Existence conditions for functional observability from an eigenspace perspective

Two theorems on conditions for nonexistence and for existence, of built functional observers, from an eigenspace perspective are presented and proved. One more theorem on Functional Observability in terms of constructed products of matrices A,C and L0 is also presented. This theorem provides an easy way to check Functional Observability before proceeding with the design of functional observers. The existence and the nonexistence theorems are used to unify previously reported theorems on Functional Observability by showing their equivalence. The connection between the concept of Functional Observability and the well known concept of State Observability is also presented.

Existence conditions for unknown input functional observers

This article presents necessary and sufficient conditions for the existence and design of an unknown input Functional observer. The existence of the observer can be verified by computing a nullspace of a known matrix and testing some matrix rank conditions. The existence of the observer does not require the satisfaction of the observer matching condition (i.e. Equation (16) in Hou and Muller 1992, ‘Design of Observers for Linear Systems with Unknown Inputs’, IEEE Transactions on Automatic Control, 37, 871–875), is not limited to estimating scalar functionals and allows for arbitrary pole placement. The proposed observer always exists when a state observer exists for the unknown input system, and furthermore, the proposed observer can exist even in some instances when an unknown input state observer does not exist.

Extreme poverty and development: the role of state in the assurance of minimal existence conditions

This paper follows the idea of Amartya Sen, Nobel Prize of economic, about the role of State in the assurance of minimal existence condition, and aim to answer how countries of Latin America (specifically Brazil) and countries of Europe (specifically United Kingdom) deal with the assurance of this minimal existence conditions. According to Amartya Sen’s view, development must be seen as a process of expanding substantive freedoms, such expansion being the primary purpose of each society and the main mean of development. Substantive freedoms can be considered as basic capabilities allocated to individuals whereby they are entitled to be architects of their own lives, providing them conditions to “live as they wish”. These basic capabilities are divided by Amartya Sen in 5 (five) kinds of substantive freedoms, but for this article’s purpose, we will consider just one of this 5 (five) kinds, specifically the Protective Safety capability. Protective Safety capability may be defined as the assurance of basic means of survival for individuals who are in extreme poverty, at risk of starvation or hypothermia, or even impending famine. Among the means available that could be used to avoid such situations are the possibility of supplemental income to the needy, distributing food and clothing to the needy, supply of energy and water, among others. But how countries deal whit this protective safety? Aiming to answer this question, we selected the problem of “fuel poverty” and how Brazil and United Kingdom solve it (if they solve), in order to assess how the solution found impacts development. The analysis and the comparison between these countries will allow an answer to the question proposed.

Existence and design of reduced-order scalar functional observers

In the existing literature, the existence conditions and design procedures for scalar functional observers are available for the cases where the observers’ order p is either p=1 or p=(v-1), where v is the observability index of the matrix pair (C,A). Therefore, if an observer with an order p=1 does not exist, the other option is to use a high-order observer with p=(v-1). This paper provides the existence conditions and a design procedure for scalar functional observers of order 0≤p≤2, and demonstrates the presented results with a numerical example. where K, M, E, H and G are constant matrices to be designed. The problem of observing a scalar functional or multi functionals (z(t)∈Rk , k>1) of the state vector has been the subject of numerous papers, and different algorithms have been proposed (see, [1]-[13] and references therein). There are also papers that deal with the order reduction of multi-dimensional functional observers [9,10,12,13]. For scalar functional observers, a well-known Luenberger’s classic result [1] provides an upper bound on the order with p=(v-1). It is interesting to note here that, except for a recent result of Darouach [12,13], little results have been reported on the order reduction for scalar functional observers.

Channel plasmon-polariton modes in V grooves filled with dielectric

We investigated the effect of dielectric filling in a V groove on the propagation parameters of channel plasmon-polariton (CPP) modes. In particular, existence conditions and critical groove angles, mode localization, field structure, dispersion, and propagation distances of CPP modes are analyzed as functions of dielectric permittivity inside the groove. It is demonstrated that increasing dielectric permittivity in the groove results in a rapid increase of mode localization near the tip of the groove and increase of both the critical angles that determine a range of groove angles for which CPP modes can exist. Detailed analysis of the field structure has demonstrated that the maximum of the field in a CPP mode is typically reached at a small distance from the tip of the groove. The effect of rounded tip is also investigated.

Stability of multi-cluster synchronization

A system of many coupled oscillators on a network can show multicluster synchronization. We obtain existence conditions and stability bounds for such a multicluster synchronization. When the oscillators are identical, we obtain the interesting result that network structure alone can cause multicluster synchronization to emerge even when all the other parameters are the same. We also study occurrence of multicluster synchronization when two different types of oscillators are coupled.

Non-linear dispersive waves with a small dissipation

The general theory of Whitham for slowly-varying non-linear wavetrains is extended to the case where some of the defining partial differential equations cannot be put into conservation form. Typical examples are considered in plasma dynamics and water waves in which the lack of a conservation form is due to dissipation; an additional non-conservative element, the presence of an external force, is treated for the plasma dynamics example. Certain numerical solutions of the water waves problem (the Korteweg-de Vries equation with dissipation) are considered and compared with perturbation expansions about the linearized solution; it is found that the first correction term in the perturbation expansion is an excellent qualitative indicator of the deviation of the dissipative decay rate from linearity.

A method for deriving necessary and sufficient conditions for the existence of a general uniform wavetrain solution is presented and illustrated in the plasma dynamics problem. Peaking of the plasma wave is demonstrated, and it is shown that the necessary and sufficient existence conditions are essentially equivalent to the statement that no wave may have an amplitude larger than the peaked wave.

A new type of fully non-linear stability criterion is developed for the plasma uniform wavetrain. It is shown explicitly that this wavetrain is stable in the near-linear limit. The nature of this new type of stability is discussed.

Steady shock solutions are also considered. By a quite general method, it is demonstrated that the plasma equations studied here have no steady shock solutions whatsoever. A special type of steady shock is proposed, in which a uniform wavetrain joins across a jump discontinuity to a constant state. Such shocks may indeed exist for the Korteweg-de Vries equation, but are barred from the plasma problem because entropy would decrease across the shock front.

Finally, a way of including the Landau damping mechanism in the plasma equations is given. It involves putting in a dissipation term of convolution integral form, and parallels a similar approach of Whitham in water wave theory. An important application of this would be towards resolving long-standing difficulties about the "collisionless" shock.

Soberania e acumulação de capital: uma análise crítica de Hugo Grotius, Pasquale Mancini e Hans Kelsen

A soberania já foi conceituada de diversos modos ao longo da história. Apesar disso, não deixou de ser a categoria mais elementar do direito internacional; expressando o fundamento de atuação dos Estados, foi através da soberania que o direito internacional se desenvolveu do Século XVII até os dias de hoje. Isso evidencia uma distinção entre o conteúdo da soberania, quer dizer, o seu modo de manifestação, o seu conceito, que se altera em cada período histórico, de um lado, e, do outro, a forma jurídica internacional expressa pela soberania, que se mantém intacta e que existe independentemente do conteúdo que lhe é dado, quer dizer, o lugar que ela ocupa no direito internacional. Através da análise do conceito de soberania fornecido por três autores clássicos de diferentes períodos históricos Hugo Grotius, Pasquale Mancini e Hans Kelsen o presente trabalho tem por objetivo demonstrar o caráter ideológico de cada teoria e, conseqüentemente, sua inexatidão. Para fazê-lo, foi adotado o método materialista dialético, através do qual a produção de idéias por parte do homem deve ser observada nos limites das suas condições de existência e as idéias produzidas como um reflexo consciente do mundo real. Cuida-se, assim, de observar o direito de superioridade afirmado por Grotius nos limites das condições de existência humana que se alteravam com a transição do feudalismo para capitalismo, e extrai-se o seu sentido da luta entre a Igreja e os monarcas que iam centralizando sob si o poder. Da mesma forma, observa-se o direito de nacionalidade de Mancini sob as condições de existência propiciadas pelo amadurecimento das classes sociais do capitalismo na Europa Ocidental como fruto da Revolução Industrial, extraindo-se seu sentido das lutas revolucionárias por libertação nacional que ali se desenrolavam. O caráter essencialmente limitado da soberania de Kelsen, enfim, será observado no contexto da passagem do capitalismo para sua época imperialista, como um reflexo consciente dos desenvolvimentos experimentados pelo direito internacional no fim do Século XIX e início do Século XX, após a Primeira Guerra Mundial. Assim, além de demonstrar o caráter ideológico e a inexatidão dos conceitos mencionados, busca-se demonstrar que o conteúdo da soberania em cada período histórico analisado encontra sua razão de ser na correspondente fase de desenvolvimento do capitalismo e que a forma jurídica soberania, isto é, o lugar que ela ocupa no direito internacional, é determinado pela necessidade do capitalismo de um instrumento de força que assegure a acumulação de capital, o Estado soberano.

Cyclic Pursuit: Symmetry, Reduction and Nonlinear Dynamics

In this dissertation, we explore the use of pursuit interactions as a building block for collective behavior, primarily in the context of constant bearing (CB) cyclic pursuit. Pursuit phenomena are observed throughout the natural environment and also play an important role in technological contexts, such as missile-aircraft encounters and interactions between unmanned vehicles. While pursuit is typically regarded as adversarial, we demonstrate that pursuit interactions within a cyclic pursuit framework give rise to seemingly coordinated group maneuvers. We model a system of agents (e.g. birds, vehicles) as particles tracing out curves in the plane, and illustrate reduction to the shape space of relative positions and velocities. Introducing the CB pursuit strategy and associated pursuit law, we consider the case for which agent i pursues agent i+1 (modulo n) with the CB pursuit law. After deriving closed-loop cyclic pursuit dynamics, we demonstrate asymptotic convergence to an invariant submanifold (corresponding to each agent attaining the CB pursuit strategy), and proceed by analysis of the reduced dynamics restricted to the submanifold. For the general setting, we derive existence conditions for relative equilibria (circling and rectilinear) as well as for system trajectories which preserve the shape of the collective (up to similarity), which we refer to as pure shape equilibria. For two illustrative low-dimensional cases, we provide a more comprehensive analysis, deriving explicit trajectory solutions for the two-particle "mutual pursuit" case, and detailing the stability properties of three-particle relative equilibria and pure shape equilibria. For the three-particle case, we show that a particular choice of CB pursuit parameters gives rise to remarkable almost-periodic trajectories in the physical space. We also extend our study to consider CB pursuit in three dimensions, deriving a feedback law for executing the CB pursuit strategy, and providing a detailed analysis of the two-particle mutual pursuit case. We complete the work by considering evasive strategies to counter the motion camouflage (MC) pursuit law. After demonstrating that a stochastically steering evader is unable to thwart the MC pursuit strategy, we propose a (deterministic) feedback law for the evader and demonstrate the existence of circling equilibria for the closed-loop pursuer-evader dynamics.

Arbitrary amplitude ion-acoustic solitary excitations in the presence of excess superthermal electrons

Velocity distribution functions with an excess of superthermal particles are commonly observed in space plasmas, and are effectively modeled by a kappa distribution. They are also found in some laboratory experiments. In this paper we obtain existence conditions for and some characteristics of ion-acoustic solitary waves in a plasma composed of cold ions and kappa-distributed electrons, where kappa>3/2 represents the spectral index. As is the case for the usual Maxwell-Boltzmann electrons, only positive potential solitons are found, and, as expected, in the limit of large kappa one recovers the usual range of possible soliton Mach numbers, viz., 1 < M < 1.58. For lower values of kappa, modeling the presence of a greater superthermal component, the range of accessible Mach numbers is reduced. It is found that the amplitude of the largest possible solitons that may be generated in a given plasma (corresponding to the highest allowed Mach number for the given plasma composition) falls off with decreasing kappa, i.e., an increasing superthermal component. On the other hand, at fixed Mach number, both soliton amplitude and profile steepness increase as kappa is decreased. These changes are seen to be important particularly for kappa < 4, i.e., when the electrons have a "hard" spectrum.

Electron-acoustic solitons in an electron-beam plasma system with kappa-distributed electrons

Interaction of a stream of high-energy electrons with the background plasma plays an important role in the astrophysical phenomena such as interplanetary and stellar bow shock and Earth's foreshock emission. It is not yet fully understood how electrostatic solitary waves are produced at the bow shock. Interestingly, a population of energetic suprathermal electrons were also found to exist in those environments. Previously, we have studied the properties of negative electrostatic potential solitary structures exist in such a plasma with excess suprathermal electrons. In the present study, we investigate the existence conditions and propagation properties of electron-acoustic solitary waves in a plasma consisting of an electron beam fluid, a cold electron fluid, and hot suprathermal electrons modeled by a kappa-distribution function. The Sagdeev pseudopotential method was used to investigate the occurrence of stationary-profile solitary waves. We have determined how the electron-acoustic soliton characteristics depend on the electron beam parameters. It is found that the existence domain for solitons becomes narrower with an increase in the suprathermality of hot electrons, increasing the beam speed, decreasing the beam-to-cold electron population ratio. These results lead to a better understanding of the formation of electron-acoustic solitary waves observed in those space plasma systems characterized by kappa-distributed electrons and inertial drifting (beam) electrons.

Electron-acoustic solitons in an electron-beam plasma system with kappa-distributed electrons

We investigate the existence conditions and propagation properties of electron-acoustic solitary waves in a plasma consisting of an electron beam fluid, a cold electron fluid, and a hot suprathermal electron component modeled by a k-distribution function. The Sagdeev pseudopotential method was used to investigate the occurrence of stationary-profile solitary waves. We have determined how the soliton characteristics depend on the electron beam parameters. It is found that the existence domain for solitons becomes narrower with an increase in the suprathermality of hot electrons, increasing the beam speed, and decreasing the beam-to-cold electron population ratio.

Design of reduced-order scalar functional observers

In the existing literature, the existence conditions and design procedures for scalar functional observers are available for the cases where the observers’ order p is either p=1 or p=(v-1), where v is the observability index of the matrix pair (C,A). Therefore, if an observer with an order p=1 does not exist, the other available option is to use a higher order observer with p=(v-1). This paper shows that there exists another option that can be used to design scalar linear functional observers of the order lower than the well-known upper bound (v-1). The paper provides the existence conditions and a design procedure for scalar functional observers of order 0≤ p ≤2, and demonstrates the presented results with a numerical example.

Design of a common observer for two linear systems with unknown inputs

This paper considers the design of a common linear functional observer for two linear time-invariant systems with unknown inputs. A structure for a common observer which only uses the available output information is proposed. Here, for the proposed structure, we show that the simultaneous functional observation problem of two plants is reduced to a problem of designing two observers: the first is a full-order unknown input observer of one of the two systems; the second observer is a common unknown input observer of a system comprises two-connected systems. In general, the existence conditions for the second observer are very difficult to satisfy. This paper thus concludes that it is indeed very difficult to find a common observer for two linear systems with unknown inputs.

Design of linear functional observers for time-delay systems of the neutral-type

This paper presents the design of reduced-order linear functional observers for a class of linear time-delay systems of the neutral-type. The type of the observer proposed in this paper is without internal delay and its order is the same as the number of linear functions to be estimated. First, conditions for the existence of the reduced-order functional observers that are capable of asymptotically estimating any given function of the state vector are derived. Then, based on the newly derived existence conditions, a procedure is given for the determination of the observer parameters. The results derived in this paper include a range of linear systems and extend some existing results of linear functional observers to linear neutral delay systems. A numerical example is given to illustrate the design procedure.