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

Proceedings 15th International Symposium on Mathematical Theory of Networks and Systems

The presence of friction in mechanical motion systems is a performance limiting factor as it induces stick-slip vibrations. To appropriately describe the stiction effect of friction, we adopt set-valued force laws. Then, the complete motion control system can be described by a Lur’e system with set-valued nonlinearities. In order to eliminate stick-slip vibrations for mechanical motion systems, a state-feedback control design is presented to stabilize the equilibrium. The proposed control design is based on an extension of a Popov-like criterion to systems with set-valued nonlinearities that guarantees input-to-state stability (ISS). The advantages of the presented controller is that it is robust to uncertainties in the friction and it is applicable to systems with non-collocation of actuation and friction where common control strategies such as direct friction compensation fail. Moreover, an observer-based output-feedback design is proposed for the case that not all the state variables are measured. The effectiveness of the proposed output-feedback control design is shown both in simulations and experiments for a typical motion control system.

http://www.dct.tue.nl/New/Wouw/ACC2008_Extended.pdf

Control of mechanical motion systems with non-collocation of actuation and set-valued friction: theory and experiments ⋆

In this paper we study a class of stochastic design problems formulated in terms of general inequality conditions on expectations. These inequalities can be used to express various mean square or almost sure stabilization conditions for stochastic systems. In contrast with existing probabilistic methods that only solve such problems with a certain probability (degree of confidence), we propose a novel method that provides a full guarantee that the constructed solution truly solves the original problem. The main idea of our method is based on overapproximating the expectations by suitably constructed upper Riemann-Stieltjes sums and imposing the inequalities on these sums instead. Next to the full guarantee on the constructed solution, the method offers three other advantages. First, it applies to arbitrary probability distributions. Second, under rather mild conditions we can derive a “converse theorem” that states that if the original problem is solvable, our method will find a solution by sufficiently refining the upper Riemann-Stieltjes sums. Finally, we will show that convexity of the function used in the expectation can be exploited to obtain convex design conditions in our approach.

http://www.nt.ntnu.no/users/skoge/prost/proceedings/cdc-ecc-2011/data/papers/1130.pdf

An upper Riemann-Stieltjes approach to stochastic design problems

Encyclopedia of life support systems: Control Systems, Robotics and Automation

Simulation of switching networks is a problem that has been studied extensively in circuit theory [1, 2, 5, 11, 12, 15, 18, 25]. Roughly speaking, there are two main approaches, namely event-tracking (see e.g. [1,15]) and time-stepping methods (see [2,11,12,18] for electrical networks and [14,16,17,22,24] for unilaterally constrained mechanical systems with friction phenomena). Having a hybrid systems point of view (see for instance [21]), event-tracking methods are based on the idea of solving corresponding DAEs of the current circuit topology (called `mode' in the hybrid systems terminology), monitoring possible changes of circuit topology (mode transition), and (if necessary) determining the exact time (event time) instant of the change of topology and the next topology. Time-stepping methods di er from this scheme by regarding the whole system as a collection of di erential equations with constraints and trying to approximate the solutions of these di erential equations with constraints. As a consequnce of this point of view, there is no need to locate exact event times. However, the convergence of the approximations in a suitable sense has to be guaranteed. Since the methods seem to work well in practice, the question of convergence is usually neglected in the literature. It is the objective of this paper to provide a rigorous basis for the use of time-stepping methods in the simulation of circuits with state events. In [7] (see also [3]) the meaning of a transient true solution to the dynamical network model with ideal diodes has already been established. Using techniques borrowed from the theory of linear complementarity systems (LCS) [8,9,13,19,20], existence and uniqueness of solutions have been proven under mild conditions. Moreover, several regularity properties have been shown from which this paper will bene t. The particular time-stepping method that we will study here is based on the well-known backward Euler scheme and has been described, for instance, in [2, 11, 12] for electrical networks. Similar methods have been used in a mechanical context in [14, 16, 17, 22, 24]. The advantage of the method is that it is straightforward to implement and many algorithms (e.g. Lemke's algorithm [4], Katzenelson's algorithm [10] and others [12]) are available to solve the one-step problems consisting of linear complementarity problems (LCPs). In [11] the use of a time-stepping method based on the backward Euler scheme (or higher order linear multistep integration methods [6] like the trapezoidal rule) has already been proposed for the class of linear complementarity systems, i.e., linear time-invariant dynamical systems coupled with ideal diode characteristics (complementarity conditions). By an example, it will be shown that the method is not suited for the general class of linear complementarity systems. This example indicates also, that although the method has proven itself in practice, one should not indiscriminately apply it to general discontinuous dynamical systems. Dept. of Electrical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, and Dept. of Econometrics, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands. On leave from Dept. of Electrical Eng., Istanbul Technical University, 80626 Maslak Istanbul, Turkey. E-mail: K.Camlibel@tue.nl yDept. of Electrical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands, and Dept. of Economics, Tilburg University, E-mail: w.p.m.h.heemels@tue.nl Dept. of Econometrics, Tilburg University, P.O. Box 90153 5000 LE Tilburg, The Netherlands, E-mail: jms@kub.nl Convergence problems of time-stepping methods for mechanical systems subject to unilateral constraints or friction have been studied by Stewart [22,23]. He shows that for a broad class of nonlinear constrained mechanical systems there always exists a subsequence of approximating time functions that converge to a real solution of the mechanical model. However, the convergence of the complete sequence has not been shown in [22,23]. The conditions used in [22,23] do not cover electrical networks containing ideal diodes, which form the subject of this paper. Speci cally, we will show that for the class of discontinuous dynamical systems consisting of linear electrical passive circuits with ideal diodes the backward Euler time-stepping method is consistent. To be speci c, we prove that the whole sequence (and not only a subsequence) of the approximating time functions converge to the real transient solution of the network model, when the step size decreases to zero. Although the results are written down here for networks containing ideal diodes (internally controlled switches) only, externally controlled switches can easily be included without destroying the convergence proof. The results presented here form a justi cation of the backward Euler time-stepping scheme in the eld of switched electrical networks. Such a justi cation seems required considering the problems that might occur due to changing con gurations of the network, the possibility of Dirac impulses and the discontinuities of the system's variables.

Wpmh Maurice Heemels

Papers

Proceedings 15th International Symposium on Mathematical Theory of Networks and Systems

Control of mechanical motion systems with non-collocation of actuation and set-valued friction: theory and experiments ⋆

An upper Riemann-Stieltjes approach to stochastic design problems

Encyclopedia of life support systems: Control Systems, Robotics and Automation

On the time-stepping methods for linear passive networks with ideal diodes