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Adaptive Synchronization of Interconnected Linear Systems

U. HELMKE, D. PRÄTZEL-WOLTERS, S. SCHMID
1991 IMA Journal of Mathematical Control and Information  
In this paper we introduce the concept of an adaptive synchronization controller. Synchronization is modelled as an adaptive tracking problem for families of interconnected linear systems.  ...  Stabilization and tracking results are obtained for minimum phase systems.  ...  Fuhrmann of the University of the Negev, Beer Sheva, who emphasized the synchronization problem and stimulated very much this paper.  ... 
doi:10.1093/imamci/8.4.397 fatcat:2zziukz5inbc3lwan3xfauexw4

Paradigms and puzzles in the theory of dynamical systems

J.C. Willems
1991 IEEE Transactions on Automatic Control  
Example: Let B denote all time-invariant dynamical systems We will use the terms "system" and "dynamical system" with time axis = R, consider the (trivial) group consisting of interchangeably.  ...  as time invariance), related to already in minimal state form (that is, very roughly speaking, the memory (as the state), involving the interaction with the that it assumes that the differential equations  ...  In Section XI.1, we have introduced linear time-invariant complete systems defined with time axis 2,.  ... 
doi:10.1109/9.73561 fatcat:m3547dn6t5gmfcma4fgfqpzyci

Distributed Robust Set-Invariance for Interconnected Linear Systems [article]

Sadra Sadraddini, Calin Belta
2017 arXiv   pre-print
We introduce a class of distributed control policies for networks of discrete-time linear systems with polytopic additive disturbances.  ...  The objective is to restrict the network-level state and controls to user-specified polyhedral sets for all times. This problem arises in many safety-critical applications. We consider two problems.  ...  For linear interconnected systems subject to additive disturbances, which are common in applications such as formation control and energy managament, it is well-known that the problem of designing optimal  ... 
arXiv:1709.10036v1 fatcat:xl2jkauuznfwfebctmklj5k3eq

Stability Analysis of a Constant Time-Headway Driving Strategy with Driver Memory Effects Modeled by Distributed Delays

Rifat Sipahi, Fatihcan M. Atay, Silviu-Iulian Niculescu
2015 IFAC-PapersOnLine  
In this article, we consider how the memory of drivers, modeled here with distributed delays, affects the decision making process in a car following scenario, in which each driver aims to keep a fixed  ...  time-headway with respect to the preceding vehicle.  ...  Consistent with the previous studies cited above, here we shall focus on time-invariant models and on the fate of the equilibrium dynamics of traffic flow through linear analysis.  ... 
doi:10.1016/j.ifacol.2015.09.407 fatcat:fskjfxsgt5g3zdhpaxjghmhglm

Three-dimensional self-organizing dynamical systems for discrete structures memorizing and retrieval

Alexander Yudashkin
2007 The European Symposium on Artificial Neural Networks  
Such models can be used in robotics, complex information systems and in pattern recognition tasks.  ...  The synthesis concept for dynamical system with the memory of multiple states defined with the quaternion algebra usage is considered.  ...  The singular linear mapping allows achieving spatial invariance in structures retrieval.  ... 
dblp:conf/esann/Yudashkin07 fatcat:wijowvk32naq7cujtdm4gdgck4

Behaviors, Latent Variables, and Interconnections (Special Issue on Mathematical Approaches to System Engineering Expository Articles)

J. C WILLEMS
1999 Systems, Control and Information  
For a linear time-invariant difft]rential plant, it is possible to prove that a behavior is implementable by a linear time-invariant controller if and only if its behavior is wedged in between the hidden  ...  In the linear time-invariant case this becomes d d R(aTt)w=M(El7t)e, with R and M polynomial. Define the mandest behavior of this system as d d i, )e}.  ...  Institute ofSystems, Control and Information Engineers Institute ofSystems, Control and Information Engineers Institute ofSystems, Control and Information Engineers Institute ofSystems, Control and Information  ... 
doi:10.11509/isciesci.43.9_453 fatcat:p5yop3r5dbfp5if3gucocjdnyy

Inversion of nonlinear and time-varying systems

Thomas A. Baran, Alan V. Oppenhiem
2011 2011 Digital Signal Processing and Signal Processing Education Meeting (DSP/SPE)  
This paper is concerned with the inversion of implementations for systems that may generally be nonlinear and time-varying.  ...  The techniques are applied to the inversion of nonlinear and time-varying systems, as well as to the problem of sparse matrix inversion.  ...  The discussion is focused on discrete-time systems involving linear interconnections that are memoryless and time-invariant, as many of the key issues carry over to arbitrary linear interconnections and  ... 
doi:10.1109/dsp-spe.2011.5739226 fatcat:4xeyqej5xncj7b35gxmyjlkocq

Page 1166 of Mathematical Reviews Vol. , Issue 93b [page]

1993 Mathematical Reviews  
He has studied es- pecially linear time-invariant discrete-time systems in great detail.  ...  In this paper we concentrate on continuous-time systems; in par- ticular we study a class of locally square integrable systems and we investigate whether closed, linear, time-invariant systems have finite  ... 

Modelling dynamical systems using manifest and latent variables

Jan C. Willems
2000 Mathematics and Computers in Simulation  
Subsequently, the notions of controllability and observability are cast in this setting.  ...  The behavioral approach provides a mathematical language for the modelling of systems, particularly dynamical systems. An introduction to behaviors is given, with emphasis to interconnected systems.  ...  For linear time-invariant differential systems, these questions are answered in the following theorem. Σ = (R, R w , B) be a linear time-invariant differential system.  ... 
doi:10.1016/s0378-4754(00)00209-3 fatcat:zgtu722fpfg4hlmz5zejagkjou

Covariance analysis algorithm for interconnected systems

ROBERT D. CURLEY, ICTOR H. L. CHENG, CHING-AN LIN
1991 Journal of Guidance Control and Dynamics  
System Interconnection and Statistics Propagation In this section, we shall first formulate the system equations for an arbitrary interconnection of N linear time-invariant finite-dimensional systems,  ...  It should be observed that even when the original nonlinear system is time-invariant, the resulting linearized model is, in general, time-varying.  ... 
doi:10.2514/3.20655 fatcat:5tna4h26ore6pmnwqar2qduhsq

An intrinsic behavioural approach to the double time axis paradox

Wenming Bian, Mark French, Harish Pillai
2009 Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference  
Behavioural theory is typically developed on the double time axis. On the other hand it is known that there are intrinsic difficulties with double time axis theorems in the input output context.  ...  Then: 1) B is said to be linear if B is a vector space. 2) B is said to be shift invariant (time invariant) if w ∈ B implies σ t w ∈ B for all t ∈ T .  ...  INTERCONNECTIONS We are primarily interested in the standard feedback interconnections shown in Figures 1 and 2 .  ... 
doi:10.1109/cdc.2009.5400257 dblp:conf/cdc/BianFP09 fatcat:wqyej4qsgjbg7gclfqb75vldbm

Higher order associative memories and their optical implementations

Demetri Psaltis, Cheol Hoon Park, John Hong
1988 Neural Networks  
Optical implementations of quadratic associative memories" are described using volume holograms for the general case and planar holograms for shift invariant memories.  ...  The properties of expansions that contain only a single order are investigated in detail and the use of the sum of outer product algorithm for training higher order memories is analyzed.  ...  The resulting system treats each of the 2N-1 shifted versions of the memory vectors as a new memory and as a result, the increased capacity of the quadratic memory over the linear one (by a factor of N  ... 
doi:10.1016/0893-6080(88)90017-2 fatcat:bhfeqssn2jfkzpavlryxejzskm

A new synthesis procedure for a class of cellular neural networks with space-invariant cloning template

Zanjun Lu, Derong Liu
1998 IEEE transactions on circuits and systems - 2, Analog and digital signal processing  
In the present synthesis procedure, the design problem is formulated as a set of linear inequalities, and the inequalities are solved using the well-known perceptron training algorithm.  ...  An algorithm is also provided to design CNN's with space-invariant cloning templates and with symmetric connection matrices to guarantee the global stability of the network.  ...  SPACE-INVARIANT CLONING TEMPLATE DESIGN A vector will be called a (stable) memory vector (or simply, a memory) of system (2) if = sat() and if is an asymptotically stable equilibrium point of system (  ... 
doi:10.1109/82.746682 fatcat:keikupsfbjgoxakgtnc7kymw34

Design and implementation of a biologically realistic olfactory cortex in analog VLSI

J.C. Principe, V.G. Tavares, J.G. Harris, W.J. Freeman
2001 Proceedings of the IEEE  
This paper reviews the problem of translating signals into symbols preserving maximally the information contained in the signal time structure.  ...  This analysis leads to a direct mixed-signal (analog amplitude/discrete time) implementation of the dynamical building block that simplifies the implementation of the interconnect.  ...  It can accept several spatial inputs that are weighted and summed, and then convolved with a linear time invariant system defined by the left hand side of (1).  ... 
doi:10.1109/5.939813 fatcat:nrdbshn5u5eptnd33sc4n6vo3a

Page 3124 of Mathematical Reviews Vol. , Issue 2003d [page]

2003 Mathematical Reviews  
Summary: “This paper considers an analysis and synthesis prob- lem of controllers for linear time-delay systems in the form of delay-dependent memory state feedback, and develops a linear matrix inequality  ...  synthesis for linear time-delay systems.  ... 
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