2,071 research outputs found
Diagnosis and Repair for Synthesis from Signal Temporal Logic Specifications
We address the problem of diagnosing and repairing specifications for hybrid
systems formalized in signal temporal logic (STL). Our focus is on the setting
of automatic synthesis of controllers in a model predictive control (MPC)
framework. We build on recent approaches that reduce the controller synthesis
problem to solving one or more mixed integer linear programs (MILPs), where
infeasibility of a MILP usually indicates unrealizability of the controller
synthesis problem. Given an infeasible STL synthesis problem, we present
algorithms that provide feedback on the reasons for unrealizability, and
suggestions for making it realizable. Our algorithms are sound and complete,
i.e., they provide a correct diagnosis, and always terminate with a non-trivial
specification that is feasible using the chosen synthesis method, when such a
solution exists. We demonstrate the effectiveness of our approach on the
synthesis of controllers for various cyber-physical systems, including an
autonomous driving application and an aircraft electric power system
Iterative actions of normal operators
Let be a normal operator in a Hilbert space , and let
be a countable set of vectors. We investigate
the relations between , , and that makes the system of
iterations complete, Bessel, a
basis, or a frame for . The problem is motivated by the dynamical
sampling problem and is connected to several topics in functional analysis,
including, frame theory and spectral theory. It also has relations to topics in
applied harmonic analysis including, wavelet theory and time-frequency
analysis.Comment: 14 pages, 0 figure
Classes of Skorokhod Embeddings for the Simple Symmetric Random Walk
The Skorokhod Embedding problem is well understood when the underlying
process is a Brownian motion. We examine the problem when the underlying is the
simple symmetric random walk and when no external randomisation is allowed. We
prove that any measure on Z can be embedded by means of a minimal stopping
time. However, in sharp contrast to the Brownian setting, we show that the set
of measures which can be embedded in a uniformly integrable way is strictly
smaller then the set of centered probability measures: specifically it is a
fractal set which we characterise as an iterated function system. Finally, we
define the natural extension of several known constructions from the Brownian
setting and show that these constructions require us to further restrict the
sets of target laws
Role of anticausal inverses in multirate filter-banks. I. System-theoretic fundamentals
In a maximally decimated filter bank with identical decimation ratios for all channels, the perfect reconstructibility property and the nature of reconstruction filters (causality, stability, FIR property, and so on) depend on the properties of the polyphase matrix. Various properties and capabilities of the filter bank depend on the properties of the polyphase matrix as well as the nature of its inverse. In this paper we undertake a study of the types of inverses and characterize them according to their system theoretic properties (i.e., properties of state-space descriptions, McMillan degree, degree of determinant, and so forth). We find in particular that causal polyphase matrices with anticausal inverses have an important role in filter bank theory. We study their properties both for the FIR and IIR cases. Techniques for implementing anticausal IIR inverses based on state space descriptions are outlined. It is found that causal FIR matrices with anticausal FIR inverses (cafacafi) have a key role in the characterization of FIR filter banks. In a companion paper, these results are applied for the factorization of biorthogonal FIR filter banks, and a generalization of the lapped orthogonal transform called the biorthogonal lapped transform (BOLT) developed
Synchronization and Control in Intrinsic and Designed Computation: An Information-Theoretic Analysis of Competing Models of Stochastic Computation
We adapt tools from information theory to analyze how an observer comes to
synchronize with the hidden states of a finitary, stationary stochastic
process. We show that synchronization is determined by both the process's
internal organization and by an observer's model of it. We analyze these
components using the convergence of state-block and block-state entropies,
comparing them to the previously known convergence properties of the Shannon
block entropy. Along the way, we introduce a hierarchy of information
quantifiers as derivatives and integrals of these entropies, which parallels a
similar hierarchy introduced for block entropy. We also draw out the duality
between synchronization properties and a process's controllability. The tools
lead to a new classification of a process's alternative representations in
terms of minimality, synchronizability, and unifilarity.Comment: 25 pages, 13 figures, 1 tabl
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