Subjects -> MATHEMATICS (Total: 1074 journals)
    - APPLIED MATHEMATICS (86 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (793 journals)
    - MATHEMATICS (GENERAL) (43 journals)
    - NUMERICAL ANALYSIS (23 journals)
    - PROBABILITIES AND MATH STATISTICS (106 journals)

MATHEMATICS (793 journals)            First | 1 2 3 4     

Showing 401 - 538 of 538 Journals sorted alphabetically
Journal of Dynamics and Differential Equations     Hybrid Journal  
Journal of Engineering Mathematics     Hybrid Journal   (Followers: 2)
Journal of Evolution Equations     Hybrid Journal  
Journal of Experimental Algorithmics     Full-text available via subscription   (Followers: 1)
Journal of Flood Risk Management     Hybrid Journal   (Followers: 12)
Journal of Formalized Reasoning     Open Access   (Followers: 2)
Journal of Function Spaces     Open Access  
Journal of Functional Analysis     Full-text available via subscription   (Followers: 2)
Journal of Geochemical Exploration     Hybrid Journal   (Followers: 1)
Journal of Geological Research     Open Access   (Followers: 1)
Journal of Geovisualization and Spatial Analysis     Hybrid Journal  
Journal of Global Optimization     Hybrid Journal   (Followers: 6)
Journal of Global Research in Mathematical Archives     Open Access   (Followers: 1)
Journal of Group Theory     Hybrid Journal   (Followers: 2)
Journal of Homotopy and Related Structures     Hybrid Journal  
Journal of Honai Math     Open Access  
Journal of Humanistic Mathematics     Open Access   (Followers: 1)
Journal of Hyperbolic Differential Equations     Hybrid Journal  
Journal of Indian Council of Philosophical Research     Hybrid Journal  
Journal of Industrial Mathematics     Open Access   (Followers: 2)
Journal of Inequalities and Applications     Open Access  
Journal of Infrared, Millimeter and Terahertz Waves     Hybrid Journal   (Followers: 2)
Journal of Integrable Systems     Open Access   (Followers: 1)
Journal of K-Theory     Full-text available via subscription  
Journal of Knot Theory and Its Ramifications     Hybrid Journal   (Followers: 1)
Journal of Kufa for Mathematics and Computer     Open Access   (Followers: 1)
Journal of Liquid Chromatography & Related Technologies     Hybrid Journal   (Followers: 7)
Journal of Logical and Algebraic Methods in Programming     Hybrid Journal  
Journal of Manufacturing Systems     Full-text available via subscription   (Followers: 4)
Journal of Mathematical Analysis and Applications     Full-text available via subscription   (Followers: 4)
Journal of mathematical and computational science     Open Access   (Followers: 7)
Journal of Mathematical and Fundamental Sciences     Open Access  
Journal of Mathematical Behavior     Hybrid Journal   (Followers: 2)
Journal of Mathematical Chemistry     Hybrid Journal   (Followers: 3)
Journal of Mathematical Cryptology     Hybrid Journal   (Followers: 1)
Journal of Mathematical Extension     Open Access   (Followers: 3)
Journal of Mathematical Finance     Open Access   (Followers: 7)
Journal of Mathematical Imaging and Vision     Hybrid Journal   (Followers: 6)
Journal of Mathematical Logic     Hybrid Journal   (Followers: 2)
Journal of Mathematical Modelling and Algorithms     Hybrid Journal   (Followers: 1)
Journal of Mathematical Neuroscience     Open Access   (Followers: 9)
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: 8)
Journal of Mathematics and the Arts     Hybrid Journal   (Followers: 2)
Journal of Mathematics in Industry     Open Access  
Journal of Mathematics Research     Open Access   (Followers: 6)
Journal of Metallurgy     Open Access   (Followers: 7)
Journal of Modern Mathematics Frontier     Open Access  
Journal of Multidisciplinary Modeling and Optimization     Open Access  
Journal of Multivariate Analysis     Hybrid Journal   (Followers: 13)
Journal of Natural Sciences and Mathematics Research     Open Access  
Journal of Nonlinear Analysis and Optimization : Theory & Applications     Open Access   (Followers: 4)
Journal of Nonlinear Mathematical Physics     Hybrid Journal   (Followers: 1)
Journal of Nonlinear Science     Hybrid Journal   (Followers: 1)
Journal of Numerical Cognition     Open Access  
Journal of Numerical Mathematics     Hybrid Journal   (Followers: 2)
Journal of Optimization     Open Access   (Followers: 4)
Journal of Peridynamics and Nonlocal Modeling     Hybrid Journal  
Journal of Problem Solving     Open Access   (Followers: 2)
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: 4)
Journal of Quantitative Analysis in Sports     Hybrid Journal   (Followers: 8)
Journal of Quantitative Linguistics     Hybrid Journal   (Followers: 6)
Journal of Scientific Computing     Hybrid Journal   (Followers: 18)
Journal of Scientific Research     Open Access  
Journal of Symbolic Computation     Hybrid Journal   (Followers: 1)
Journal of the Australian Mathematical Society     Full-text available via subscription  
Journal of the Egyptian Mathematical Society     Open Access  
Journal of the European Mathematical Society     Full-text available via subscription   (Followers: 1)
Journal of the Indian Mathematical Society     Hybrid Journal   (Followers: 1)
Journal of the Institute of Mathematics of Jussieu     Hybrid Journal  
Journal of the London Mathematical Society     Hybrid Journal   (Followers: 2)
Journal of the Nigerian Mathematical Society     Open Access   (Followers: 1)
Journal of Theoretical and Applied Physics     Open Access   (Followers: 8)
Journal of Topology and Analysis     Hybrid Journal  
Journal of Transport and Supply Chain Management     Open Access   (Followers: 14)
Journal of Turbulence     Hybrid Journal   (Followers: 7)
Journal of Uncertainty Analysis and Applications     Open Access  
Journal of Universal Mathematics     Open Access  
Journal of Urban Regeneration & Renewal     Full-text available via subscription   (Followers: 10)
Journal of Water and Land Development     Open Access   (Followers: 3)
JRAMathEdu : Journal of Research and Advances in Mathematics Education     Open Access   (Followers: 4)
JUMLAHKU : Jurnal Matematika Ilmiah STKIP Muhammadiyah Kuningan     Open Access   (Followers: 1)
JURING (Journal for Research in Mathematics Learning)     Open Access   (Followers: 1)
Jurnal Ilmiah AdMathEdu     Open Access  
Jurnal Matematika     Open Access   (Followers: 1)
Jurnal Matematika Integratif     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  
Kreano, Jurnal Matematika Kreatif-Inovatif     Open Access   (Followers: 5)
Le Matematiche     Open Access  
Learning and Teaching Mathematics     Full-text available via subscription   (Followers: 7)
Lettera Matematica     Hybrid Journal  
Lietuvos Matematikos Rinkinys     Open Access   (Followers: 1)
Limits : Journal of Mathematics and Its Applications     Open Access   (Followers: 1)
Linear Algebra and its Applications     Full-text available via subscription   (Followers: 23)
Linear and Multilinear Algebra     Hybrid Journal   (Followers: 8)
Lithuanian Mathematical Journal     Hybrid Journal  
LMS Journal of Computation and Mathematics     Free  
Lobachevskii Journal of Mathematics     Open Access  
Logic and Analysis     Hybrid Journal  
Logic Journal of the IGPL     Hybrid Journal  
Logica Universalis     Hybrid Journal  
manuscripta mathematica     Hybrid Journal  
MaPan : Jurnal Matematika dan Pembelajaran     Open Access  
Marine Genomics     Hybrid Journal   (Followers: 2)
Matemáticas, Educación y Sociedad     Open Access  
Matematicheskie Zametki     Full-text available via subscription  
Matematika     Open Access  
Matematychni Studii     Open Access  
Mathematica Eterna     Open Access  
Mathematica Scandinavica     Open Access   (Followers: 1)
Mathematica Slovaca     Hybrid Journal   (Followers: 1)
Mathematical and Computational Forestry & Natural-Resource Sciences     Free  
Mathematical Communications     Open Access  
Mathematical Computation     Open Access   (Followers: 1)
Mathematical Geosciences     Hybrid Journal   (Followers: 3)
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 in Civil Engineering     Open Access   (Followers: 5)
Mathematical Modelling of Natural Phenomena     Full-text available via subscription   (Followers: 1)
Mathematical Models and Methods in Applied Sciences     Hybrid Journal   (Followers: 2)
Mathematical Notes     Hybrid Journal  
Mathematical Proceedings of the Cambridge Philosophical Society     Full-text available via subscription   (Followers: 1)
Mathematical Programming Computation     Hybrid Journal   (Followers: 3)
Mathematical Sciences     Open Access  
Mathematical Social Sciences     Hybrid Journal   (Followers: 1)
Mathematical Theory and Modeling     Open Access   (Followers: 13)
Mathematical Thinking and Learning     Hybrid Journal   (Followers: 3)
Mathematics and Statistics     Open Access   (Followers: 5)
Mathematics Education Forum Chitwan     Open Access   (Followers: 1)
Mathematics Education Journal     Open Access   (Followers: 1)
Mathematics Education Research Journal     Partially Free   (Followers: 17)
Mathematics in Science and Engineering     Full-text available via subscription  
Mathematics of Control, Signals, and Systems (MCSS)     Hybrid Journal   (Followers: 5)
Mathematics of Quantum and Nano Technologies     Open Access  
Mathématiques et sciences humaines     Open Access   (Followers: 7)
Mathematische Annalen     Hybrid Journal   (Followers: 1)
Mathematische Nachrichten     Hybrid Journal   (Followers: 1)
Mathematische Semesterberichte     Hybrid Journal  
Mathematische Zeitschrift     Hybrid Journal   (Followers: 1)
MATI : Mathematical Aspects of Topological Indeces     Open Access  
MATICS     Open Access   (Followers: 2)
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  
Metascience     Hybrid Journal   (Followers: 1)
Milan Journal of Mathematics     Hybrid Journal  
Mitteilungen der DMV     Hybrid Journal  
MLQ- Mathematical Logic Quarterly     Hybrid Journal  
Monatshefte fur Mathematik     Hybrid Journal  
Moroccan Journal of Pure and Applied Analysis     Open Access   (Followers: 4)
Moscow University Mathematics Bulletin     Hybrid Journal  
MSOR Connections     Open Access   (Followers: 1)
Multiscale Modeling and Simulation     Hybrid Journal   (Followers: 3)
MUST : Journal of Mathematics Education, Science and Technology     Open Access   (Followers: 1)
Nagoya Mathematical Journal     Hybrid Journal  
Nano Research     Hybrid Journal   (Followers: 3)
Nanotechnologies in Russia     Hybrid Journal   (Followers: 1)
Natural Resource Modeling     Hybrid Journal  
New Mathematics and Natural Computation     Hybrid Journal  
Nonlinear Analysis : Modelling and Control     Open Access   (Followers: 1)
Nonlinear Analysis : Theory, Methods & Applications     Hybrid Journal   (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  
Nonlinear Engineering     Open Access  
Nonlinear Oscillations     Hybrid Journal   (Followers: 1)
North Carolina Journal of Mathematics and Statistics     Open Access  
North-Holland Mathematical Library     Full-text available via subscription   (Followers: 1)
North-Holland Mathematics Studies     Full-text available via subscription  
North-Holland Series in Applied Mathematics and Mechanics     Full-text available via subscription   (Followers: 1)
Note di Matematica     Open Access  
NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin     Hybrid Journal   (Followers: 4)
Numeracy : Advancing Education in Quantitative Literacy     Open Access  
Numerical Analysis and Applications     Hybrid Journal   (Followers: 1)
Numerical Functional Analysis and Optimization     Hybrid Journal   (Followers: 2)
Numerical Linear Algebra with Applications     Hybrid Journal   (Followers: 7)
Numerical Mathematics : Theory, Methods and Applications     Full-text available via subscription  
Numerische Mathematik     Hybrid Journal  
Open Journal of Discrete Mathematics     Open Access   (Followers: 5)
Open Journal of Modelling and Simulation     Open Access   (Followers: 1)
Open Mathematics     Open Access   (Followers: 1)

  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  [2570 journals]
  • Approximability models and optimal system identification
    • Abstract: This article considers the problem of optimally recovering stable linear time-invariant systems observed via linear measurements made on their transfer functions. A common modeling assumption is replaced here by the related assumption that the transfer functions belong to a model set described by approximation capabilities. Capitalizing on recent optimal recovery results relative to such approximability models, we construct some optimal algorithms and characterize the optimal performance for the identification and evaluation of transfer functions in the framework of the Hardy Hilbert space and of the disk algebra. In particular, we determine explicitly the optimal recovery performance for frequency measurements taken at equispaced points on an inner circle or on the torus.
      PubDate: 2020-02-13
       
  • Sampled-data output regulation of unstable well-posed infinite-dimensional
           systems with constant reference and disturbance signals
    • Abstract: We study the sample-data control problem of output tracking and disturbance rejection for unstable well-posed linear infinite-dimensional systems with constant reference and disturbance signals. We obtain a sufficient condition for the existence of finite-dimensional sampled-data controllers that are solutions of this control problem. To this end, we study the problem of output tracking and disturbance rejection for infinite-dimensional discrete-time systems and propose a design method of finite-dimensional controllers by using a solution of the Nevanlinna–Pick interpolation problem with both interior and boundary conditions. We apply our results to systems with state and output delays.
      PubDate: 2019-12-12
       
  • A Poincaré–Bendixson theorem for hybrid dynamical systems on
           directed graphs
    • Abstract: The purpose of this work is to obtain restrictions on the asymptotic structure of two-dimensional hybrid dynamical systems. Previous results have been achieved by the authors concerning hybrid dynamical systems with a single impact surface and a single state space. Here, this work is extended to hybrid dynamical systems defined on a directed graph; each vertex corresponds to a state space and each directed edge corresponds to an impact.
      PubDate: 2019-11-16
       
  • The persistence of impulse controllability
    • Abstract: This paper shows that within the space of all LTI systems, equipped with the Zariski topology, the set of impulse controllable systems contains an open dense set of systems; in other words, impulse controllable systems are generic. This genericity persists for many closed subsets of LTI systems of interest, such as the class of singular descriptor systems.
      PubDate: 2019-10-28
       
  • Non-asymptotic error bounds for constant stepsize stochastic approximation
           for tracking mobile agents
    • Abstract: This work revisits the constant stepsize stochastic approximation algorithm for tracking a slowly moving target and obtains a bound for the tracking error that is valid for the entire time axis, using the Alekseev nonlinear variation of constants formula. It is the first non-asymptotic bound for the entire time axis in the sense that it is not based on the vanishing stepsize limit and associated limit theorems unlike prior works, and captures clearly the dependence on problem parameters and the dimension.
      PubDate: 2019-10-25
       
  • Weak input-to-state stability: characterizations and counterexamples
    • Abstract: We establish characterizations of weak input-to-state stability for abstract dynamical systems with inputs, which are similar to characterizations of uniform and of strong input-to-state stability established in a recent paper by A. Mironchenko and F. Wirth. We also investigate the relation of weak input-to-state stability to other common stability concepts, thus contributing to a better theoretical understanding of input-to-state stability theory.
      PubDate: 2019-10-11
       
  • Symmetry and motion primitives in model predictive control
    • Abstract: Symmetries, e.g.  rotational and translational invariances for the class of mechanical systems, allow to characterize solution trajectories of nonlinear dynamical systems. Thus, the restriction to symmetry-induced dynamics, e.g.  by using the concept of motion primitives, may be considered as a quantization of the system. Symmetry exploitation is well established in both motion planning and control. However, the linkage between the respective techniques to optimal control is not yet fully explored. In this manuscript, we want to lay the foundation for the usage of symmetries in Model Predictive Control (MPC). To this end, we investigate a mobile robot example in detail where our contribution is twofold: Firstly, we establish asymptotic stability of a desired set point w.r.t. the MPC closed loop, which is also demonstrated numerically by using motion primitives applied to the parallel parking scenario. Secondly, if the optimization criterion is not consistent with the symmetry action, we provide guidelines to rigorously derive stability guarantees based on symmetry exploitation.
      PubDate: 2019-09-27
       
  • Continuity/constancy of the Hamiltonian function in a Pontryagin maximum
           principle for optimal sampled-data control problems with free sampling
           times
    • Abstract: In a recent paper by Bourdin and Trélat, a version of the Pontryagin maximum principle (in short, PMP) has been stated for general nonlinear finite-dimensional optimal sampled-data control problems. Unfortunately, their result is only concerned with fixed sampling times, and thus, it does not take into account the possibility of free sampling times. The present paper aims to fill this gap in the literature. Precisely, we establish a new version of the PMP that can handle free sampling times. As in the aforementioned work by Bourdin and Trélat, we obtain a first-order necessary optimality condition written as a nonpositive averaged Hamiltonian gradient condition. Furthermore, from the freedom of choosing sampling times, we get a new and additional necessary optimality condition which happens to coincide with the continuity of the Hamiltonian function. In an autonomous context, even the constancy of the Hamiltonian function can be derived. Our proof is based on the Ekeland variational principle. Finally, a linear–quadratic example is numerically solved using shooting methods, illustrating the possible discontinuity of the Hamiltonian function in the case of fixed sampling times and highlighting its continuity in the instance of optimal sampling times.
      PubDate: 2019-09-17
       
  • Geometry and dynamics of the Schur–Cohn stability algorithm for one
           variable polynomials
    • Abstract: We provided a detailed study of the Schur–Cohn stability algorithm for Schur stable polynomials of one complex variable. Firstly, a real analytic principal \(\mathbb {C}\times \mathbb {S}^1\) -bundle structure in the family of Schur stable polynomials of degree n is constructed. Secondly, we consider holomorphic \(\mathbb {C}\) -actions \(\mathscr {A}\) on the space of polynomials of degree n. For each orbit \(\{ s \cdot P(z) \ \vert \ s \in \mathbb {C}\}\) of \(\mathscr {A}\) , we study the dynamical problem of the existence of a complex rational vector field \(\mathbb {X}(z)\) on \(\mathbb {C}\) such that its holomorphic s-time describes the geometric change of the n-root configurations of the orbit \(\{ s \cdot P(z) = 0 \}\) . Regarding the above \(\mathbb {C}\) -action coming from the \(\mathbb {C}\times \mathbb {S}^1\) -bundle structure, we prove the existence of a complex rational vector field \(\mathbb {X}(z)\) on \(\mathbb {C}\) , which describes the geometric change of the n-root configuration in the unitary disk \(\mathbb {D}\) of a \(\mathbb {C}\) -orbit of Schur stable polynomials. We obtain parallel results in the framework of anti-Schur polynomials, which have all their roots in \(\mathbb {C}\backslash \overline{\mathbb {D}}\) , by constructing a principal \(\mathbb {C}^* \times \mathbb {S}^1\) -bundle structure in this family of polynomials. As an application for a cohort population model, a study of the Schur stability and a criterion of the loss of Schur stability are described.
      PubDate: 2019-09-05
       
  • Exact controllability to the trajectories for parabolic PDEs with nonlocal
           nonlinearities
    • Abstract: This paper deals with the analysis of the internal control of a parabolic PDE with nonlinear diffusion, nonlocal in space. In our main result, we prove the local exact controllability to the trajectories with distributed controls, locally supported in space. The main ingredients of the proof are a compactness–uniqueness argument and Kakutani’s fixed-point theorem in a suitable functional setting. Some possible extensions and open problems concerning other nonlocal systems are presented.
      PubDate: 2019-08-26
       
  • The set of controllable multi-input systems is generically convex
    • Abstract: In this paper, we investigate connectedness and convexity properties of the subspace \(\mathbf {L}_{n,m}^c(\mathbb {R})\) of controllable input pairs \((A,B)\in \mathbf {L}_{n,m}(\mathbb {R}):= \mathbb {R}^{n\times n}\times \mathbb {R}^{n\times m}\) . We introduce three restricted convexity properties (“dense”, “almost sure” and “generic” convexity). In order to prove that the space \(\mathbf {L}_{n,m}^c(\mathbb {R})\) possesses these properties, we study the intersection of straight lines in \(\mathbf {L}_{n,m}(\mathbb {R})\) with the algebraic variety of uncontrollable input pairs in \(\mathbf {L}_{n,m}(\mathbb {R})\) . While in the single-input case ( \(m=1\) ), the space \(\mathbf {L}_{n,1}^c(\mathbb {R})\) consists of two connected components, we prove that the space \(\mathbf {L}_{n,m}^c(\mathbb {R})\) is generically convex in the multi-input case. This is our main result. It directly implies Brockett’s theorem that \(\mathbf {L}_{n,m}^c(\mathbb {R})\) is pathwise connected if \(m\ge 2\) . As another application, we derive the theorem of Hazewinkel and Kalman about the non-existence of continuous canonical forms for multi-input systems.
      PubDate: 2019-08-16
       
  • Exit time risk-sensitive control for systems of cooperative agents
    • Abstract: We study a sequence of many-agent exit time stochastic control problems, parameterized by the number of agents, with risk-sensitive cost structure. We identify a fully characterizing assumption, under which each such control problem corresponds to a risk-neutral stochastic control problem with additive cost, and sequentially to a risk-neutral stochastic control problem on the simplex that retains only the distribution of states of agents, while discarding further specific information about the state of each agent. Under some additional assumptions, we also prove that the sequence of value functions of these stochastic control problems converges to the value function of a deterministic control problem, which can be used for the design of nearly optimal controls for the original problem, when the number of agents is sufficiently large.
      PubDate: 2019-08-01
       
  • Robust stability of linear time-varying implicit dynamic equations: a
           general consideration
    • Abstract: In this paper, the problem of robust stability for linear time-varying implicit dynamic equations is generally studied. We consider the effect of uncertain structured perturbations on all coefficient matrices of equations. A formula of stability radius with respect to dynamic structured perturbations acting on the right-hand side coefficients is obtained. In case where structured perturbations affect on both derivative and the right-hand side, the lower bounds for the stability radius are derived. The results are novel and extend many previous results about robust stability for time-varying ordinary differential/difference equations, time-varying differential algebraic equations and time-varying implicit difference equations.
      PubDate: 2019-07-26
       
  • Optimal interpolants on Grassmann manifolds
    • Abstract: The Grassmann manifold \(Gr_m({\mathbb {R}}^n)\) of all m-dimensional subspaces of the n-dimensional space \({\mathbb {R}}^n\) \((m<n)\) is widely used in image analysis, statistics and optimization. Motivated by interpolation in the manifold \(Gr_2({\mathbb {R}}^4)\), we first formulate the differential equation for desired interpolation curves called Riemannian cubics in symmetric spaces by the Pontryagin maximum principle (PMP) and then narrow down to it in \(Gr_2({\mathbb {R}}^4)\). Although computation on this low-dimensional manifold may not occur heavy burden for modern machines, theoretical analysis for Riemannian cubics is very limited in references due to its highly nonlinearity. This paper focuses on presenting analytical and geometrical structures for the so-called Lie quadratics associated with Riemannian cubics. By analysing asymptotics of Lie quadratics, we find asymptotics of Riemannian cubics in \(Gr_2({\mathbb {R}}^4)\). Finally, we illustrate our results by numerical simulations.
      PubDate: 2019-07-26
       
  • Approximately reachable directions for piecewise linear switched systems
    • Abstract: This paper deals with some reachability issues for piecewise linear switched systems with time-dependent coefficients and multiplicative noise. Namely, it aims at characterizing data that are almost reachable at some fixed time \(T>0\) (belong to the closure of the reachable set in a suitable \({\mathbb {L}}^2\)-sense). From a mathematical point of view, this provides the missing link between approximate controllability toward 0 and approximate controllability toward given targets. The methods rely on linear–quadratic control and Riccati equations. The main novelty is that we consider an LQ problem with controlled backward stochastic dynamics and, since the coefficients are not deterministic (unlike some of the cited references), neither is the backward stochastic Riccati equation. Existence and uniqueness of the solution of such equations rely on structure arguments [inspired by Confortola (Ann Appl Probab 26(3):1743–1773, 2016)]. Besides solvability, Riccati representation of the resulting control problem is provided as is the synthesis of optimal (non-Markovian) control. Several examples are discussed.
      PubDate: 2019-07-26
       
  • Periodic adaptive stabilization of rapidly time-varying linear systems
    • Abstract: Adaptive control deals with systems that have unknown and/or time-varying parameters. Most techniques are proven for the case in which any time variation is slow, with results for systems with fast time variations limited to those for which the time variation is of a known form or for which the plant has stable zero dynamics. In this paper, a new adaptive controller design methodology is proposed in which the time variation can be rapid and the plant may have unstable zero dynamics. Under the structural assumptions that the plant is relative degree one and that the plant uncertainty is a single scalar variable, as well as some mild regularity assumptions, it is proven that the closed-loop system is exponentially stable under fast parameter variations with persistent jumps. The proposed controller is nonlinear and periodic, and in each period the parameter is estimated and an appropriate stabilizing control signal is applied.
      PubDate: 2019-06-19
       
  • Structure theory for ensemble controllability, observability, and duality
    • Abstract: Ensemble control deals with the problem of using a finite number of control inputs to simultaneously steer a large population (in the limit, a continuum) of control systems. Dual to the ensemble control problem, ensemble estimation deals with the problem of using a finite number of measurement outputs to estimate the initial state of every individual system in the ensemble. We introduce in the paper a novel class of ensemble systems, termed distinguished ensemble systems, and establish sufficient conditions for controllability and observability of such systems. Every distinguished ensemble system has two key components, namely a set of distinguished control vector fields and a set of codistinguished observation functions. Roughly speaking, a set of vector fields is distinguished if it is closed (up to scaling) under Lie bracket, and moreover, every vector field in the set can be obtained by a Lie bracket of two vector fields in the same set. Similarly, a set of functions is codistinguished to a set of vector fields if the Lie derivatives of the functions along the given vector fields yield (up to scaling) the same set of functions. We demonstrate in the paper that the structure of a distinguished ensemble system can significantly simplify the analysis of ensemble controllability and observability. Moreover, such a structure can be used as a guiding principle for ensemble system design. We further address in the paper the problem about existence of a distinguished ensemble system for a given manifold. We provide an affirmative answer for the case where the manifold is a connected semi-simple Lie group. Specifically, we show that every such Lie group admits a set of distinguished vector fields, together with a set of codistinguished functions. The proof is constructive, leveraging the structure theory of semi-simple real Lie algebras and representation theory. Examples will be provided along the presentation of the paper illustrating key definitions and main results.
      PubDate: 2019-06-18
       
  • Infinite-dimensional bilinear and stochastic balanced truncation with
           explicit error bounds
    • Abstract: Along the ideas of Curtain and Glover (in: Bart, Gohberg, Kaashoek (eds) Operator theory and systems, Birkhäuser, Boston, 1986), we extend the balanced truncation method for (infinite-dimensional) linear systems to arbitrary-dimensional bilinear and stochastic systems. In particular, we apply Hilbert space techniques used in many-body quantum mechanics to establish new fully explicit error bounds for the truncated system and prove convergence results. The functional analytic setting allows us to obtain mixed Hardy space error bounds for both finite-and infinite-dimensional systems, and it is then applied to the model reduction of stochastic evolution equations driven by Wiener noise.
      PubDate: 2019-05-06
       
  • Existence of non-coercive Lyapunov functions is equivalent to integral
           uniform global asymptotic stability
    • Abstract: In this paper, a class of abstract dynamical systems is considered which encompasses a wide range of nonlinear finite- and infinite-dimensional systems. We show that the existence of a non-coercive Lyapunov function without any further requirements on the flow of the forward complete system ensures an integral version of uniform global asymptotic stability. We prove that also the converse statement holds without any further requirements on regularity of the system. Furthermore, we give a characterization of uniform global asymptotic stability in terms of the integral stability properties and analyze which stability properties can be ensured by the existence of a non-coercive Lyapunov function, provided either the flow has a kind of uniform continuity near the equilibrium or the system is robustly forward complete.
      PubDate: 2019-03-14
       
  • A geometric approach for the optimal control of difference inclusions
    • Abstract: Difference inclusions provide a discrete-time analogue of differential inclusions, which in turn play an important role in the theories of optimal control, implicit differential equations, and invariance and viability, to name a few. In this paper we: (i) introduce a framework suitable for the study of difference inclusions for which the state evolves on a manifold; (ii) use this framework to develop necessary conditions for optimality for a broad class of discrete-time problems of dynamic optimization in which the state evolves on a manifold M. The necessary conditions for optimality we derive include the case for which the state \(q_i\) is subject to constraints \(q_i \in S_i \subseteq M\) , for \(S_i\) a closed set. The resulting necessary conditions for optimality appear as discrete-time versions of the Euler–Lagrange inclusion studied by Ioffe (in Trans Am Math Soc 349(7):2871–2900, 1997), Ioffe and Rockafellar (in Calc Var Partial Differ Equ 4(1):59–87, 1996), Mordukhovich (in SIAM J Control Optim 33(3):882–915, 1995), Mordukhovich (in Variational analysis and generalized differentiation II: applications. Springer, Berlin, 2006), and Vinter and Zheng (in SIAM J Control Optim 35(1):56–77, 1997) generalized in a natural way to the case in which the state is evolving on a manifold.
      PubDate: 2019-03-06
       
 
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