Subjects -> MATHEMATICS (Total: 1013 journals)
    - APPLIED MATHEMATICS (92 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (714 journals)
    - MATHEMATICS (GENERAL) (45 journals)
    - NUMERICAL ANALYSIS (26 journals)
    - PROBABILITIES AND MATH STATISTICS (113 journals)

MATHEMATICS (714 journals)            First | 1 2 3 4     

Showing 401 - 538 of 538 Journals sorted alphabetically
Journal of Mathematical and Fundamental Sciences     Open Access  
Journal of Mathematical Behavior     Hybrid Journal   (Followers: 6)
Journal of Mathematical Chemistry     Hybrid Journal   (Followers: 5)
Journal of Mathematical Finance     Open Access   (Followers: 6)
Journal of Mathematical Imaging and Vision     Hybrid Journal   (Followers: 6)
Journal of Mathematical Logic     Hybrid Journal   (Followers: 2)
Journal of Mathematical Sciences     Hybrid Journal  
Journal of Mathematical Sciences and Applications     Open Access   (Followers: 2)
Journal of Mathematical Sociology     Hybrid Journal   (Followers: 3)
Journal of Mathematics     Open Access  
Journal of Mathematics and Statistics     Open Access   (Followers: 6)
Journal of Mathematics and Statistics Studies     Open Access  
Journal of Mathematics and the Arts     Hybrid Journal   (Followers: 1)
Journal of Mathematics Education at Teachers College     Open Access   (Followers: 4)
Journal of Mathematics in Industry     Open Access  
Journal of Mathematics Research     Open Access  
Journal of Metallurgy     Open Access   (Followers: 8)
Journal of Modern Mathematics Frontier     Open Access  
Journal of Multidisciplinary Modeling and Optimization     Open Access   (Followers: 1)
Journal of Multivariate Analysis     Hybrid Journal   (Followers: 15)
Journal of Nonlinear Analysis and Optimization : Theory & Applications     Open Access   (Followers: 4)
Journal of Nonlinear Mathematical Physics     Hybrid Journal   (Followers: 2)
Journal of Nonlinear Science     Hybrid Journal   (Followers: 1)
Journal of Numerical Cognition     Open Access   (Followers: 1)
Journal of Optimization     Open Access   (Followers: 5)
Journal of Peridynamics and Nonlocal Modeling     Hybrid Journal  
Journal of Progressive Research in Mathematics     Open Access   (Followers: 1)
Journal of Pseudo-Differential Operators and Applications     Hybrid Journal  
Journal of Pure and Applied Algebra     Full-text available via subscription   (Followers: 3)
Journal of Quantitative Linguistics     Hybrid Journal   (Followers: 6)
Journal of Scientific Computing     Hybrid Journal   (Followers: 19)
Journal of Scientific Research     Open Access  
Journal of Symbolic Computation     Hybrid Journal   (Followers: 2)
Journal of the Australian Mathematical Society     Full-text available via subscription  
Journal of the Egyptian Mathematical Society     Open Access  
Journal of the Indian Mathematical Society     Hybrid Journal  
Journal of the Institute of Mathematics of Jussieu     Hybrid Journal  
Journal of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Journal of the Nigerian Mathematical Society     Open Access  
Journal of Theoretical and Applied Physics     Open Access   (Followers: 9)
Journal of Topology and Analysis     Hybrid Journal  
Journal of Transport and Supply Chain Management     Open Access   (Followers: 10)
Journal of Turbulence     Hybrid Journal   (Followers: 7)
Journal of Universal Mathematics     Open Access  
Journal of Urban Regeneration & Renewal     Full-text available via subscription   (Followers: 8)
JRAMathEdu : Journal of Research and Advances in Mathematics Education     Open Access   (Followers: 4)
JUMLAHKU : Jurnal Matematika Ilmiah STKIP Muhammadiyah Kuningan     Open Access  
JURING (Journal for Research in Mathematics Learning)     Open Access  
Jurnal Didactical Mathematics     Open Access   (Followers: 4)
Jurnal Matematika     Open Access  
Jurnal Matematika, Sains, Dan Teknologi     Open Access  
Jurnal Natural     Open Access  
Jurnal Pendidikan Matematika Raflesia     Open Access  
Jurnal Penelitian Pembelajaran Matematika Sekolah     Open Access  
Jurnal Penelitian Sains (JPS)     Open Access  
Jurnal Riset Pendidikan Matematika     Open Access  
Jurnal Sains Matematika dan Statistika     Open Access  
Jurnal Tadris Matematika     Open Access  
Jurnal Teknologi dan Sistem Komputer     Open Access  
Kontinu : Jurnal Penelitian Didaktik Matematika     Open Access  
Kreano, Jurnal Matematika Kreatif-Inovatif     Open Access  
Le Matematiche     Open Access  
Lettera Matematica     Hybrid Journal  
Lietuvos Matematikos Rinkinys     Open Access  
Limits : Journal of Mathematics and Its Applications     Open Access  
Linear Algebra and its Applications     Full-text available via subscription   (Followers: 22)
Linear and Multilinear Algebra     Hybrid Journal   (Followers: 7)
Lithuanian Mathematical Journal     Hybrid Journal  
Lobachevskii Journal of Mathematics     Open Access  
Logic Journal of the IGPL     Hybrid Journal   (Followers: 1)
Logica Universalis     Hybrid Journal  
manuscripta mathematica     Hybrid Journal   (Followers: 1)
MaPan : Jurnal Matematika dan Pembelajaran     Open Access  
Marine Genomics     Hybrid Journal   (Followers: 1)
Matemáticas, Educación y Sociedad     Open Access  
Matematicheskie Zametki     Full-text available via subscription  
Mathematica Scandinavica     Full-text available via subscription   (Followers: 1)
Mathematical Analysis and its Contemporary Applications     Open Access   (Followers: 1)
Mathematical Communications     Open Access  
Mathematical Computation     Open Access   (Followers: 1)
Mathematical Geosciences     Hybrid Journal   (Followers: 4)
Mathematical Journal of Interdisciplinary Sciences     Open Access   (Followers: 1)
Mathematical Medicine and Biology: A Journal of the IMA     Hybrid Journal   (Followers: 1)
Mathematical Methods in the Applied Sciences     Hybrid Journal   (Followers: 4)
Mathematical Methods of Statistics     Hybrid Journal   (Followers: 4)
Mathematical Modelling and Analysis     Open Access   (Followers: 1)
Mathematical Modelling of Natural Phenomena     Open Access   (Followers: 1)
Mathematical Models and Methods in Applied Sciences     Hybrid Journal   (Followers: 1)
Mathematical Notes     Hybrid Journal  
Mathematical Proceedings of the Cambridge Philosophical Society     Full-text available via subscription   (Followers: 2)
Mathematical Programming Computation     Hybrid Journal   (Followers: 2)
Mathematical Sciences     Open Access  
Mathematical Social Sciences     Hybrid Journal   (Followers: 1)
Mathematical Theory and Modeling     Open Access   (Followers: 6)
Mathematical Thinking and Learning     Hybrid Journal   (Followers: 4)
Mathematics and Statistics     Open Access   (Followers: 2)
Mathematics Education Forum Chitwan     Open Access   (Followers: 1)
Mathematics Education Journal     Open Access   (Followers: 4)
Mathematics Education Research Journal     Partially Free   (Followers: 16)
Mathematics of Control, Signals, and Systems (MCSS)     Hybrid Journal   (Followers: 5)
Mathematics Teacher: Learning and Teaching PK-12     Full-text available via subscription   (Followers: 9)
Mathematics Teaching in the Middle School     Full-text available via subscription   (Followers: 8)
Mathematische Annalen     Hybrid Journal   (Followers: 2)
Mathematische Nachrichten     Hybrid Journal   (Followers: 1)
Mathematische Semesterberichte     Hybrid Journal  
Mathematische Zeitschrift     Hybrid Journal   (Followers: 2)
MATICS     Open Access  
Matrix Science Mathematic     Open Access   (Followers: 1)
Measurement Science Review     Open Access   (Followers: 3)
Mediterranean Journal of Mathematics     Hybrid Journal  
Memetic Computing     Hybrid Journal  
Mendel : Soft Computing Journal     Open Access  
Metaheuristics     Hybrid Journal  
Metals and Materials International     Hybrid Journal   (Followers: 1)
Metascience     Hybrid Journal   (Followers: 1)
Metrology and Instruments / Метрологія та прилади     Open Access  
Milan Journal of Mathematics     Hybrid Journal  
MLQ- Mathematical Logic Quarterly     Hybrid Journal   (Followers: 1)
Modelling in Civil and Environmental Engineering     Open Access   (Followers: 4)
MONA : Matematik- og Naturfagsdidaktik     Hybrid Journal  
Monatshefte fur Mathematik     Hybrid Journal  
Moroccan Journal of Pure and Applied Analysis     Open Access  
Moscow University Mathematics Bulletin     Hybrid Journal  
MSOR Connections     Open Access   (Followers: 1)
Multiscale Modeling and Simulation     Hybrid Journal   (Followers: 2)
MUST : Journal of Mathematics Education, Science and Technology     Open Access   (Followers: 4)
Nagoya Mathematical Journal     Hybrid Journal   (Followers: 1)
Nano Research     Hybrid Journal   (Followers: 4)
Nanotechnologies in Russia     Hybrid Journal  
Natural Resource Modeling     Hybrid Journal  
New Mathematics and Natural Computation     Hybrid Journal   (Followers: 1)
Nonlinear Analysis     Hybrid Journal   (Followers: 1)
Nonlinear Analysis : Modelling and Control     Open Access   (Followers: 1)
Nonlinear Analysis: Hybrid Systems     Hybrid Journal  
Nonlinear Analysis: Real World Applications     Hybrid Journal   (Followers: 2)
Nonlinear Differential Equations and Applications NoDEA     Hybrid Journal  
North Carolina Journal of Mathematics and Statistics     Open Access  
Note di Matematica     Open Access  
NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin     Hybrid Journal   (Followers: 3)
Numeracy : Advancing Education in Quantitative Literacy     Open Access   (Followers: 1)
Numerical Analysis and Applications     Hybrid Journal   (Followers: 1)
Numerical Functional Analysis and Optimization     Hybrid Journal   (Followers: 3)
Numerical Linear Algebra with Applications     Hybrid Journal   (Followers: 7)
Numerische Mathematik     Hybrid Journal  
Open Journal of Discrete Mathematics     Open Access   (Followers: 3)
Open Journal of Modelling and Simulation     Open Access   (Followers: 2)
Operations Research Letters     Hybrid Journal   (Followers: 11)
Optimization Letters     Hybrid Journal   (Followers: 2)
Optimization Methods and Software     Hybrid Journal   (Followers: 6)
Opuscula Mathematica     Open Access  
Order     Hybrid Journal  
ORiON     Open Access  
P-Adic Numbers, Ultrametric Analysis, and Applications     Hybrid Journal  
PAMM : Proceedings in Applied Mathematics and Mechanics     Free  
Parallel Processing Letters     Hybrid Journal   (Followers: 3)
Peking Mathematical Journal     Hybrid Journal  
Periodica Mathematica Hungarica     Full-text available via subscription   (Followers: 1)
Petroleum Science     Open Access  
Philosophia Mathematica     Hybrid Journal   (Followers: 1)
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences     Full-text available via subscription   (Followers: 9)
PNA. Revista de Investigación en Didáctica de la Matemática     Open Access  
Polar Science     Hybrid Journal   (Followers: 3)
Positivity     Hybrid Journal  
Press Start     Open Access   (Followers: 1)
Prime Number     Full-text available via subscription  
Probability in the Engineering and Informational Sciences     Hybrid Journal   (Followers: 1)
Problemy Peredachi Informatsii     Full-text available via subscription  
Proceedings - Mathematical Sciences     Open Access   (Followers: 5)
Proceedings of the American Mathematical Society, Series B     Open Access   (Followers: 3)
Proceedings of the Edinburgh Mathematical Society     Hybrid Journal  
Proceedings of the Institution of Civil Engineers - Engineering and Computational Mechanics     Hybrid Journal   (Followers: 2)
Proceedings of the Latvian Academy of Sciences. Section B: Natural, Exact and Applied Sciences     Open Access   (Followers: 1)
Proceedings of the London Mathematical Society     Hybrid Journal   (Followers: 4)
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences     Full-text available via subscription   (Followers: 6)
Proceedings of the Royal Society of Edinburgh Section A Mathematics     Full-text available via subscription  
Proceedings of the Steklov Institute of Mathematics     Hybrid Journal  
Progress in Photovoltaics: Research & Applications     Hybrid Journal   (Followers: 6)
Proyecciones : Revista de Matematica     Open Access   (Followers: 1)
Publications Mathématiques de Besançon : Algèbre et Théorie des Nombres     Open Access  
Publications Mathématiques de L'IHÉS     Hybrid Journal   (Followers: 3)
Punjab University Journal of Mathematics     Open Access   (Followers: 2)
Pure Mathematics and Applications     Open Access  
Pythagoras     Open Access  
Quaestiones Mathematicae     Hybrid Journal  
Qualitative Theory of Dynamical Systems     Hybrid Journal  
Quantum Studies : Mathematics and Foundations     Hybrid Journal   (Followers: 2)
Quarterly Journal of Mathematics     Hybrid Journal  
Rare Metals     Hybrid Journal   (Followers: 2)
Recreational Mathematics Magazine     Open Access  
REDIMAT : Journal of Research in Mathematics Education     Open Access   (Followers: 6)
REMAT : Revista Eletrônica da Matemática     Open Access  
Rendiconti del Circolo Matematico di Palermo     Hybrid Journal  
Reportes Científicos de la FaCEN     Open Access  
Research in Mathematics Education     Hybrid Journal   (Followers: 13)
Research in Nondestructive Evaluation     Hybrid Journal   (Followers: 7)
Research in Number Theory     Hybrid Journal  
Research in the Mathematical Sciences     Open Access  
Research Journal of Pure Algebra     Open Access   (Followers: 1)
Researches in Mathematics     Open Access  
Results in Control and Optimization     Open Access  

  First | 1 2 3 4     

Similar Journals
Journal Cover
Mathematics of Control, Signals, and Systems (MCSS)
Journal Prestige (SJR): 0.855
Citation Impact (citeScore): 1
Number of Followers: 5  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 0932-4194 - ISSN (Online) 1435-568X
Published by Springer-Verlag Homepage  [2469 journals]
  • Manifold turnpikes, trims, and symmetries

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      Abstract: Abstract Classical turnpikes correspond to optimal steady states which are attractors of infinite-horizon optimal control problems. In this paper, motivated by mechanical systems with symmetries, we generalize this concept to manifold turnpikes. Specifically, the necessary optimality conditions projected onto a symmetry-induced manifold coincide with those of a reduced-order problem defined on the manifold under certain conditions. We also propose sufficient conditions for the existence of manifold turnpikes based on a tailored notion of dissipativity with respect to manifolds. Furthermore, we show how the classical Legendre transformation between Euler–Lagrange and Hamilton formalisms can be extended to the adjoint variables. Finally, we draw upon the Kepler problem to illustrate our findings.
      PubDate: 2022-05-03
       
  • Output feedback control with prescribed performance via funnel
           pre-compensator

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      Abstract: Abstract We study output reference tracking of systems with high relative degree via output feedback only; this is, tracking where the output derivatives are unknown. To this end, we prove that the conjunction of the funnel pre-compensator with a minimum phase system of arbitrary relative degree yields a system of the same relative degree which is minimum phase as well. The error between the original system’s output and the pre-compensator’s output evolves within a prescribed performance funnel; moreover, the derivatives of the funnel pre-compensator’s output are known explicitly. Therefore, output reference tracking with prescribed transient behaviour of the tracking error is possible without knowledge of the derivatives of the original system’s output; via funnel control schemes for instance.
      PubDate: 2022-04-27
       
  • The circle criterion for a class of sector-bounded dynamic nonlinearities

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      Abstract: Abstract We present a circle criterion which is necessary and sufficient for absolute stability with respect to a natural class of sector-bounded nonlinear causal operators. This generalized circle criterion contains the classical result as a special case. Furthermore, we develop a version of the generalized criterion which guarantees input-to-state stability.
      PubDate: 2022-04-18
       
  • Logarithmic regret in online linear quadratic control using Riccati
           updates

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      Abstract: Abstract An online policy learning problem of linear control systems is studied. In this problem, the control system is known and linear, and a sequence of quadratic cost functions is revealed to the controller in hindsight, and the controller updates its policy to achieve a sublinear regret, similar to online optimization. A modified online Riccati algorithm is introduced that under some boundedness assumption leads to logarithmic regret bound. In particular, the logarithmic regret for the scalar case is achieved without boundedness assumption. Our algorithm, while achieving a better regret bound, also has reduced complexity compared to earlier algorithms which rely on solving semi-definite programs at each stage.
      PubDate: 2022-04-07
       
  • Optimal portfolio and certainty equivalence estimator for the appreciation
           rate

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      Abstract: Abstract We study the optimal portfolio selection problem for the class of strategies which do not use direct observations of the appreciation rates of the prices, but rather use historical prices. We consider a multi-stock incomplete diffusion market model with random coefficients. An explicit solution exploring a modification of certainty equivalence principle is found for case of power utilities and for a case when the problem can be embedded to a Markovian setting. Some new estimators for the appreciation rates are given.
      PubDate: 2022-03-19
       
  • Direct coupling coherent quantum observers with discounted mean square
           performance criteria and penalized back-action

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      Abstract: Abstract This paper is concerned with quantum harmonic oscillators consisting of a quantum plant and a directly coupled coherent quantum observer. We employ discounted quadratic performance criteria in the form of exponentially weighted time averages of the second-order moments of the system variables. Small-gain-theorem bounds are obtained for the back-action of the observer on the covariance dynamics of the plant in terms of the plant–observer coupling. A coherent quantum filtering (CQF) problem is formulated as the minimization of the discounted mean square of an estimation error, with which the dynamic variables of the observer approximate those of the plant. The cost functional also involves a quadratic penalty on the plant–observer coupling matrix in order to mitigate the back-action effect. For the discounted mean square optimal CQF problem with penalized back-action, we establish the first-order necessary conditions of optimality in the form of algebraic matrix equations. By using the Hamiltonian structure of the Heisenberg dynamics and Lie-algebraic techniques, this set of equations is represented in a more explicit form for equally dimensioned plant and observer. For a class of such observers with autonomous estimation error dynamics, we obtain a solution of the CQF problem and outline a homotopy method. The computation of the performance criteria and the observer synthesis are illustrated by numerical examples.
      PubDate: 2022-03-05
      DOI: 10.1007/s00498-022-00315-4
       
  • Input-to-state stability for infinite-dimensional systems

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      PubDate: 2022-03-01
      DOI: 10.1007/s00498-021-00302-1
       
  • Exponential stability of a general slope limiter scheme for scalar
           conservation laws subject to a dissipative boundary condition

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      Abstract: Abstract In this paper, we establish the exponential BV stability of general systems of discretized scalar conservation laws with positive speed. The focus is on numerical approximation of such systems using a wide class of slope limiter schemes built from the upwind monotone flux. The proof is based on a Lyapunov analysis taken from the continuous theory (Coron et al. in J Differ Equ 262(1):1–30, 2017) and a careful use of Harten formalism.
      PubDate: 2022-03-01
      DOI: 10.1007/s00498-021-00301-2
       
  • Robust Stackelberg controllability for the Kuramoto–Sivashinsky
           equation

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      Abstract: Abstract In this article, the robust Stackelberg controllability (RSC) problem is studied for a nonlinear fourth-order parabolic equation, namely the Kuramoto–Sivashinsky equation. When three external sources are acting into the system, the RSC problem consists essentially in combining two subproblems: the first one is a saddle point problem among two sources. Such sources are called the “follower control” and its associated “disturbance signal.” This procedure corresponds to a robust control problem. The second one is a hierarchic control problem (Stackelberg strategy), which involves the third force, so-called leader control. The RSC problem establishes a simultaneous game for these forces in the sense that the leader control has as objective to verify a controllability property, while the follower control and perturbation solve a robust control problem. In this paper, the leader control obeys to the exact controllability to the trajectories. Additionally, iterative algorithms to approximate the robust control problem as well as the robust Stackelberg strategy for the nonlinear Kuramoto–Sivashinsky equation are developed and implemented.
      PubDate: 2022-02-24
      DOI: 10.1007/s00498-022-00316-3
       
  • Delayed stabilization of the Korteweg–de Vries equation on a
           star-shaped network

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      Abstract: Abstract In this work, we deal with the exponential stability of the nonlinear Korteweg–de Vries equation on a finite star-shaped network in the presence of delayed internal feedback. We start by proving the well-posedness of the system and some regularity results. Then, we state an exponential stabilization result using a Lyapunov function by imposing small initial data and a restriction over the lengths. In this part also, we are able to obtain an explicit expression for the decay rate. Then, we prove a semi-global exponential stability result, which is based on an observability inequality working directly on the nonlinear system. Next, we study the case where it may happen that a control domain with delay is outside the control domain without delay. In that case, we obtain also a local exponential stabilization result. Finally, we present some numerical simulations to illustrate the stabilization.
      PubDate: 2022-02-24
      DOI: 10.1007/s00498-022-00319-0
       
  • Stabilization of capital accumulation games

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      Abstract: Abstract In this paper, the potential differential game concept introduced by Fonseca-Morales and Hernández-Lerma (2018) is used in analyzing stabilization problems for n-player noncooperative capital accumulation games (CAGs). By first identifying a CAG as a potential game, an associated optimal control problem (OCP) of the CAG is obtained, whose optimal solution is an open-loop Nash equilibrium for the CAG. Compared with a saddle-point stability condition obtained for undiscounted CAG in the literature, a sufficient and easily verifiable condition is obtained for both discounted and undiscounted CAGs. In addition, the concept allows the turnpike property obtained for OCPs in Trélat and Zuazua (2015) to be verified for CAGs. Lastly, an illustrative example is given to verify the latter stability result for some CAGs.
      PubDate: 2022-02-19
      DOI: 10.1007/s00498-022-00314-5
       
  • The coarsest lattice that determines a discrete multidimensional system

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      Abstract: Abstract A discrete multidimensional system is the set of solutions to a system of linear partial difference equations defined on the lattice \(\mathbb {Z}^n\) . This paper shows that it is determined by a unique coarsest sublattice, in the sense that the solutions of the system on this sublattice determine the solutions on \(\mathbb {Z}^n\) ; it is therefore the correct domain of definition of the discrete system. In turn, the defining sublattice is determined by a Galois group of symmetries that leave invariant the equations defining the system. These results find application in understanding properties of the system such as controllability and autonomy, and in its order reduction.
      PubDate: 2022-02-16
      DOI: 10.1007/s00498-022-00318-1
       
  • Controllability and semigroups of invariant control systems on $${\mathrm
           {Sl}}\left( n,{\mathbb {H}}\right) $$ Sl n , H

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      Abstract: Abstract Let \({\mathrm {Sl}}\left( n,{\mathbb {H}}\right) \) be the Lie group of \(n\times n \) quaternionic matrices g with \(\left \det g\right =1\) . We prove that a subsemigroup \(S \subset {\mathrm {Sl}}\left( n,{\mathbb {H}}\right) \) with nonempty interior is equal to \({\mathrm {Sl}}\left( n,{\mathbb {H}}\right) \) if S contains a special subgroup isomorphic to \({\mathrm {Sl}}\left( 2,{\mathbb {H}}\right) \) . From this, we give sufficient conditions on \(A,B\in \mathfrak {sl}\left( n, {\mathbb {H}}\right) \) to ensure that the invariant control system \({\dot{g}} =Ag+uBg\) is controllable on \({\mathrm {Sl}}\left( n,{\mathbb {H}}\right) \) . We prove also that these conditions are generic in the sense that we obtain an open and dense set of controllable pairs \(\left( A,B\right) \in \mathfrak {sl}\left( n,{\mathbb {H}}\right) ^{2}\) .
      PubDate: 2022-02-11
      DOI: 10.1007/s00498-022-00317-2
       
  • Integral input-to-state stability of unbounded bilinear control systems

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      Abstract: Abstract We study integral input-to-state stability of bilinear systems with unbounded control operators and derive natural sufficient conditions. The results are applied to a bilinearly controlled Fokker–Planck equation.
      PubDate: 2022-02-07
      DOI: 10.1007/s00498-021-00308-9
       
  • Unified reinforcement Q-learning for mean field game and control problems

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      Abstract: Abstract We present a Reinforcement Learning (RL) algorithm to solve infinite horizon asymptotic Mean Field Game (MFG) and Mean Field Control (MFC) problems. Our approach can be described as a unified two-timescale Mean Field Q-learning: The same algorithm can learn either the MFG or the MFC solution by simply tuning the ratio of two learning parameters. The algorithm is in discrete time and space where the agent not only provides an action to the environment but also a distribution of the state in order to take into account the mean field feature of the problem. Importantly, we assume that the agent cannot observe the population’s distribution and needs to estimate it in a model-free manner. The asymptotic MFG and MFC problems are also presented in continuous time and space, and compared with classical (non-asymptotic or stationary) MFG and MFC problems. They lead to explicit solutions in the linear-quadratic (LQ) case that are used as benchmarks for the results of our algorithm.
      PubDate: 2022-01-15
      DOI: 10.1007/s00498-021-00310-1
       
  • Control sets for bilinear and affine systems

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      Abstract: Abstract For homogeneous bilinear control systems, the control sets are characterized using a Lie algebra rank condition for the induced systems on projective space. This is based on a classical Diophantine approximation result. For affine control systems, the control sets around the equilibria for constant controls are characterized with particular attention to the question when the control sets are unbounded.
      PubDate: 2021-11-12
      DOI: 10.1007/s00498-021-00311-0
       
  • Parameter calibration with stochastic gradient descent for interacting
           particle systems driven by neural networks

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      Abstract: Abstract We propose a neural network approach to model general interaction dynamics and an adjoint-based stochastic gradient descent algorithm to calibrate its parameters. The parameter calibration problem is considered as optimal control problem that is investigated from a theoretical and numerical point of view. We prove the existence of optimal controls, derive the corresponding first-order optimality system and formulate a stochastic gradient descent algorithm to identify parameters for given data sets. To validate the approach, we use real data sets from traffic and crowd dynamics to fit the parameters. The results are compared to forces corresponding to well-known interaction models such as the Lighthill–Whitham–Richards model for traffic and the social force model for crowd motion.
      PubDate: 2021-10-27
      DOI: 10.1007/s00498-021-00309-8
       
  • Nonlinear robust periodic output regulation of minimum phase systems

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      Abstract: Abstract In linear system theory, it is a well-known fact that a regulator given by the cascade of an oscillatory dynamics, driven by some regulated variables, and of a stabiliser stabilising the cascade of the plant and of the oscillators has the ability of blocking on the steady state of the regulated variables any harmonics matched with the ones of the oscillators. This is the well-celebrated internal model principle. In this paper, we are interested to follow the same design route for a controlled plant that is a nonlinear and periodic system with period T: we add a bunch of linear oscillators, embedding \(n_o\) harmonics that are multiple of \(2 \pi /T\) , driven by a “regulated variable” of the nonlinear system, we look for a stabiliser for the nonlinear cascade of the plant and the oscillators, and we study the asymptotic properties of the resulting closed-loop regulated variable. In this framework, the contributions of the paper are multiple: for specific class of minimum-phase systems we present a systematic way of designing a stabiliser, which is uniform with respect to \(n_o\) , by using a mix of high-gain and forwarding techniques; we prove that the resulting closed-loop system has a periodic steady state with period T with a domain of attraction not shrinking with \(n_o\) ; similarly to the linear case, we also show that the spectrum of the steady-state closed-loop regulated variable does not contain the n harmonics embedded in the bunch of oscillators and that the \(L_2\) norm of the regulated variable is a monotonically decreasing function of \(n_o\) . The results are robust, namely the asymptotic properties on the regulated variable hold also in the presence of any uncertainties in the controlled plant not destroying closed-loop stability.
      PubDate: 2021-10-26
      DOI: 10.1007/s00498-021-00307-w
       
  • Stability conditions for impulsive dynamical systems

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      Abstract: Abstract In this work, we consider impulsive dynamical systems evolving on an infinite-dimensional space and subjected to external perturbations. We look for stability conditions that guarantee the input-to-state stability for such systems. Our new dwell-time conditions allow the situation, where both continuous and discrete dynamics can be unstable simultaneously. Lyapunov like methods are developed for this purpose. Illustrative finite and infinite dimensional examples are provided to demonstrate the application of the main results. These examples cannot be treated by any other published approach and demonstrate the effectiveness of our results.
      PubDate: 2021-09-22
      DOI: 10.1007/s00498-021-00305-y
       
  • Analysis of periodic linear systems over finite fields with and without
           Floquet Transform

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      Abstract: Abstract This paper develops the analysis of discrete-time periodically time-varying linear systems over finite fields. It is shown that the conditions for the existence of Floquet Transform for periodic linear systems over reals (or complex) do not carry forward for this case over finite fields. The existence of Floquet Transform is shown to be equivalent to the existence of an Nth root of the monodromy matrix for the class of non-singular periodic linear systems. As the verification of existence and computation of the Nth root is a computationally hard problem, an independent analysis of the solutions of such systems is carried without the use of Floquet Transform. It is proved that all initial conditions of such systems lie either in a periodic orbit or a chain leading to a periodic orbit. A subspace of the state space is also identified, containing all initial conditions lying on a periodic orbit. Further, whenever the Floquet Transform exists, more concrete results on the orbit lengths are established depending on the coprimeness of the orbit length with the system period.
      PubDate: 2021-09-07
      DOI: 10.1007/s00498-021-00304-z
       
 
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