Based on the Lyapunov stability theorem, a design methodology of adaptive block backstepping control scheme is proposed in this thesis for a class of multi-input perturbed nonlinear systems with input nonlinearities to solve regulation problems. Fuzzy control method is utilized to estimate the unknown inverse input functions in order to facilitate the design of the proposed control scheme, so that the sector condition need not to be satisfied. According to the number of block m in the plant to be controlled, m−1 virtual input controllers are designed from the first block to the (m−1)th block. Then the proposed robust controller is designed from the last block. Adaptive mechanisms are also employed in the virtual input controllers as well as the robust controller, so that the least upper bounds of perturbations and estimation errors of inverse input functions are not required. The resultant control system is able to achieve asymptotic stability. Finally, a numerical example and a practical example are given for demonstrating the feasibility of the proposed control scheme.

Neural networks have been extensively used for adaptive system identification as well as adaptive and neuroadaptive control of highly uncertain systems. The goal of adaptive and neuroadaptive control is to achieve system performance without excessive reliance on system models. To improve robustness and the speed of adaptation of adaptive and neuroadaptive controllers several controller architectures have been proposed in the literature. In this dissertation, we developed a new neuroadaptive control architecture for nonlinear uncertain dynamical systems as well as nonlinear nonnegative uncertain dynamical systems. Nonnegative systems are essential in capturing the behavior of a wide range of dynamical systems involving dynamic states whose values are nonnegative. A subclass of nonnegative dynamical systems are compartmental systems. These systems are derived from mass and energy balance considerations and are comprised of homogeneous interconnected microscopic subsystems or compartments which exchange variable quantities of material via intercompartmental flow laws. In this research, we developed a direct adaptive and neuroadaptive control framework for stabilization, disturbance rejection and noise suppression for nonnegative and compartmental dynamical systems with exogenous system disturbances. Furthermore, we developed a new neuroadaptive control architecture for nonlinear uncertain dynamical systems. Specifically, the proposed framework involves a new and novel controller architecture involving additional terms, or Q-modification terms, in the update laws that are constructed using a moving time window of the integrated system uncertainty. The Q-modification terms can be used to identify the ideal neural network system weights which can be used in the adaptive law. In addition, these terms effectively suppress system uncertainty. Finally, neuroadaptive output feedback control architecture for nonlinear nonnegative dynamical systems with input amplitude and integral constraints is developed. This architecture is used to control lung volume and minute ventilation with input pressure constraints that also accounts for spontaneous breathing by the patient. Specifically, we develop a pressure- and work-limited neuroadaptive controller for mechanical ventilation based on a nonlinear multi-compartmental lung model. The control framework does not rely on any averaged data and is designed to automatically adjust the input pressure to the patient's physiological characteristics capturing lung resistance and compliance modeling uncertainty. Moreover, the controller accounts for input pressure constraints as well as work of breathing constraints. The effect of spontaneous breathing is incorporated within the lung model and the control framework.

Made available in DSpace on 2014-06-11T19:27:07Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-02-26Bitstream added on 2014-06-13T19:06:47Z : No. of bitstreams: 1 santos_ild_me_sjrp.pdf: 434711 bytes, checksum: 230caec3d969a14efac9b1700fd1dd97 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho introduzimos uma classe de sistemas dinâmicos descontínuos com espaço tempo contínuo e analisamos Teoremas que asseguram condições suficientes para a estabilidade de Lyapunov utilizando funções de Lyapunov. Além disso, consideramos também Teoremas de Recíproca, que sob algumas condições garantem uma determinada necessidade para esses Teoremas de estabilidade de Lyapunov. / In this work we introduce a class of discontinuous dynamical systems with time space continuous and we analyze Theorems that ensure sufficient conditions for the Lyapunov stability using Lyapunov functions. Moreover, we also consider Converse Theorems, which under some conditions guarantee a determined necessity for those Theorems of Lyapunov stability.

Doctor of Philosophy / Electrical and Computer Engineering / Balasubramaniam Natarajan / A cyber-physical system (CPS) typically consists of networked computational elements that control physical processes. As an integral part of CPS, the widespread deployment of communicable sensors makes the task of monitoring and control quite challenging especially from the viewpoint of scalability and complexity. This research investigates two unique aspects of overcoming such barriers, making a CPS more robust against data explosion and network vulnerabilities. First, the correlated characteristics of high-resolution sensor data are exploited to significantly reduce the fused data volume. Specifically, spatial, temporal and spatiotemporal compressed sensing approaches are applied to sample the measurements in compressed form. Such aggregation can directly be used in centralized static state estimation even for a nonlinear system. This approach results in a remarkable reduction in communication overhead as well as memory/storage requirement. Secondly, an agent based architecture is proposed, where the communicable sensors (identified as agents) also perform local information processing. Based on the local and underdetermined observation space, each agent can monitor only a specific subset of global CPS states, necessitating neighborhood information exchange. In this framework, we propose an agent based static state estimation encompassing local consensus and least square solution. Necessary bounds for the consensus weights are obtained through the maximum eigenvalue based convergence analysis and are verified for a radial power distribution network. The agent based formulation is also applied for a linear dynamical system and the consensus approach is found to exhibit better and more robust performance compared to a diffusion filter. The agent based Kalman consensus filter (AKCF) is further investigated, when the agents can choose between measurements and/or consensus, allowing the economic allocation of sensing and communication tasks as well as the temporary omission of faulty agents. The filter stability is guaranteed by deriving necessary consensus bounds through Lyapunov stability analysis. The states dynamically estimated from AKCF can be used for state-feedback control in a model predictive fashion. The effect of lossy communication is investigated and critical bounds on the link failure rate and the degree of consensus that ensure stability of the agent based control are derived and verified via simulations.

Cette thèse concerne l'élaboration de stratégies de commande prédictive pour certaines classes de systèmes dynamiques continus, discrets et hybrides modélisés par des extensions de réseaux de Petri ad hoc. Pour les systèmes continus et en vue de limiter la complexité de calcul inhérente à la forme standard de la commande prédictive, plusieurs améliorations sont proposées. Celles-ci permettent de surmonter le problème de "hill climbing" caractéristique des trajectoires obtenues avec certains réseaux de Petri. Elles assurent également la possibilité d'implémenter la commande en temps réel en adaptant l'horizon de prédiction pour réduire la complexité algorithmique. Enfin, elles permettent de limiter la sollicitation des actionneurs tout en garantissant la stabilité asymptotique du système commandé. Pour les systèmes discrets temporisés et pour éviter l'exploration exhaustive du graphe d'atteignabilité, une méthode de commande est proposée, basée sur la commande prédictive appliquée à une approximation continue du système discret. Enfin pour les systèmes hybrides, une commande prédictive hybride est développée, inspirée de la commande prédictive continue. Les performances de ces différentes stratégies de commande sont évaluées et comparées avec différentes simulations numériques / This thesis concerns the development of predictive control strategies for some classes of continuous, discrete and hybrid dynamic systems modeled by specific extensions of Petri nets. For continuous systems and in order to limit the computational complexity inherent to the standard form of the predictive control, several improvements are proposed. These improvements allow overcoming the problem of hill climbing that characterizes trajectories obtained with some Petri nets. They also ensure the possibility to implement real-time control by adapting the prediction horizon in order to reduce the algorithmic complexity. Finally, they limit actuators solicitation while ensuring the asymptotic stability of the controlled system. For timed discrete systems and in order to avoid the exhaustive exploration of the reachability graph, a control method is proposed, based on the predictive control applied to a continuous approximation of the discrete system. Finally for hybrid systems, hybrid predictive control is developed, inspired by the continuous predictive control. The performance of these different control strategies are evaluated and compared to different numerical simulations.

Orientador: Gustavo Luiz Chagas Manhães de Abreu / Resumo: O presente trabalho propõe uma nova estratégia para supressão ativa robusta do fenômeno Ground Resonance (GR) em Helicópteros. O modelo clássico de análise deste fenômeno é desenvolvido para um rotor isotrópico e a análise de estabilidade é feita no domínio de Coleman, para encontrar as fronteiras de instabilidade. Também é proposta uma nova estratégia para lidar com essas fronteiras de instabilidade e suprimir o GR usando controladores com formulação descrita por conjuntos politópicos convexos. Controladores são projetados via desigualdades lineares matriciais (LMIs, Linear Matrix Inequalities), formulados de acordo com a Teoria de Estabilidade de Lyapunov. Adicionalmente, incertezas paramétricas na frequência de lead-lag das pás e a apresentação de uma falha estrutural nos atuadores são consideradas e, assim, novos controladores robustos são projetados a fim de expandir o envelope operacional da aeronave. Ainda, são considerados diferentes tipos de não-linearidades estruturais na rigidez e amortecimento do trem de pouso do helicóptero e a caracterização da estabilidade não-linear do sistema exibe oscilações em ciclo limite (LCO, Limit Cycle Oscillation), que são determinadas a partir da construção de Diagramas de Bifurcação. Utiliza-se a modelagem Fuzzy-TS do sistema para cada caso de estudo e, com base nas fronteiras de estabilidade não-linear do GR, definidas a partir dos Diagramas de Bifurcação, têm-se o projeto de controladores para supressão das LCOs do sistema. Os res... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The present work proposes a new strategy for robust active suppression of Ground Resonance (GR) phenomenon in Helicopters. The classical model to analysis of this phenomenon is developed for an isotropic rotor and stability analysis is done in Coleman domain, to nd the boundaries of instability. It is also proposed a new strategy for dealing with these boundaries of instability and suppressing GR using controllers with polytopic convex hulls formulation. Controllers are designed via Linear Matrix Inequalities (LMIs), formulated according to the Lyapunov Stability Theory. Additionally, parametric uncertainties in the lead-lag frequency of the blades and actuators faults are considered and thus new robust controllers are designed to expand the aircraft operating envelope. Also, di erent types of structural nonlinearities in the landing gear sti ness and damping of the helicopter are considered, and the characterization of the nonlinear stability of the system exhibits Limit Cycle Oscillation (LCO), which are determined from the construction of Bifurcation Diagrams. Fuzzy-TS modeling is used for each case study and, based on the nonlinear stability boundaries of the GR, de ned from the Bifurcation Diagrams, the controllers to suppress the LCO are designed. The results of numerical simulations, discussions and conclusions are presented and show that the control strategy proposed is an attractive solution to suppress the linear and nonlinear GR problem, being able to expand the o... (Complete abstract click electronic access below) / Doutor

Nesta dissertação de mestrado o problema da estabilidade de geodésicas do tipo luz e do tipo tempo é estudado sobre o ponto de vista do formalismo de sistemas dinâmicos. Uma breve revisão bibliográfica sobre aspectos importantes de sistemas dinâmicos contínuos no tempo é realizada, bem como uma sucinta revisão de tópicos de interesse em relatividade geral. As equações de movimento para as geodésicas são deduzidas para geometrias com simetria esférica, e o caso Schwarzschild é inicialmente analisado. Em seguida, analisamos o caso das geometrias proposta por Casadio, Fabbri e Mazzacurati e um caso de buraco de minhoca assintoticamente de Sitter. A caracterização dos pontos fixos dos sistemas de interesse é feita, e a sua estabilidade é analisada sob a ótica dos métodos de Lyapunov e Jacobi, assim como bifurcações foram mapeadas. A fotosfera é caracterizada como um ciclo limite, sendo um ponto fixo estritamente instável no espaço de estados de buracos negros. A análise dos buracos de minhoca revelam a existência de uma fotosfera estável em determinadas regiões do espaço de parâmetros do sistema / In this dissertation, the problem associated with the stability of timelike and null geodesics is studied from the dynamical system point of view. A succinct bibliographical review covering important aspects of time-continuous dynamical systems is made, and a short review about some topics of interest of general relativity is also presented. The geodesic equations of motion are shown for geometries with spherical symmetry, and the Schwarzschild case is first analyzed. In the following, we analyze the geometries proposed by Casadio, Fabbri, and Mazzacurati and an asymptotically de Sitter wormhole case. The characterization of the fixed points of the system is performed, and their stability is studied from the perspective of the Lyapunov and Jacobi methods, as well as the bifurcation analysis. The photon sphere is characterized as a limit cycle, being a strictly unstable fixed point in the state space of the system. The wormhole analysis reveals the existence of a stable photon sphere in certain regions of the parameter space of the system

Esta tese trata das propriedades estruturais e do controle de sistemas lineares singulares sujeitos a saltos Markovianos (SLSSM). Três questões fundamentais são consideradas para esta classe de sistemas. A primeira estabelece condições necessárias para que o sistema seja estocasticamente regular em um período de tempo determinado. A segunda trata da estabilidade exponencial estocástica de SLSSM. Equações de Lyapunov acopladas generalizadas são deduzidas para caracterizar estabilidade deste tipo de sistema. Em virtude da complexidade das soluções numéricas dessas equações, cada equação de Lyapunov do conjunto acoplado está em função de duas variáveis desconhecidas, estamos propondo um algoritmo para resolver este problema. A terceira questão diz respeito à síntese de um regulador para este tipo de sistema singular definida em termos de equações algébricas generalizadas de Riccati acopladas. / This thesis deals with the structural features and with the control of singular linear systems with Markovian jump parameters (SLSMJP). Three fundamental questions are considered to this class of systems. The first provides necessary conditions to characterize stochastic regularity in a determined period of time. The second deals with exponential stability of SLSMJP. Coupled generalized Lyapunov Equations are deduced to check the stability of this class of systems. In virtue of the complexity of the numerical solutions of these equations, there exist two unknown variables for each equation of the set of coupled Lyapunov equations, we are proposing an algorithm to solve this problem. The third question is related with the synthesis of a regulator for this class of singular systems defined in terms of coupled algebraic generalized Riccati equations.

" The chemical engineering literature is dominated by physical and (bio)-chemical processes that exhibit complex nonlinear behavior, and as a consequence, the associated requirements of their analysis, optimization, control and monitoring pose considerable challenges in the face of emerging competitive pressures on the chemical, petrochemical and pharmaceutical industries. The above operational requirements are now increasingly imposed on processes that exhibit inherently nonlinear behavior over a wide range of operating conditions, rendering the employment of linear process control and monitoring methods rather inadequate. At the same time, increased research efforts are now concentrated on the development of new process control and supervisory systems that could be digitally implemented with the aid of powerful computer software codes. In particular, it is widely recognized that the important objective of process performance reliability can be met through a comprehensive framework for process control and monitoring. From: (i) a process safety point of view, the more reliable the process control and monitoring scheme employed and the earlier the detection of an operationally hazardous problem, the greater the intervening power of the process engineering team to correct it and restore operational order (ii) a product quality point of view, the earlier detection of an operational problem might prevent the unnecessary production of o-spec products, and subsequently minimize cost. The present work proposes a new methodological perspective and a novel set of systematic analytical tools aiming at the synthesis and tuning of well-performing digital controllers and the development of monitoring algorithms for nonlinear processes. In particular, the main thematic and research axis traced are: (i) The systematic integrated synthesis and tuning of advanced model-based digital controllers using techniques conceptually inspired by Zubov’s advanced stability theory. (ii) The rigorous quantitative characterization and monitoring of the asymptotic behavior of complex nonlinear processes using the notion of invariant manifolds and functional equations theory. (iii) The systematic design of nonlinear state observer-based process monitoring systems to accurately reconstruct unmeasurable process variables in the presence of time-scale multiplicity. (iv) The design of robust nonlinear digital observers for chemical reaction systems in the presence of model uncertainty. "

This dissertation seeks to merge the ideas from robust control theory such as H-Infinity control design and the Small Gain Theorem, L stability theory and Lyapunov stability from nonlinear control, and recent theoretical achievements in adaptive control. The fusion of frequency domain and linear time domain ideas allows the derivation of an H-Infinity Norm Minimization Approach (H-Infinity-NMA) for adaptive control architecture that permits a control designer to simplify the adaptive tuning process and tune the uncertainty compensation characteristics via linear control design techniques, band limit the adaptive control signal, efficiently handle redundant actuators, and handle unmatched uncertainty and matched uncertainty in a single design framework. The two stage design framework is similar to that used in robust control, but without sacrificing performance. The first stage of the design considers an ideal system with the system uncertainty completely known. For this system, a control law is designed using linear H-Infinity theory. Then in the second stage, an adaptive process is implemented that emulates the behavior of the ideal system. If the linear H-Infinity design is applied to control the emulated system, it then guarantees closed loop system stability of the actual system. All of this is accomplished while providing notions of transient performance bounds between the ideal system and the true system. Extensions to the theory include architectures for a class of output feedback systems, limiting the authority of an adaptive control system, and a method for improving the performance of an adaptive system with slow dynamics without any modification terms. Applications focus on using aerodynamic flow control for aircraft flight control and the Crew Launch Vehicle.