Dimensional Subsystems Research Articles

Asynchronous Rendezvous Analysis via Set-valued Consensus Theory

This paper presents the design and analysis result for asynchronous rendezvous control of multiagent systems with continuous-time dynamics and intermittent interactions. The protocol-designing strategies only impose weak restrictions on anticipated-way-point sets (from which the way-points are selected) and path-planning of each agent and can be applied to the networks of arbitrary dimensional subsystems. Explicitly, the anticipated-way-point sets are in a polytope-like form and the path between any two consecutive way-points is required to be included within the minimum convex region covering the two associated anticipated-way-point sets. Under the assumption of directed and switching interaction topology and the assumption of intermittent and asynchronous interactions with time-varying delays, we perform the set-valued consensus analysis on the evolution of anticipated-way-point sets with respect to update times and provide mild sufficient conditions for the solvability of the asynchronous rendezvous problem. The proof techniques rely much on graph theory and nonnegative matrix theory. The obtained result extends greatly the existing work in the literature and several examples demonstrate its broad potential applications. Particularly, additional distributed control rules, different from the circumcenter algorithm, are devised for network connectivity maintenance.

Optimal Sliding Mode Control for Linear Singualr System with Input and State Time-Delays

Synthetic problem of variable structure control (VSC) for linear singular system with input and state time-delays is studied. Firstly, the original system with both input and state time-delays is written into a form without time-delay by a linear transformation. Secondly, the system without time-delay is decomposed into two low dimensional subsystems by a restricted system equivalent decomposed method. Thirdly, the quadratic performance index optimal control technique is introduced to design the optimal sliding mode for the restricted equivalent subsystems. By applying reaching law approach, the selected control law ensures that the solution trajectories of the system reach the switching manifold in finite time and have low chattering in the sliding motion. Finally, a simulation example is given to illustrate the feasibility and validity of the proposed method.

Complexity reduction through a Schur-based decomposition for reachability analysis of linear time-invariant systems

This article presents a method for complexity reduction in reachability analysis and safety-preserving controller synthesis via Schur-based decomposition. The decomposition results in either decoupled or weakly-coupled (lower dimensional) subsystems. Reachable sets, computed independently for each subsystem, are back-projected and intersected to yield an overapproximation of the actual reachable set. Moreover, applying this technique to a class of unstable LTI systems, we show that when certain eigenvalue and state-constraint conditions are satisfied, further reduction of complexity is possible. Evaluating our method for a variety of examples we demonstrate that significant reduction in the computational costs can be achieved. This technique has considerable potential utility for use in conjunction with computationally intensive reachability tools.

Controller Based on Spectral Decomposition for Neutral Delay Systems

A controller design is proposed based on spectral decomposition of operator semigroup for linear neutral delay systems (NDSs).When the norm of the neutral term is less than one,by spectral theory and projection operator,the in- finite dimensional solution space of system is decomposed into the direct sum of finite dimensional unstable generalized eigen- subspace and infinite dimensional stable subspace.Then for the finite dimensional subsystem,the control law of state feedback is obtained.And the asymptotic stability of the colsed loop system with state feedback control is proved by the projection operator.Finally,a numerical example demonstrates the effectiveness of the proposed approach.

CONSTRUCTIONS OF SUBSYSTEM CODES OVER FINITE FIELDS

Subsystem codes protect quantum information by encoding it in a tensor factor of a subspace of the physical state space. They generalize all major quantum error protection schemes, and therefore are especially versatile. This paper introduces numerous constructions of subsystem codes. It is shown how one can derive subsystem codes from classical cyclic codes. Methods to trade the dimensions of subsystem and co-subsystem are introduced that maintain or improve the minimum distance. As a consequence, many optimal subsystem codes are obtained. Furthermore, it is shown how given subsystem codes can be extended, shortened, or combined to yield new subsystem codes. These subsystem code constructions are used to derive tables of upper and lower bounds on the subsystem code parameters.

Vanishing components in autonomous competitive Lotka–Volterra systems

Sufficient conditions are found for an n -dimensional autonomous competitive Lotka–Volterra system to have a component vanishing in an exponential rate as t → ∞ . These conditions incorporate a typical known result in the literature as a particular case. Moreover, if the n -dimensional system degenerates asymptotically to an m -dimensional subsystem as t → ∞ , then, under these conditions on the subsystem, the property that the i th component of every solution of the subsystem vanishes in an exponential rate is also preserved for the n -dimensional system.

Monetary Independence under Floating Exchange Rates: Evidence Based on International Breakeven Inflation Rates

It is widely assumed that, under flexible foreign exchange (FX) rates, countries may pursue an independent monetary policy with respect to domestic goals. By contrast, recent empirical evidence suggests that, similar to pegs, floating regimes are affected by transmissions of nominal quantities such as inflation or nominal interest rates from abroad. For the case of a four dimensional subsystem of the G7, we highlight the strength of international comovements in liquidity adjusted breakeven inflation interpreted as a measure of future inflation prospects. Results indicate that economies with geographical proximity and strong trade linkages (e.g. Canada and the U.S., the UK and EMU) share highest realized correlations of nonstationary breakeven rates. Moreover, these linkages appear strengthened if corresponding exchange rates are relatively stable or if the respective large economy is in a state of relatively uncertain inflation expectations.

Variable structure control of linear time-delay uncertain singular system

Synthesis and designing of variable structure controller for time-delay singular uncertain system are studied. Firstly, the system is decomposed into two low dimensional subsystems. Secondly, switching function and variable structure controller are designed with regard to uncertain part of the system satisfies matching conditions or not. The designing guarantee the movement of the system in switching manifolds is asymptotically stable and the variable structure controller can force trajectory of the system to arrive at the switching manifold in finite time. Finally, a numerical example and its simulation figure are given to demonstrate feasibility and validity of the design method.

Interpolatory projection methods for structure-preserving model reduction

We present a framework for interpolatory model reduction that treats systems having a generalized coprime factorization C ( s ) ▪ ( s ) − 1 B ( s ) + D . This includes rational Krylov-based interpolation methods as a special case. The broader framework allows retention of special structure in reduced models such as symmetry, second- and higher order structure, state constraints, internal delays, and infinite dimensional subsystems. Two numerical examples are provided for systems associated with viscoelastic dynamics and with an internal state delay that demonstrate the effectiveness and flexibility of the approach.

Distributing the Kalman Filter for Large-Scale Systems

This paper presents a distributed Kalman filter to estimate the state of a sparsely connected, large-scale, n -dimensional, dynamical system monitored by a network of N sensors. Local Kalman filters are implemented on n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</sub> -dimensional subsystems, n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</sub> Lt n, obtained by spatially decomposing the large-scale system. The distributed Kalman filter is optimal under an Lth order Gauss-Markov approximation to the centralized filter. We quantify the information loss due to this Lth-order approximation by the divergence, which decreases as L increases. The order of the approximation L leads to a bound on the dimension of the subsystems, hence, providing a criterion for subsystem selection. The (approximated) centralized Riccati and Lyapunov equations are computed iteratively with only local communication and low-order computation by a distributed iterate collapse inversion (DICI) algorithm. We fuse the observations that are common among the local Kalman filters using bipartite fusion graphs and consensus averaging algorithms. The proposed algorithm achieves full distribution of the Kalman filter. Nowhere in the network, storage, communication, or computation of n-dimensional vectors and matrices is required; only n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</sub> Lt n dimensional vectors and matrices are communicated or used in the local computations at the sensors. In other words, knowledge of the state is itself distributed.

Self-Sustained Spatiotemporal Oscillations Induced by Membrane-Bulk Coupling

We propose a novel mechanism leading to spatiotemporal oscillations in extended systems that does not rely on local bulk instabilities. Instead, oscillations arise from the interaction of two subsystems of different spatial dimensionality. Specifically, we show that coupling a passive diffusive bulk of dimension d with an excitable membrane of dimension d-1 produces a self-sustained oscillatory behavior. An analytical explanation of the phenomenon is provided for d=1. Moreover, in-phase and antiphase synchronization of oscillations are found numerically in one and two dimensions. This novel dynamic instability could be used by biological systems such as cells, where the dynamics on the cellular membrane is necessarily different from that of the cytoplasmic bulk.

Experimental modeling of controlled suspension vehicles from onboard sensors

In this article, identification of vertical dynamics of vehicles with controlled suspensions is considered. Identification is performed from experimental data measured on a four-poster bench test of a segment C car, equipped with a CDC-Skyhook dampers control system. The measurements are obtained from the onboard accelerometers needed by the control system. A nonlinear model in regression form is identified, having the road profile and damper control currents as inputs and chassis accelerations as outputs. The model is identified by means of a set membership structured identification method, which takes advantage of physical information on the structure of the system, decomposing the system into three subsystems: one represents the chassis and engine and the other two represent the overall behavior of front and rear suspensions, wheels and tires. This decomposition allows us to avoid the complexity accuracy problems derived from the high dimension of required regression space. Indeed, the overall high-dimensional identification problem is reduced to the identification of lower dimensional subsystems and to the estimation of their interactions. An iterative scheme is used for solving the decomposed identification problem. As the chassis pitch is small for the usual road profiles, the chassis-engine block is considered linear and standard linear methods are used for its identification. The other two subsystems are the main sources of nonlinearities in the system, mainly due to the significant nonlinearities of controlled dampers and of tires. Owing to the complexity/accuracy problems of a physical modeling of these subsystems, an input–output approach is taken. In particular, a nonlinear set membership method that does not require the search of the functional form of involved nonlinearities is used for the identification of these subsystems. The iterative algorithm converged in two iterations to a model providing a quite satisfactory simulation accuracy for all the considered road profiles and CDC-Skyhook settings.

GEOMETRIC CONSTRUCTION OF PERIODIC TRAJECTORIES

In this paper a method for generating periodic trajectories to a class of Hamiltonian systems is presented. A periodic Hamiltonian system will be defined as the target equilibrium for systems in strict feedback form. Parameter dependent nonlinear oscillation is introduced in a two dimensional subsystem and extended to higher dimensions using backstepping. A parameter update law which guarantees that the system converges to the optimal periodic orbit with respect to a given parametrization is then used for on-line implementation. A simple control problem is used to illustrate the application of this approach.

Approximation capabilities of hierarchical hybrid systems

This paper investigates the approximation capabilities of hierarchical hybrid systems, which are motivated by research in hierarchical fuzzy systems, hybrid intelligent systems, and modeling of model partly known systems. For a function (system) with known hierarchical structure (i.e., one that can be represented as a composition of some simpler and lower dimensional subsystems), it is shown that hierarchical hybrid systems have the structure approximation capability in the sense that such a hybrid approximation scheme can approximate both the overall system and all the subsystems to any desired degree of accuracy. For a function (system) with unknown hierarchical structure, Kolmogorov's theorem is used to construct the hierarchical structure of the given function (system). It is then shown that hierarchical hybrid systems are universal approximators

Probabilistic approach to Page's formula for the entropy of a quantum subsystem

Page conjectured [Phys. Rev. Lett. 71, 1291–1294 (1993)] that if a quantum system of Hilbert space dimension mn is in a random pure state, the average entropy of a subsystem of dimension should be given by the simple and elegant formula . This formula appeared to be true and was first proved by Foong and Kanno [Phys. Rev. Lett. 72, 1148–1151 (1994)] by using Fourier transform, and next by Sánchez-Ruiz [Phys. Rev. E 52, 5653–5655 (1995)] and by Sen [Phys. Rev. Lett. 77, 1–3 (1996)] by using random matrix theory connected with generalized Laguerre polynomials. Adopting this last viewpoint, we detail the probabilistic approach to this problem. Especially, viewing any Gaussian vector as a product of a uniformly distributed unitary vector by an Erlang distribution, we give a new insight for the different entropies introduced by Page.

CMOS-Compatible Through Silicon Vias for 3D Process Integration

ABSTRACTAs the limits of traditional CMOS scaling are approached, process integration has become increasingly difficult and resulting in a diminished rate of performance improvement over time. Consequently, the search for new two- and three- dimensional sub-system solutions has been pursued. One such solution is a silicon carrier-based System-on-Package (SOP) that enables high-density interconnection of heterogeneous die beyond current first level packaging densities. Silicon carrier packaging contains through silicon vias (TSV), fine pitch Cu wiring and high-density solder pads/joins, all of which are compatible with traditional semiconductor methods and tools. These same technology elements, especially the through silicon via process, also enable three dimensional stacking and integration. An approach to fabricating electrical through-vias in silicon is described, featuring annular-shaped vias instead of the more conventional cylindrical via. This difference enables large-area, uniform arrays to be produced with high yield as it is simpler to integrate into a conventional CMOS back-end-of-line (BEOL) process flow. Furthermore, the CTE-matched silicon core provides improved mechanical stability and the dimensions of the annular via allows for metallization by various means including copper electroplating or CVD tungsten deposition. An annular metal conductor process flow will be described. Through-via resistance measurements of 50, 90, and 150μm deep tungsten-filled annular vias will be compared. Two silicon carrier test vehicle designs, containing more than 2,200 and 9,600 electrical through-vias, respectively, were built to determine process yield and uniformity of via resistance. Through silicon via resistances range from 15-40 mΩ, and yields in excess of 99.99% have been demonstrated.

Structured SM identification of vehicle vertical dynamics

In this paper the problem of identifying discrete time nonlinear systems in regression form from finite and noise corrupted measurements is considered. According to the specifications about identification accuracy that may be needed, a good exploration of the regressor domain of interest has to be ensured by the experimental conditions. This problem becomes very significant for growing dimension of the regressor space, leading very easily to computational complexity problems and to inaccurate identified models. These difficulties are significantly reduced if, using information about the physical structure of the system to be identified, this can be decomposed into interacting subsystems. Using this structural information, the high-dimensional identification problem may be reduced to the identification of lower dimensional subsystems and to the estimation of their interactions. Typical cases considered in the literature are Hammerstein, Wiener and Lur'e systems, but the paper shows that the approach can be extended to more complex structures composed of many subsystems and with nonlinear dynamic blocks, using as an example the identification of a half-car model for vehicle vertical dynamics, where nonlinear suspensions and tyres are considered. Assuming that the road profile is given and that front and rear vertical accelerations are measured, an experimental setup easily realizable in actual experiments on real cars, the half-car model, is decomposed as a generalized Lur'e system, consisting of a linear MIMO system, connected in a feedback form with the two nonlinear dynamic systems through non-measured signals. An iterative identification scheme is proposed, which makes use of a set membership method for the identification of the nonlinear dynamic blocks. This method does not require assumptions on the functional form of the involved nonlinearities, thus circumventing the identification accuracy problems that may be generated by considering approximate functional forms. The numerical results demonstrate the effectiveness of the proposed approach.

Experimental Modeling of Controlled Suspension Vehicles from Onboard Sensors

In the paper, identification of vertical dynamics of vehicles With controlled suspensions is considered. Identification is performed from experimental data measured on a four-poster bench test of a segment C car, equipped with a CDC-Skyhook dampers control system. The measurements are obtained from the onboard accelerometers, needed by the control system. A nonlinear model in regression form is identified, having the road profile and damper control currents as inputs and chassis accelerations as outputs. The model is identified by means of a Set Membership structured identification method, which takes advantage of physical information on the structure of the system, decomposing the system in three subsystems: one represents the chassis and engine and the other two represent the overall behavior of front and rear suspensions, wheels and tires. This decomposition allows to avoid the complexity accuracy problems deriving from the high dimension of required regression space. Indeed, a high-dimensional identification problem is reduced to the identification of lower dimensional subsystems and to the estimation of their interactions. An iterative scheme is used for solving the decomposed identification problem. Since for usual road profiles the chassis pitch angle are small, the chassis-engine block is considered linear and standard linear methods are used for its identification. The other two subsystems are the main sources of nonlinearities in the system, mainly due to the significant nonlinearities of controlled dampers and of tires. Due to the complexity/accuracy problems of a physical modeling of these subsystems, an input-output approach is taken. In particular, a Nonlinear Set Membership (NSM) method, which does not require the search of the functional form of involved nonlinearities is used for the identification of these subsystems.

Radiation Induced Instability

In this paper we discuss the stability and instability properties of two classes of conservative dynamical systems which are comprised of a finite dimensional and an infinite dimensional subsystem. The finite dimensional component is a linear mechanical system with gyroscopic terms. The mechanical system is coupled to a wave equation defined on an infinite spatial domain via two different types of coupling which we denote by Lamb coupling and wave field coupling. We also investigate the effect of dispersion on the coupled system. In particular, we analyze the conditions under which coupling to a wave system induces instability in the finite dimensional system. Analytic results are compared to computer simulations.

Smooth Feedback, Global Stabilization, and Disturbance Attenuation of Nonlinear Systems with Uncontrollable Linearization

Problems of global asymptotic stabilization and disturbance attenuation are addressed for a class of highly nonlinear systems that are comprised of a lower dimensional zero-dynamics subsystem and a chain of power integrators perturbed by a nontriangular vector field. It is shown in this paper that global stabilization and disturbance attenuation are solvable by smooth state feedback if one takes full advantage of the characteristics of the system in the feedback design to dominate the nonlinearity rather than to cancel it. A systematic design procedure which is based upon, but generalizes, the recent technique of adding a power integrator is developed for the explicit construction of the smooth controllers. Several examples are presented to demonstrate the key features of the proposed nonlinear control schemes.