The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Andrey V Savkin - One of the best experts on this subject based on the ideXlab platform.
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analysis and synthesis of networked control systems Topological Entropy observability robustness and optimal control
Automatica, 2006Co-Authors: Andrey V SavkinAbstract:This paper extends the concept of Topological to the case of uncertain dynamical systems. We address problems of observability and optimal control via limited capacity digital communication channels. The main results are given in terms of inequalities between date rate of the communication channel and Topological Entropy of the open-loop system. Topological Entropy is calculated for some classes of uncertain dynamical systems.
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analysis and synthesis of networked control systems Topological Entropy observability robustness and optimal control
IFAC Proceedings Volumes, 2005Co-Authors: Andrey V SavkinAbstract:Abstract This paper extends the concept of Topological Entropy to the case of uncertain dynamical systems. We address problems of observability and optimal control via limited capacity digital communication channels. The main results are given in terms of inequalities between date rate of the communication channel and Topological Entropy of the open-loop system. Topological Entropy is calculated for some classes of uncertain dynamical systems.
Emanuela Merelli - One of the best experts on this subject based on the ideXlab platform.
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a new Topological Entropy based approach for measuring similarities among piecewise linear functions
Signal Processing, 2017Co-Authors: Matteo Rucco, Rocio Gonzalezdiaz, Maria Jose Jimenez, Nieves Atienza, Cristina Cristalli, Enrico Concettoni, Andrea Ferrante, Emanuela MerelliAbstract:In this paper we present a novel methodology based on a Topological Entropy, the so-called persistent Entropy, for addressing the comparison between discrete piecewise linear functions. The comparison is certified by the stability theorem for persistent Entropy that is presented here. The theorem is used in the implementation of a new algorithm. The algorithm transforms a discrete piecewise linear function into a filtered simplicial complex that is analyzed via persistent homology and persistent Entropy. Persistent Entropy is used as a discriminant feature for solving the supervised classification problem of real long-length noisy signals of DC electrical motors. The quality of classification is stated in terms of the area under receiver operating characteristic curve (AUC=93.87%). HighlightsDefinition of a new Entropy from the persistent barcode.Proof of the stability theorem for the persistent Entropy.Development of a new Entropy-based methodology for studying piecewise linear function.Development of a new Entropy-based algorithm for the classification of real signals
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a new Topological Entropy based approach for measuring similarities among piecewise linear functions
arXiv: Discrete Mathematics, 2015Co-Authors: Matteo Rucco, Rocio Gonzalezdiaz, Maria Jose Jimenez, Nieves Atienza, Cristina Cristalli, Enrico Concettoni, Andrea Ferrante, Emanuela MerelliAbstract:In this paper we present a novel methodology based on a Topological Entropy, the so-called persistent Entropy, for addressing the comparison between discrete piecewise linear functions. The comparison is certified by the stability theorem for persistent Entropy. The theorem is used in the implementation of a new algorithm. The algorithm transforms a discrete piecewise linear function into a filtered simplicial complex that is analyzed with persistent homology and persistent Entropy. Persistent Entropy is used as discriminant feature for solving the supervised classification problem of real long length noisy signals of DC electrical motors. The quality of classification is stated in terms of the area under receiver operating characteristic curve (AUC=94.52%).
Wen Huang - One of the best experts on this subject based on the ideXlab platform.
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positive Topological Entropy and δ weakly mixing sets
Advances in Mathematics, 2017Co-Authors: Wen Huang, Xiaoyao ZhouAbstract:Abstract The notion of Δ-weakly mixing set is introduced and studied. It is proved that Δ-weakly mixing sets share many properties with weakly mixing sets, in particular, if a dynamical system has positive Topological Entropy, then the collection of Δ-weakly mixing sets is residual in the closure of the collection of Entropy sets in the hyperspace. The existence of Δ-weakly mixing sets in a Topological dynamical system admitting an ergodic invariant measure which is not measurable distal is obtained. These results generalize several well known results and also answer several open questions.
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variational principles for Topological entropies of subsets
Journal of Functional Analysis, 2012Co-Authors: Dejun Feng, Wen HuangAbstract:Let (X,T) be a Topological dynamical system. We define the measure-theoretical lower and upper entropies hμ(T), h¯μ(T) for any μ∈M(X), where M(X) denotes the collection of all Borel probability measures on X. For any non-empty compact subset K of X, we show that htopB(T,K)=sup{hμ(T):μ∈M(X),μ(K)=1},htopP(T,K)=sup{h¯μ(T):μ∈M(X),μ(K)=1}, where htopB(T,K) denotes the Bowen Topological Entropy of K, and htopP(T,K) the packing Topological Entropy of K. Furthermore, when htop(T)<∞, the first equality remains valid when K is replaced by any analytic subset of X. The second equality always extends to any analytic subset of X.
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variational principles for Topological entropies of subsets
arXiv: Dynamical Systems, 2010Co-Authors: Dejun Feng, Wen HuangAbstract:Let $(X,T)$ be a Topological dynamical system. We define the measure-theoretical lower and upper entropies $\underline{h}_\mu(T)$, $\bar{h}_\mu(T)$ for any $\mu\in M(X)$, where $M(X)$ denotes the collection of all Borel probability measures on $X$. For any non-empty compact subset $K$ of $X$, we show that $$\htop^B(T, K)= \sup \{\underline{h}_\mu(T): \mu\in M(X),\; \mu(K)=1\}, $$ $$\htop^P(T, K)= \sup \{\bar{h}_\mu(T): \mu\in M(X),\; \mu(K)=1\}. $$ where $\htop^B(T, K)$ denotes Bowen's Topological Entropy of $K$, and $\htop^P(T, K)$ the packing Topological Entropy of $K$. Furthermore, when $\htop(T)<\infty$, the first equality remains valid when $K$ is replaced by an arbitrarily analytic subset of $X$. The second equality always extends to any analytic subset of $X$.
Daniel Liberzon - One of the best experts on this subject based on the ideXlab platform.
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Topological Entropy of switched nonlinear systems
International Conference on Hybrid Systems: computation and control, 2021Co-Authors: Guosong Yang, Daniel Liberzon, Joao P HespanhaAbstract:This paper studies Topological Entropy of switched nonlinear systems. We construct a general upper bound for the Topological Entropy in terms of an average of the asymptotic suprema of the measures of Jacobian matrices of individual modes, weighted by the corresponding active rates. A general lower bound is constructed in terms of an active-rate-weighted average of the asymptotic infima of the traces of these Jacobian matrices. For switched systems with diagonal modes, we construct upper and lower bounds that only depend on the eigenvalues of Jacobian matrices, their relative order among individual modes, and the active rates. For both cases, we also construct more conservative upper bounds that require less information on the switching, with their relations illustrated by numerical examples of a switched Lotka-Volterra ecosystem model.
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Topological Entropy of switched linear systems: general matrices and matrices with commutation relations
Mathematics of Control Signals and Systems, 2020Co-Authors: Guosong Yang, Daniel Liberzon, A. James Schmidt, Joao P HespanhaAbstract:This paper studies a notion of Topological Entropy for switched systems, formulated in terms of the minimal number of trajectories needed to approximate all trajectories with a finite precision. For general switched linear systems, we prove that the Topological Entropy is independent of the set of initial states. We construct an upper bound for the Topological Entropy in terms of an average of the measures of system matrices of individual modes, weighted by their corresponding active times, and a lower bound in terms of an active-time-weighted average of their traces. For switched linear systems with scalar-valued state and those with pairwise commuting matrices, we establish formulae for the Topological Entropy in terms of active-time-weighted averages of the eigenvalues of system matrices of individual modes. For the more general case with simultaneously triangularizable matrices, we construct upper bounds for the Topological Entropy that only depend on the eigenvalues, their order in a simultaneous triangularization, and the active times. In each case above, we also establish upper bounds that are more conservative but require less information on the system matrices or on the switching, with their relations illustrated by numerical examples. Stability conditions inspired by the upper bounds for the Topological Entropy are presented as well.
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on Topological Entropy and stability of switched linear systems
ACM International Conference Hybrid Systems: Computation and Control, 2019Co-Authors: Guosong Yang, Joao P Hespanha, Daniel LiberzonAbstract:This paper studies Topological Entropy and stability properties of switched linear systems. First, we show that the exponential growth rates of solutions of a switched linear system are essentially upper bounded by its Topological Entropy. Second, we estimate the Topological Entropy of a switched linear system by decomposing it into a part that is generated by scalar multiples of the identity matrix and a part that has zero Entropy, and proving that the overall Topological Entropy is upper bounded by that of the former. Third, we prove that a switched linear system is globally exponentially stable if its Topological Entropy remains zero under a destabilizing perturbation. Finally, the Entropy estimation via decomposition and the Entropy-based stability condition are applied to three classes of switched linear systems to construct novel upper bounds for Topological Entropy and novel sufficient conditions for global exponential stability.
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on Topological Entropy of switched linear systems with diagonal triangular and general matrices
Conference on Decision and Control, 2018Co-Authors: Guosong Yang, James A Schmidt, Daniel LiberzonAbstract:This paper introduces a notion of Topological Entropy for switched systems, formulated using the minimal number of initial states needed to approximate all initial states within a finite precision. We show that it can be equivalently defined using the maximal number of initial states separable within a finite precision, and introduce switching-related quantities such as the active time of each mode, which prove to be useful in calculating the Topological Entropy of switched linear systems. For general switched linear systems, we show that the Topological Entropy is independent of the set of initial states, and establish upper and lower bounds using the active-time-weighted averages of the norms and traces of system matrices in individual modes, respectively. For switched linear systems with scalar-valued state or simultaneously diagonalizable matrices, we derive formulae for the Topological Entropy using active-time-weighted averages of eigenvalues, which can be extended to the case with simultaneously triangularizable matrices to obtain an upper bound. In these three cases with special matrix structure, we also provide more general but more conservative upper bounds for the Topological Entropy.
Matteo Rucco - One of the best experts on this subject based on the ideXlab platform.
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a new Topological Entropy based approach for measuring similarities among piecewise linear functions
Signal Processing, 2017Co-Authors: Matteo Rucco, Rocio Gonzalezdiaz, Maria Jose Jimenez, Nieves Atienza, Cristina Cristalli, Enrico Concettoni, Andrea Ferrante, Emanuela MerelliAbstract:In this paper we present a novel methodology based on a Topological Entropy, the so-called persistent Entropy, for addressing the comparison between discrete piecewise linear functions. The comparison is certified by the stability theorem for persistent Entropy that is presented here. The theorem is used in the implementation of a new algorithm. The algorithm transforms a discrete piecewise linear function into a filtered simplicial complex that is analyzed via persistent homology and persistent Entropy. Persistent Entropy is used as a discriminant feature for solving the supervised classification problem of real long-length noisy signals of DC electrical motors. The quality of classification is stated in terms of the area under receiver operating characteristic curve (AUC=93.87%). HighlightsDefinition of a new Entropy from the persistent barcode.Proof of the stability theorem for the persistent Entropy.Development of a new Entropy-based methodology for studying piecewise linear function.Development of a new Entropy-based algorithm for the classification of real signals
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a new Topological Entropy based approach for measuring similarities among piecewise linear functions
arXiv: Discrete Mathematics, 2015Co-Authors: Matteo Rucco, Rocio Gonzalezdiaz, Maria Jose Jimenez, Nieves Atienza, Cristina Cristalli, Enrico Concettoni, Andrea Ferrante, Emanuela MerelliAbstract:In this paper we present a novel methodology based on a Topological Entropy, the so-called persistent Entropy, for addressing the comparison between discrete piecewise linear functions. The comparison is certified by the stability theorem for persistent Entropy. The theorem is used in the implementation of a new algorithm. The algorithm transforms a discrete piecewise linear function into a filtered simplicial complex that is analyzed with persistent homology and persistent Entropy. Persistent Entropy is used as discriminant feature for solving the supervised classification problem of real long length noisy signals of DC electrical motors. The quality of classification is stated in terms of the area under receiver operating characteristic curve (AUC=94.52%).
