The dissertation addresses direct adaptive control frameworks for Lyapunov stabilization of the MIMO nonlinear uncertain systems for both uncertain discrete-time and continuous-time systems. For system theory, the development of continuous-time theory always comes along with its discrete-time counterpart. However, for direct adaptive control frameworks we find relative few Lyapunov-based results published, which is mainly due to difficulty to find feasible Lyapunov candidates and to prove negative definiteness of the Lyapunov difference. Furthermore, digital computer is widely used in all fields. Most of time, we have to deal with the direct source of discrete-time signals, even the discrete-time signals arise from continuous-time settings as results of measurement or data collection process. These motivate our study in this field. For discrete-time systems, we have investigated the results with trajectory dependent hypothesis, where the Lyapunov candidate function V combines the information from the current state k and one step ahead k-1 along the track x(k), for k≥0. The proposed frameworks guarantee partial stability of the closed-loop systems, such that the feedback gains stabilize the closed-loop system without the knowledge of the system parameters. In addition, our results show that the adaptive feedback laws can be characterized by Kronecker calculus. Later, we release this trajectory dependent hypothesis for normal discrete-time nonlinear systems. At the same time, the continuous-time cases are also studied when system with matched disturbances, where the disturbances can be characterized by known continuous function matrix and unknown parameters. Here, the trajectory dependent Lyapunov candidates (tdLC), so long as the time step |t(k)-t(k-1) | ≤ £_ and the corresponding track |x(k)-x(k-1)| ≤ £` are sufficiently small, only exist in discrete-time case. In addition, we have extended the above control designs to systems with exogenous disturbances and £d2 disturbances. Finally, we develop a robust direct adaptive control framework for linear uncertain MIMO systems under the variance of unknow system matrix from given stable solution is bounded, that is |A-Ac| ¡Ý |B Kg| ≤ |£GA|. In general, through Lyapunov-based design we can obtain the global solutions and direct adaptive control design can simultaneously achieve parameter estimation and closed-loop stability.

In modern cyber-physical systems (CPSs) where the control signals are generally transmitted via shared communication networks, there is a desire to balance the closed-loop control performance with the communication cost necessary to achieve it. In this context, aperiodic real-time scheduling of control tasks comes into being and has received increasing attention recently. It is well known that model predictive control (MPC) is currently widely utilized in industrial control systems and has greatly increased profits in comparison with the proportional integral-derivative (PID) control. As communication and networks play more and more important roles in modern society, there is a great trend to upgrade and transform traditional industrial systems into CPSs, which naturally requires extending conventional MPC to communication-efficient MPC to save network resources. Motivated by this fact, we in this thesis propose robust MPC and scheduling co-design algorithms to networked CPSs possibly affected by both parameter uncertainties and additive disturbances. In Chapter 2, a dynamic event-triggered robust tube-based MPC for constrained linear systems with additive disturbances is developed, where a time-varying pre-stabilizing gain is obtained by interpolating multiple static state feedbacks and the interpolating coefficient is determined via optimization at the time instants when the MPC-based control is triggered. The original constraints are properly tightened to achieve robust constraint optimization and a sequence of dynamic sets used to test events are derived according to the optimized coefficient. We theoretically show that the proposed algorithm is recursively feasible and the closed-loop system is input-to-state stable (ISS) in the attraction region. Numerical results are presented to verify the design. In Chapter 3, a self-triggered min-max MPC strategy is developed for constrained nonlinear systems subject to both parametric uncertainties and additive disturbances, where the robust constraint satisfaction is achieved by considering the worst case of all possible uncertainty realizations. First, we propose a new cost function that relaxes the penalty on the system state in a time period where the controller will not be invoked. With this cost function, the next triggering time instant can be obtained at current time instant by solving a min-max optimization problem where the maximum triggering period becomes a decision variable. The proposed strategy is proved to be input-to-state practical stable (ISpS) in the attraction region at triggering time instants under some standard assumptions. Extensions are made to linear systems with additive disturbances, for which the conditions reduce to a linear matrix inequality (LMI). Comprehensive numerical experiments are performed to verify the correctness of the theoretical results. / Graduate

Orientador: Marcelo Carvalho Minhoto Teixeira / Resumo: Neste trabalho são propostos novos métodos de controle chaveado para uma classe de sistemas não lineares incertos utilizando a decomposição em soma de quadrados. Inicialmente é apresentada uma revisão dos conceitos e projetos de controladores baseados em desigualdades matriciais lineares (do inglês Linear Matrix Inequalities - LMIs) e a decomposição em soma de quadrados (do inglês Sum of Squares - SOS), buscando evidenciar as diferenças e vantagens das metodologias para a área de controle. Comumente são utilizados modelos fuzzy para realizar a análise da estabilidade e projeto de controladores para sistemas não lineares, e estes modelos podem ser classificados de acordo com a parte consequente linear ou polinomial. Busca-se neste trabalho evidenciar as diferenças entre os dois modelos fuzzy e a metodologia para projeto de controladores. Para o caso de sistemas cujas dinâmicas podem ser descritas apenas por funções polinomiais, serão consideradas incertezas politópicas. Então, visando flexibilizar o projeto utilizando um controlador composto por um único ganho polinomial e aumentar a região de factibilidade, são propostos controladores com ganhos polinomiais chaveados. O objetivo desta lei de chaveamento é minimizar a derivada da função de Lyapunov empregada no projeto. Considerando uma classe de sistemas não lineares mais geral, são propostos controladores com ganhos chaveados para modelos fuzzy polinomiais. A metodologia proposta não necessita do conhecimento das funções de ... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: In this manuscript new control methods are proposed for a class of uncertain nonlinear systems using a sum of squares decomposition. Initially is presented a revision of concepts and control design procedures based on Linear Matrix Inequalities (LMIs) and on sum of squares (SOS) evidencing the differences and advantages of these methodologies in the control system design. Fuzzy models are commonly used to perform stability analysis and controller design for nonlinear systems, and can be classified by a linear or polynomial consequent model. A goal of this dissertation is to compare these two methodologies in the control system design of a class of uncertain nonlinear systems. For the case of systems whose dynamics can be described only by polynomial functions will be also considered polytopic uncertainty. Therefore, in order to make the design more flexible than that obtained with only one controller with polynomial gain and increase the feasibility region, a new procedure for designing controllers with switched polynomial gains is proposed. The purpose of this switching law is to minimize the time derivative of the Lyapunov function employed in the design. For a more general class of nonlinear systems, controllers with switched gains for polynomial fuzzy models are proposed. The proposed methodology does not require the knowledge of the membership functions for an implementation of the control law. This fact is an important advantage over the many methods that consider avail... (Complete abstract click electronic access below) / Mestre

In the past decade, the integration of spatiotemporal constraints into control systems has emerged as a crucial necessity, driven by the demand for enhanced performance, guaranteed safety, and the execution of complex tasks. Spatiotemporal constraints involve criteria that are dependent on both space and time, which can be represented by time-varying constraints in nonlinear control systems. Funnel-based control methods provide computationally tractable and robust feedback control laws to enforce time-varying constraints in uncertain nonlinear systems. This thesis begins by exploring the application of funnel-based control designs to address performance specifications in coordinate-free formation control of multi-agent systems. Moreover, we develop new robust feedback control schemes dealing with coupled spatiotemporal constraints in uncertain nonlinear systems that cannot be directly addressed by conventional funnel-based control methods. In the first part of the thesis, we present a novel coordinate-free formation control scheme for directed leader-follower multi-agent systems, exhibiting almost global convergence to the desired shape. The synthesis of fully decentralized robust controllers for agents is achieved through the application of the Prescribed Performance Control (PPC) method. This method imposes spatiotemporal funnel constraints on each agent's formation errors, ensuring a predefined transient and steady-state performance while maintaining robustness to system uncertainties. The core idea in this work is the utilization of bipolar coordinates to achieve orthogonal (decoupled) formation errors for each follower agent. This approach not only ensures the global convergence to the desired shape but also facilitates the effective application of the PPC method. In the second part of the thesis, first, we introduce a novel approach that extends funnel-based control schemes to deal with a specific class of time-varying hard and soft constraints. In this work, we employ an online Constraint Consistent Funnel (CCF) planning scheme to tackle couplings between hard and soft constraints. By satisfying these CCF constraints, we ensure adherence to hard (safety) constraints, while soft (performance) constraints are met only when they do not conflict with the hard constraints. Subsequently, we directly employ the PPC design method to craft a robust, low-complexity control law, ensuring that the system's outputs consistently stay within the online planned CCF constraints. In subsequent work, we tackle the challenge of satisfying a generalized class of potentially coupled time-varying output constraints. We show that addressing multiple constraints effectively boils down to formulating a single consolidating constraint. Ensuring the fulfillment of this consolidating constraint guarantees both convergence to and invariance of the time-varying output-constrained set within a user-defined finite time. Building on the PPC design method, we introduce a novel, robust low-complexity feedback control framework to handle this issue in uncertain high-order MIMO nonlinear control systems. Additionally, we present a mechanism for online modification of the consolidating constraint to secure a least-violating solution when constraint infeasibilities occur for an unknown time interval. / Under det senaste decenniet har integrationen av bivillkor i tid och rum för reglersystem framstått som en nödvändighet, driven av efterfrågan på förbättrad prestanda, garanterad säkerhet och utförandet av komplexa uppgifter. Bivillkor i tid och rum för icke-linjära reglersystem kan representeras av tidsvarierande bivillkor. Trattbaserade reglermetoder ("funnel-based control") tillhandahåller beräkningsmässigt hanterbara och robusta återkopplingslagar för att garantera tidsvarier-ande bivillkor i osäkra icke-linjära system. Denna avhandling börjar med att utforska tillämpningen av trattbaserade kontrollmetoder för att hantera prestanda-specifikationer i koordinatfri formationskontroll av multiagentsystem. Dessutom utvecklar vi nya robusta återkopplingslagar som hanterar kopplade bivillkor i tid och rum för osäkra icke-linjära system som inte direkt kan hanteras av konventionella trattbaserade kontrollmetoder. I den första delen av avhandlingen presenterar vi en ny koordinatfri formationskontrollmetod för riktade ledare-följare multiagentsystem, vilken uppvisar nästan global konvergens till den önskade formen. Syntesen av helt decentraliserade robusta regulatorer för agenter uppnås genom tillämpning av Prescribed Performance Control (PPC)-metoden. Denna metod lägger på trattbivillkor i tid och rum på varje agents formationsfel och säkerställer en fördefinierad transient och stationär prestanda samtidigt som robusthet mot systemosäkerheter bibehålls. Kärnan i detta arbete är användningen av bipolära koordinater för att uppnå ortogonala (frikopplade) formationsfel för varje följande agent. Detta tillvägagångssätt säkerställer inte bara global konvergens till den önskade formen utan underlättar också en effektiva tillämpning av PPC-metoden. I den andra delen av avhandlingen introducerar vi först ett nytt tillvägagångssätt som utökar trattbaserade kontrollmetoder för att hantera en specifik klass av tidsvar-ierande hårda och mjuka bivillkor. I detta arbete använder vi en online Constraint Consistent Funnel (CCF)-planeringsmetod för att tackla sammankopplingar mellan hårda och mjuka bivillkor. Genom att uppfylla dessa CCF-bivillkor säkerställer vi efterlevnad av hårda (säkerhets-) bivillkor, medan mjuka (prestanda-) bivillkor uppfylls endast när de inte strider mot de hårda bivillkoren. Därefter tillämpar vi direkt PPC-designmetoden för att utforma en robust reglerlag med låg komplexitet som säkerställer att systemets utsignal konsekvent håller sig inom de online planerade CCF-bivillkoren. Därefter hanterar vi utmaningen med att uppfylla en generaliserad klass av potentiellt kopplade tidsvarierande utsignals-bivillkor. Vi visar att effektiv hantering av flera bivillkor i grund och botten handlar om att formulera ett sammanfattande bivillkor. Uppfyllandet av detta sammanfattande bivillkor garanterar både konvergens till och invarians av den tidsvarierande mängden som uppfyller utsignalsbivillkoren, inom en användardefinierad begränsad tid. Baserat på PPC-designmetoden introducerar vi en ny, robust återkopplingsregulatorstruktur för att hantera detta problem i osäkra högordnings MIMO icke-linjära reglersystem. Dessutom presenterar vi en mekanism för online-modifiering av det sammanfattande bivillkoret för att säkra en lösning med minsta möjliga kränkning då bivillkoren blir omöjliga att uppfylla under en okänd tidsperiod. / <p>QC 20231229</p>