There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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Convex Analysisの二,三の進展について

Electrical energy storage technologies for stationary applications are reviewed. Particular attention is paid to pumped hydroelectric storage, compressed air energy storage, battery, flow battery, fuel cell, solar fuel, superconducting magnetic energy storage, flywheel, capacitor/supercapacitor, and thermal energy storage. Comparison is made among these technologies in terms of technical characteristics, applications and deployment status.

http://promexico.me/Rubenius/WhitePapers/sdarticle%20(1).pdf

Progress in electrical energy storage system: A critical review

During the past several years, there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems. This paper aims to briefly survey recent results in this field. First, the stability analysis for switched systems is reviewed. We focus on the stability analysis for switched linear systems under arbitrary switching, and we highlight necessary and sufficient conditions for asymptotic stability. After a brief review of the stability analysis under restricted switching and the multiple Lyapunov function theory, the switching stabilization problem is studied, and a variety of switching stabilization methods found in the literature are outlined. Then the switching stabilizability problem is investigated, that is under what condition it is possible to stabilize a switched system by properly designing switching control laws. Note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature. A necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here.

Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results

This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.

Coverage control for mobile sensing networks

In this paper existence and uniqueness of solutions to linear complementarity systems (LCS) are considered. Complementarity systems are systems that are composed of differential equations, inequalities and switching logic. These systems can therefore be seen as a subclass of hybrid dynamical systems. The main result of this paper states that dissipativity of the underlying state space description of a LCS is a sufficient condition for existence of so-called initial solutions and guarantees uniqueness of the state trajectory. Applications of the results include electrical networks with diodes.

Dissipative systems and complementarity conditions

Dynamical analysis of linear passive networks with ideal diodes:part I: Well-posedness : Well-posedness

We propose a model-based event-triggered control scheme where state measurements are transmitted to the controller only if the deviation between the real system state and the state of a nominal closed-loop model crosses a certain threshold. In contrast to earlier results, the size of the thresholds is dynamically adapted to the unknown magnitude of the disturbances acting on the system. The closed-loop system is shown to be input-to-state stable. For a particular choice of the parameters, the guaranteed asymptotic bound on the system state is the same as for a periodically triggered scheme while still allowing a reduction in communication.

Dynamic thresholds in robust event-triggered control for discrete-time linear systems

Projected dynamical systems (PDS) are discontinuous dynamical systems obtained by projecting a vector field on the tangent cone of a given constraint set As such, PDS provide a convenient formalism to model constrained dynamical systems When dealing with vector fields, which satisfy certain monotonicity properties, but not necessarily with respect to usual Euclidean norm, the resulting PDS does not necessarily inherit this monotonicity, as we will show However, we demonstrate that if the projection is carried out with respect to a well-chosen norm, then the resulting “oblique PDS” preserves the monotonicity of the unconstrained dynamics This feature is especially desirable as monotonicity allows to guarantee important (incremental) stability properties and stability of periodic solutions (under periodic excitation) These properties can now be guaranteed based on the unconstrained dynamics using “smart” projection instead of having to carry out a difficult a posteriori analysis on a constrained discontinuous dynamical system To illustrate this, an application in the context of observer re-design is presented, which guarantees that the state estimate lies in the same state set as the observed state trajectory

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Oblique Projected Dynamical Systems and Incremental Stability Under State Constraints

Linear complementarity systems are used to model discontinuous dynamical systems such as networks with ideal diodes and mechanical systems with unilateral constraints. In these systems mode changes are modeled by a relation between nonnegative, complementarity variables. We consider approximating systems obtained by replacing this non-Lipschitzian relation with a Lipschitzian function and investigate the convergence of the solutions of the approximating system to those of the ideal system as the Lipschitzian characteristic approaches to the (non-Lipschitzian) complementarity relation. It is shown that this kind of convergence holds for linear passive complementarity systems for which solutions are known to exist and to be unique. Moreover, this result is extended to systems that can be made passive by pole shifting.

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Wpmh Maurice Heemels

Papers

Dissipative systems and complementarity conditions

Dynamical analysis of linear passive networks with ideal diodes:part I: Well-posedness : Well-posedness

Dynamic thresholds in robust event-triggered control for discrete-time linear systems

Oblique Projected Dynamical Systems and Incremental Stability Under State Constraints

From Lipschitzian to non-Lipschitzian characteristics: continuity of behaviors