1,085 research outputs found
Periodic behaviors
This paper studies behaviors that are defined on a torus, or equivalently,
behaviors defined in spaces of periodic functions, and establishes their basic
properties analogous to classical results of Malgrange, Palamodov, Oberst et
al. for behaviors on R^n. These properties - in particular the Nullstellensatz
describing the Willems closure - are closely related to integral and rational
points on affine algebraic varieties.Comment: 13 page
Causal and Stable Input/Output Structures on Multidimensional Behaviours
In this work we study multidimensional (nD) linear differential behaviours with a distinguished independent variable called "time". We define in a natural way causality and stability on input/output structures with respect to this distinguished direction. We make an extension of some results in the theory of partial differential equations, demonstrating that causality is equivalent to a property of the transfer matrix which is essentially hyperbolicity of the Pc operator defining the behaviour (Bc)0,y We also quote results which in effect characterise time autonomy for the general systems case. Stability is likewise characterized by a property of the transfer matrix. We prove this result for the 2D case and for the case of a single equation; for the general case it requires solution of an open problem concerning the geometry of a particular set in Cn. In order to characterize input/output stability we also develop new results on inclusions of kernels, freeness of variables, and closure with respect to S,S' and associated spaces, which are of independent interest. We also discuss stability of autonomous behaviours, which we beleive to be governed by a corresponding condition
Dissipativity preserving model reduction by retention of trajectories of minimal dissipation
We present a method for model reduction based on ideas from the behavioral theory of dissipative systems, in which the reduced order model is required to reproduce a subset of the set of trajectories of minimal dissipation of the original system. The passivity-preserving model reduction method of Antoulas (Syst Control Lett 54:361-374, 2005) and Sorensen (Syst Control Lett 54:347-360, 2005) is shown to be a particular case of this more general class of model reduction procedures
State Amplification
We consider the problem of transmitting data at rate R over a state dependent
channel p(y|x,s) with the state information available at the sender and at the
same time conveying the information about the channel state itself to the
receiver. The amount of state information that can be learned at the receiver
is captured by the mutual information I(S^n; Y^n) between the state sequence
S^n and the channel output Y^n. The optimal tradeoff is characterized between
the information transmission rate R and the state uncertainty reduction rate
\Delta, when the state information is either causally or noncausally available
at the sender. This result is closely related and in a sense dual to a recent
study by Merhav and Shamai, which solves the problem of masking the state
information from the receiver rather than conveying it.Comment: 9 pages, 4 figures, submitted to IEEE Trans. Inform. Theory, revise
Algebraic characterization of approximate controllability of behaviours of spatially invariant systems
An algebraic characterization of the property of approximate controllability is given, for behaviours of spatially invariant dynamical systems, consisting of distributional solutions w, that are periodic in the spatial variables, to a system of partial differential equations [formula presented] corresponding to a polynomial matrix M â (C[Ξ1,...,Ξd,Ď])mĂn. This settles an issue left open in Sasane (2004)
Derivatives and Default Risk
Upstream producers that possess market power, sell forwards with a lengthy duration to regional electricity companies (REC). As part of the liberalization of the electricity market, RECs have been privatized and exposed to a possible bankruptcy threat if spot prices have fallen below their expected value. The downstream firmsâ expected profit is larger, when it is less likely to be bailed out, the effect on upstream profits is ambiguous while consumers loose. Options are less welfare increasing than forwards, but the difference is minimal. In the presence of bankruptcy, options are the preferred welfare maximizing market instrument.Forwards; Options; Default Risk; Market Efficiency
Stochastic control system parameter identifiability
The parameter identification problem of general discrete time, nonlinear, multiple input/multiple output dynamic systems with Gaussian white distributed measurement errors is considered. The knowledge of the system parameterization was assumed to be known. Concepts of local parameter identifiability and local constrained maximum likelihood parameter identifiability were established. A set of sufficient conditions for the existence of a region of parameter identifiability was derived. A computation procedure employing interval arithmetic was provided for finding the regions of parameter identifiability. If the vector of the true parameters is locally constrained maximum likelihood (CML) identifiable, then with probability one, the vector of true parameters is a unique maximal point of the maximum likelihood function in the region of parameter identifiability and the constrained maximum likelihood estimation sequence will converge to the vector of true parameters
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