two study cases, where the former is used to detail the steps in the methodology, and the second presents a practical function with more complex specification, corroborating the use of formal methods to ensure the correctness of the process logic. In order to demonstrate the independence of the methodology regarding to the technology used to control such processes, algorithms resulting from the application of the methodology were implemented in PLC and FPGA, and the use of control equipment with parallel features shows a trend of industrial automation projects.
118

Nonlinear control studies for circadian models in system biology

Ton That, Long January 2011 (has links)
Circadian rhythms exist in almost all of living species, and they occupy an important role in daily biological activities of these species. This thesis deals with reduction of measurements in circadian models, and recovery of circadian phases. Two mathematical models of circadian rhythms are considered, with a 3rd order model for Neurospora, and a 7th order model for Mammals. The reduction of measurements of circadian models is shown by the proposals of observer designs to the two mathematical models of circadian rhythms. Both mathematical models contain strong nonlinearities, which make the observer design challenging. Two observer designs, reduced-order and one-sided Lipschitz, are applied to the circadian models to tackle the nonlinearities. Reduced-order observer design is based on a state transformation to make certain nonlinearities have no impact on the observer errors, and the design of one-sided Lipschitz observer is based on systems with one-sided Lipschitz nonlinearities. Both observer designs are based on the existing methods in literature. The existing method of reduced-order observer has been applied to a class of multi-output nonlinear systems. A new reduced-order observer design which extends the existing one in literature is presented in this thesis. In this new reduced-order observer method, the observer error dynamics can be designed by choosing the observer gain, unlike the existing one, of which the observer error dynamics depend on the invariant zeros under certain input-output map. The recovery of circadian phases is carried out to provide a solution to phase shifts occurred in circadian disorders. The restoration of circadian phases is performed by the synchronizations of trajectories of a controlled model with trajectories of a reference model. The reference model and the controlled model have phase differences, and both these models are based on a given 3rd order model of Neurospora circadian rhythms. The phase differences are reflected by different initial conditions, and by parameter uncertainty. The synchronizations of the two models are performed by using back-stepping method for the case of different initial conditions, and by using adaptive back-stepping method for the remaining case. Several simulation studies of the proposed observer designs and the proposed schemes of synchronizations are carried out with the results shown in this thesis.
119

Stabilizability preserving quotients for non-linear systems

Chingozha, Tinashe 03 November 2019 (has links)
A thesis submitted to the Faculty of Engineering and the Built Environment in fulfilment of the requirement for the degree Doctor of Philosophy, University of the Witwatersrand, Johannesburg, 2019 / The design of feedback stabilizing controllers is an essential component of control engineering theory and practice. A large part of the modern literature in control theory is devoted to coming up with new methods of designing feedback stabilizing controllers. This sustained interest in answering the question \how to design a feedback stabilizing controller" has not been accompanied by equal interest in the more existential and fundamental problem of \when is a system stabilizable by feedback". As such the theory of control Lyapunov functions still remains the most general framework that characterizes stabilizability as a system property. This approach however simply replaces one elusive and di cult concept (i.e stabilizability) with an equally diffcult concept, the existence of control Lyapunov functions. In this thesis we analyse control system stabilizability from the perspective of control system quotients which are generalized control system reductions, the focus being on the propagation of the stabilizability property from the lower order quotient system to the original system. For the case where the quotient system is a linear controllable system we prove that propagation of the stabilizability property to the original system is possible if the zero dynamics of the original system are stable. A novel way of constructing the zero dynamics which does not involve the solution of a system of partial differential equations is devised. More generally for analytic non-linear systems given a stabilizable quotient system, we develop a new method of constructing a control Lyapunov function for the original system, this construction involves the solution of a system of partial di erential equations. By studying the integrability conditions of this associated system of partial differential equations we are able to characterize obstructions to our proposed method of constructing control Lyapunov functions in terms of the structure of the original control system. / PH2020
120

Integrated Optimal and Robust Control of Spacecraft in Proximity Operations

Pan, Hejia 09 December 2011 (has links)
With the rapid growth of space activities and advancement of aerospace science and technology, many autonomous space missions have been proliferating in recent decades. Control of spacecraft in proximity operations is of great importance to accomplish these missions. The research in this dissertation aims to provide a precise, efficient, optimal, and robust controller to ensure successful spacecraft proximity operations. This is a challenging control task since the problem involves highly nonlinear dynamics including translational motion, rotational motion, and flexible structure deformation and vibration. In addition, uncertainties in the system modeling parameters and disturbances make the precise control more difficult. Four control design approaches are integrated to solve this challenging problem. The first approach is to consider the spacecraft rigid body translational and rotational dynamics together with the flexible motion in one unified optimal control framework so that the overall system performance and constraints can be addressed in one optimization process. The second approach is to formulate the robust control objectives into the optimal control cost function and prove the equivalency between the robust stabilization problem and the transformed optimal control problem. The third approach is to employ the è-D technique, a novel optimal control method that is based on a perturbation solution to the Hamilton-Jacobi-Bellman equation, to solve the nonlinear optimal control problem obtained from the indirect robust control formulation. The resultant optimal control law can be obtained in closedorm, and thus facilitates the onboard implementation. The integration of these three approaches is called the integrated indirect robust control scheme. The fourth approach is to use the inverse optimal adaptive control method combined with the indirect robust control scheme to alleviate the conservativeness of the indirect robust control scheme by using online parameter estimation such that adaptive, robust, and optimal properties can all be achieved. To show the effectiveness of the proposed control approaches, six degree-offreedom spacecraft proximity operation simulation is conducted and demonstrates satisfying performance under various uncertainties and disturbances.

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