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

In this paper, tractable stability and performance conditions are presented for systems consisting of an infinite number of spatially invariant, i.e., identical subsystems that are described by (non)linear differential equations and interconnected (partly) through packet-based communication networks. These networks transmit packets asynchronously and independently of each other and are equipped with scheduling protocols that determine which actuator, sensor, or controller node is allowed access to the network. The overall system is modeled as an infinite interconnection of spatially invariant hybrid subsystems. To underline the relevance of this framework, it is shown how two well-known and natural system configurations can be captured in this hybrid modeling framework. Moreover, for the resulting overall infinite-dimensional hybrid system, a proper solution concept is introduced, which is necessary as many standard concepts do not apply as Zeno behavior is inevitable for the systems under study. Based on the proposed hybrid modeling framework, conditions leading to a maximally allowable transmission interval (MATI) for all of the individual communication networks are derived such that uniform global asymptotic stability (UGAS) or $\mathcal {L}_{p}$ -stability of the overall system is guaranteed. Interestingly, by exploiting the interconnection structure, the conditions guaranteeing UGAS or $\mathcal {L}_{p}$ -stability can be stated locally in the sense that they only involve the (local) dynamics of one subsystem in the interconnection and local conditions on the scheduling protocol. Finally, it is shown that in the linear case the derived conditions can even be stated in terms of “local” LMIs, making them amenable for computational verification.

Stability and Performance Analysis of Spatially Invariant Systems with Networked Communication

In this paper we will extend the input-to-state stability (ISS) framework to continuous-time discontinuous dynamical systems adopting Filippov's solution concept and using non-smooth ISS Lyapunov functions. The main motivation for adopting non-smooth ISS Lyapunov functions is that "multiple Lyapunov functions" are commonly used in the stability theory for hybrid systems. We will show that the existence of a non-smooth (but Lipschitz continuous) ISS Lyapunov function for a discontinuous system implies ISS. Next, we will prove an ISS interconnection theorem for two discontinuous dynamical systems that both admit an ISS Lyapunov function. The interconnection will be shown to be globally asymptotically stable under a small gain condition. The developed ISS theory will be applied to observer-based controller design for a class of piecewise linear systems using an observer structure proposed by the authors. The LMI-based design of the state feedback and the observer can be performed separately.

/pdf/input-to-state-stability-of-discontinuous-dynamical-systems-c4kz5p2dbj.pdf

Input-to-state stability of discontinuous dynamical systems with an observer-based control application

In this paper, the Linear Quadratic Regulator Problem with a positivity constraint on the admissible control set is addressed. Necessary and sufficient conditions for optimality are presented in terms of inner products, projections on closed convex sets, Pontryagin's maximum principle and dynamic programming. The main results are concerned with smoothness of the optimal control and the value function. The maximum principle will be extended to the infinite horizon case. Based on these analytical methods, we propose a numerical algorithm for the computation of the optimal controls for the finite and infinite horizon problem. The numerical methods will be justified by convergence properties between the finite and infinite horizon case on one side and discretized optimal controls and the true optimal control on the other.

Linear quadratic regulator problem with positive controls

A popular design framework for networked control systems (NCSs) is the emulation-based approach combined with hybrid systems analysis techniques. In the rich literature regarding this framework, bounds on the maximally allowable transmission interval (MATI) are provided to guarantee stability properties of the NCS, while the minimal allowable transmission interval (MIATI) is always taken to be (essentially) zero. In this letter, we show for the first time how knowledge of the MIATI can also be exploited in the hybrid systems/emulation-based framework leading to (guaranteed) higher values for the MATI, while still obtaining stability of the NCS.

/pdf/computing-minimal-and-maximal-allowable-transmission-27d24h7ven.pdf

Computing minimal and maximal allowable transmission intervals for networked control systems using the hybrid systems approach

http://www.mate.tue.nl/mate/pdfs/8199.pdf

Wpmh Maurice Heemels

Papers

Stability and Performance Analysis of Spatially Invariant Systems with Networked Communication

Input-to-state stability of discontinuous dynamical systems with an observer-based control application

Linear quadratic regulator problem with positive controls

Computing minimal and maximal allowable transmission intervals for networked control systems using the hybrid systems approach

On robustness of constrained discrete-time systems to state measurement errors