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

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

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

https://heemels.tue.nl/content/papers/LazHee_AUT09a.pdf

Brief paper: Predictive control of hybrid systems: Input-to-state stability results for sub-optimal solutions

In this paper we propose an observer design procedure for a class of bi-modal piece-wise affine systems. The designed observers have the characteristic feature that they do not require information on the currently active dynamics of the piecewise linear system. A design procedure which guarantees global asymptotic stability of the estimation error is presented. It is shown that the applicability of the presented procedure is limited to continuous piece-wise affine systems. Therefore, we present an observer design procedure, applicable also to discontinuous systems, which guarantees that the estimation error is bounded, with respect to the state bounds, asymptotically. Sliding motions in the observed system, and the observer are discussed. The presented theory is illustrated with an example.

Observer design for a class of piece-wise affine systems

This paper considers the design of state observers for Lur'e systems with multivalued mappings in the feedback path. In particular, we focus on maximal monotone mappings that that do not require any compactness and local boundedness properties and include various models for relays, friction characteristics and complementarity conditions. We propose two types of observers that are constructed by rendering a suitable operator passive in an appropriate sense. The well-posedness properties of the observer dynamics are carefully analyzed and the global asymptotic stability of the observation error is formally proven.

/pdf/observer-design-for-lur-e-systems-with-multivalued-mappings-47et0167u9.pdf

Observer Design for Lur'e Systems With Multivalued Mappings: A Passivity Approach

In this paper, a novel event-triggered control (ETC) strategy is proposed by striking a balance between periodic sampled-data control and ETC. This leads to so-called periodic event-triggered control (PETC), in which the advantage of reduced resource utilisation is preserved on the one hand, while, on the other hand, the conditions that trigger the events still have a periodic character. The latter aspect has the advantage that the event-triggering condition has to be verified only at the periodic sampling times, instead of continuously, as in conventional ETC. To analyse the stability and the L 2 -gain properties of the resulting PETC systems, two different approaches will be presented based on (i) piecewise linear systems, and (ii) impulsive systems, respectively. Moreover, the advantages and disadvantages of each of the methods will be highlighted. The developed theory will be illustrated using a numerical example.

/pdf/periodic-event-triggered-control-based-on-state-feedback-2bovkbixrz.pdf

Periodic event-triggered control based on state feedback

The problem of checking certain controllability properties of even very simple piecewise linear systems is known to be undecidable. This paper focuses on conewise linear systems, i.e., systems for which the state space is partitioned into conical regions and a linear dynamics is active on each of these regions. For this class of systems, we present algebraic necessary and sufficient conditions for controllability. We also show that the classical results of controllability of linear systems and input-constrained linear systems can be recovered from our main result. Our treatment employs tools both from geometric control theory and mathematical programming.

/pdf/algebraic-necessary-and-sufficient-conditions-for-the-4wyvuy0g0r.pdf

Wpmh Maurice Heemels

Papers

Brief paper: Predictive control of hybrid systems: Input-to-state stability results for sub-optimal solutions

Observer design for a class of piece-wise affine systems

Observer Design for Lur'e Systems With Multivalued Mappings: A Passivity Approach

Periodic event-triggered control based on state feedback

Algebraic Necessary and Sufficient Conditions for the Controllability of Conewise Linear Systems