Hybrid Feedback Control Methods for Robust and Global Power Conversion

In this paper, the applicability and importance of hybrid system tools for the design of control algorithms for energy conversion in power systems is illustrated in two hybrid control designs, one pertaining to DC/DC conversion and the other to DC/AC inversion. In particular, the mathematical models considered consist of constrained switched differential equations/inclusions that include all possible modes of operation of the systems. Furthermore, the obtained models can be analyzed and their algorithms designed using hybrid system tools so as to attain key desired properties, such as stability, forward invariance, global convergence, and robustness. We argue that hybrid system tools provide a systematic approach for analysis and controller design of power systems. In particular, hybrid system tools usually leads to power quantities that have better performance and robustness to state perturbations. Furthermore, they provide guidelines on how to tune the controller parameters based on design requirements. These factors motivate the implementation of the proposed hybrid controllers in modern power conversion systems that use renewable energy sources. Simulations illustrating the main results and benchmark tests are included

One name, several (wo)men: reflections on Virginia Woolf's Orlando: a biography

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro de Comunicação e Expressão. Programa de Pós-Graduação em Letras/Inglês e Literatura Correspondente.This study discusses queer theory as regards the portrayal of Orlando in Virginia Woolf's novel, Orlando: A Biography. The character is first analyzed in light of the intersections between gender, race, class, and nation, and subsequently in terms of the poetic persona, understood from both liberal and radical perspectives. The findings show that the character can be understood to destabilize gender fixity in the construction of a poetic persona, which confirms the tentative hypothesis. Findings also show that there is a conflict in the novel as it presents at the same time a transgressive text and a normatizing subtext, a conflict that must be criticized for its implications in cultural studies regarding queer theories, gender studies, and emancipatory politics. Este estudo discute teoria queer na caracterização de Orlando no romance de Virginia Woolf, Orlando: A Biography. O personagem é analisado primeiramente em relação às intersecções entre gênero, raça, classe e nação, e na seqüência em termos de persona poética, entendida tanto de uma perspectiva liberal quanto radical. Os resultados do estudo mostram que o personagem desestabiliza a fixidez de gênero na construção da persona poética, o que confirma a hipótese inicial do estudo. Os resultados também mostram que existe um conflito no romance por este conter ao mesmo tempo um texto transgressivo e um subtexto normatizante, conflito este que deve ser criticado por suas implicações nos estudos culturais de teorias queer, estudos de gênero e políticas emancipatórias

Linear Temporal Logic for Hybrid Dynamical Systems: Characterizations and Sufficient Conditions

This paper introduces operators, semantics, characterizations, and solution-independent conditions to guarantee temporal logic specifications for hybrid dynamical systems. Hybrid dynamical systems are given in terms of differential inclusions -- capturing the continuous dynamics -- and difference inclusions -- capturing the discrete dynamics or events -- with constraints. State trajectories (or solutions) to such systems are parameterized by a hybrid notion of time. For such broad class of solutions, the operators and semantics needed to reason about temporal logic are introduced. Characterizations of temporal logic formulas in terms of dynamical properties of hybrid systems are presented -- in particular, forward invariance and finite time attractivity. These characterizations are exploited to formulate sufficient conditions assuring the satisfaction of temporal logic formulas -- when possible, these conditions do not involve solution information. Combining the results for formulas with a single operator, ways to certify more complex formulas are pointed out, in particular, via a decomposition using a finite state automaton. Academic examples illustrate the results throughout the paper.Comment: 35 pages. The technical report accompanying "Linear Temporal Logic for Hybrid Dynamical Systems: Characterizations and Sufficient Conditions" submitted to Nonlinear Analysis: Hybrid Systems, 201

Dynamical Properties of a Two-gene Network with Hysteresis

A mathematical model for a two-gene regulatory network is derived and several of their properties analyzed. Due to the presence of mixed continuous/discrete dynamics and hysteresis, we employ a hybrid systems model to capture the dynamics of the system. The proposed model incorporates binary hysteresis with different thresholds capturing the interaction between the genes. We analyze properties of the solutions and asymptotic stability of equilibria in the system as a function of its parameters. Our analysis reveals the presence of limit cycles for a certain range of parameters, behavior that is associated with hysteresis. The set of points defining the limit cycle is characterized and its asymptotic stability properties are studied. Furthermore, the stability property of the limit cycle is robust to small perturbations. Numerical simulations are presented to illustrate the results.Comment: 55 pages, 31 figures.Expanded version of paper in Special Issue on Hybrid Systems and Biology, Elsevier Information and Computation, 201

Sufficient Conditions for Temporal Logic Specifications in Hybrid Dynamical Systems.

In this paper, we introduce operators, semantics, and conditions that, when possible, are solution-independent to guarantee basic temporal logic specifications for hybrid dynamical systems. Employing sufficient conditions for forward invariance and finite time attractivity of sets for such systems, we derive such sufficient conditions for the satisfaction of formulas involving temporal operators and atomic propositions. Furthermore, we present how to certify formulas that have more than one operator. Academic examples illustrate the results throughout the paper

Interconnected Observers for Robust Decentralized Estimation with Performance Guarantees and Optimized Connectivity Graph

Motivated by the need of observers that are both robust to disturbances and guarantee fast convergence to zero of the estimation error, we propose an observer for linear time-invariant systems with noisy output that consists of the combination of N coupled observers over a connectivity graph. At each node of the graph, the output of these interconnected observers is defined as the average of the estimates obtained using local information. The convergence rate and the robustness to measurement noise of the proposed observer's output are characterized in terms of $\mathcal{KL}$ bounds. Several optimization problems are formulated to design the proposed observer so as to satisfy a given rate of convergence specification while minimizing the $H_\infty$ gain from noise to estimates or the size of the connectivity graph. It is shown that that the interconnected observers relax the well-known tradeoff between rate of convergence and noise amplification, which is a property attributed to the proposed innovation term that, over the graph, couples the estimates between the individual observers. Sufficient conditions involving information of the plant only, assuring that the estimate obtained at each node of the graph outperforms the one obtained with a single, standard Luenberger observer are given. The results are illustrated in several examples throughout the paper.Comment: The technical report accompanying "Interconnected Observers for Robust Decentralized Estimation with Performance Guarantees and Optimized Connectivity Graph" to be published in IEEE Transactions on Control of Network Systems, 201

Robust hybrid global asymptotic stabilization of rigid body dynamics using dual quaternions

A hybrid feedback control scheme is proposed for stabilization of rigid body dynamics (pose and velocities) using unit dual quaternions, in which the dual quaternions and veloc- ities are used for feedback. It is well-known that rigid body attitude control is subject to topological constraints which often result in discontinuous control to avoid the unwinding phenomenon. In contrast, the hybrid scheme allows the controlled system to be robust in the presence of uncertainties, which would otherwise cause chattering about the point of discontinuous control while also ensuring acceptable closed-loop response characteristics. The stability of the closed-loop system is guaranteed through a Lyapunov analysis and the use of invariance principles for hybrid systems. Simulation results for a rigid body model are presented to illustrate the performance of the proposed hybrid dual quaternion feedback control scheme