Recent zbMATH articles in MSC 93Chttps://www.zbmath.org/atom/cc/93C2021-04-16T16:22:00+00:00WerkzeugSecond-order necessary optimality conditions for a discrete optimal control problem.https://www.zbmath.org/1456.490212021-04-16T16:22:00+00:00"Toan, N. T."https://www.zbmath.org/authors/?q=ai:nguyen-thi-toan."Ansari, Q. H."https://www.zbmath.org/authors/?q=ai:ansari.qamrul-hasan"Yao, J.-C."https://www.zbmath.org/authors/?q=ai:yao.jen-chihSummary: In this paper, we study second-order necessary optimality conditions for a discrete optimal control problem with a nonconvex cost function and control constraints. By establishing an abstract result on second-order necessary optimality conditions for a mathematical programming problem, we derive second-order optimality conditions for a discrete optimal control problem.Analysis of Krylov subspace approximation to large-scale differential Riccati equations.https://www.zbmath.org/1456.650192021-04-16T16:22:00+00:00"Antti, Koskela"https://www.zbmath.org/authors/?q=ai:antti.koskela"Mena, Hermann"https://www.zbmath.org/authors/?q=ai:mena.hermannSummary: We consider a Krylov subspace approximation method for the symmetric differential Riccati equation \(\dot{X} = AX + XA^T + Q - XSX, X(0)=X_0\). The method we consider is based on projecting the large-scale equation onto a Krylov subspace spanned by the matrix \(A\) and the low-rank factors of \(X_0\) and \(Q\). We prove that the method is structure preserving in the sense that it preserves two important properties of the exact flow, namely the positivity of the exact flow and also the property of monotonicity. We provide a theoretical a priori error analysis that shows superlinear convergence of the method. Moreover, we derive an a posteriori error estimate that is shown to be effective in numerical examples.Coupled systems of linear differential-algebraic and kinetic equations with application to the mathematical modelling of muscle tissue.https://www.zbmath.org/1456.340512021-04-16T16:22:00+00:00"Plunder, Steffen"https://www.zbmath.org/authors/?q=ai:plunder.steffen"Simeon, Bernd"https://www.zbmath.org/authors/?q=ai:simeon.berndSummary: We consider a coupled system composed of a linear differential-algebraic equation (DAE) and a linear large-scale system of ordinary differential equations where the latter stands for the dynamics of numerous identical particles. Replacing the discrete particles by a kinetic equation for a particle density, we obtain in the mean-field limit the new class of partially kinetic systems.
We investigate the influence of constraints on the kinetic theory of those systems and present necessary adjustments. We adapt the mean-field limit to the DAE model and show that index reduction and the mean-field limit commute. As a main result, we prove Dobrushin's stability estimate for linear systems. The estimate implies convergence of the mean-field limit and provides a rigorous link between the particle dynamics and their kinetic description.
Our research is inspired by mathematical models for muscle tissue where the macroscopic behaviour is governed by the equations of continuum mechanics, often discretised by the finite element method, and the microscopic muscle contraction process is described by Huxley's sliding filament theory. The latter represents a kinetic equation that characterises the state of the actin-myosin bindings in the muscle filaments. Linear partially kinetic systems are a simplified version of such models, with focus on the constraints.
For the entire collection see [Zbl 1445.34004].Laplacian controllability for graphs with integral Laplacian spectrum.https://www.zbmath.org/1456.051092021-04-16T16:22:00+00:00"Stanić, Zoran"https://www.zbmath.org/authors/?q=ai:stanic.zoranSummary: If \(G\) is a graph with \(n\) vertices, \(L_G\) is its Laplacian matrix, and \(\mathfrak{b}\) is a binary vector of length \(n\), then the pair \((L_G, \mathfrak{b})\) is said to be controllable, and we also say that \(G\) is Laplacian controllable for \(\mathfrak{b}\), if \(\mathfrak{b}\) is non-orthogonal to any of the eigenvectors of \(L_G\). It is known that if \(G\) is Laplacian controllable, then it has no repeated Laplacian eigenvalues. If \(G\) has no repeated Laplacian eigenvalues and each of them is an integer, then \(G\) is decomposable into a (dominate) induced subgraph, say \(H\), and another induced subgraph with at most three vertices. We express the Laplacian controllability of \(G\) in terms of that of \(H\). In this way, we address the question on the Laplacian controllability of cographs and, in particular, threshold graphs.Practical methods to investigate observability of linear time-varying systems.https://www.zbmath.org/1456.930042021-04-16T16:22:00+00:00"Morozov, V. M."https://www.zbmath.org/authors/?q=ai:morozov.victor-m"Baklanov, F. Yu."https://www.zbmath.org/authors/?q=ai:baklanov.f-yuSummary: The work proposes a practical methodology to investigate observability of linear time-varying systems. The methodology comprises analytical and numerical methods, as well as a technique to verify results of analytical investigation numerically. Employing reducibility in the analysis of observability is demonstrated.Optimal Petri net supervisor synthesis for forbidden state problems using marking mask.https://www.zbmath.org/1456.930052021-04-16T16:22:00+00:00"Li, Yuting"https://www.zbmath.org/authors/?q=ai:li.yuting"Yin, Li"https://www.zbmath.org/authors/?q=ai:yin.li"Chen, Yufeng"https://www.zbmath.org/authors/?q=ai:chen.yufeng"Yu, Zhenhua"https://www.zbmath.org/authors/?q=ai:yu.zhenhua"Wu, Naiqi"https://www.zbmath.org/authors/?q=ai:wu.naiqiSummary: This article addresses the forbidden state problem in discrete-event systems (DESs) modeled with Petri nets. Given a control specification, we first decide the sets of forbidden and admissible markings. Then, the minimal mask set of first-met forbidden markings (FFMs) and the minimal root set of admissible markings are computed by marking mask that is implemented using a class of special places in a plant, called competitive places. Marking mask can effectively filtrate the markings to be processed such that the two obtained sets are in general much smaller than the sets of originally specified forbidden and admissible markings, respectively. Monitors computed by place invariants are used to forbid the forbidden markings. It is shown that a maximally permissive (optimal) supervisor can be computed if it exists. Integer linear programming is used to optimize the structure of a supervisor. The minimal mask set of FFMs and root set of admissible markings efficiently reduce the computational overhead because of much fewer constraints and variables in the formulated programming problem. The developed methodology is illustrated by parameterized examples.Bogolyubov's theorem for a controlled system related to a variational inequality.https://www.zbmath.org/1456.490152021-04-16T16:22:00+00:00"Tolstonogov, A. A."https://www.zbmath.org/authors/?q=ai:tolstonogov.alexander-aAsymptotic analysis of an advection-diffusion equation and application to boundary controllability.https://www.zbmath.org/1456.352042021-04-16T16:22:00+00:00"Amirat, Youcef"https://www.zbmath.org/authors/?q=ai:amirat.youcef-ait"Münch, Arnaud"https://www.zbmath.org/authors/?q=ai:munch.arnaudThe authors consider the advection-diffusion equation
\[
y^{\varepsilon}_t-\varepsilon y^{\varepsilon}_{xx}+My^{\varepsilon}_x=0,\quad (x,t)\in (0,1)\times(0,T),
\]
\[
y^{\varepsilon}(0,t)=v^{\varepsilon}(t),\quad y^{\varepsilon}(1,t)=0,\quad t\in (0,T),\quad (1)
\]
\[
y^{\varepsilon}(x.0)=y^{\varepsilon}_0(x)\quad x\in (0,1),
\]
where \(\varepsilon\) is the diffusion coefficient, \(M\) is the transport coefficient, \(v^{\varepsilon}\)=\(v^{\varepsilon}(t)\) is the control function, \(y^{\varepsilon}_0\) is the initial data, and \(y^{\varepsilon}=y^{\varepsilon}(x,t)\) is the associated state.
The main purpose of the article is to perform the asymptotic analysis of (1) for the case \(M>0\), assuming \(v^{\epsilon}\) fixed and satisfying compatibility conditions at the initial time \(t=0\) with the initial condition \(y^{\varepsilon}_0\) as \(x=0\).
Supposing that the initial condition does not depend on \(\varepsilon\) and that the control function \(v^{\varepsilon}\) is given in the form \(v^{\varepsilon}=\sum\limits_{k=0}^m \varepsilon^k v^k\), the authors construct the accurate asymptotic approximation \(w^{\varepsilon}\) of the solution \(y^{\varepsilon}\) by using the method of matched asymptotic expansions. The inner and outer solutions are determined by using explicit formulae, and \(w^{\varepsilon}_m\) is obtained by combining the inner and outer solutions through a process of matching. It is proved that \(w^{\varepsilon}_m\) is a regular and strong approximation of \(y^{\varepsilon}\), as \(\varepsilon \to 0^{+}\). The error estimate is obtained. The same approach is applied to the solution \(\varphi^{\varepsilon}\) of the adjoint problem
\[
-\varphi^{\varepsilon}_t-\varepsilon \varphi^{\varepsilon}_{xx}-M\varphi^{\varepsilon}_x=0,\quad (x,t)\in (0,1)\times(0,T),
\]
\[
\varphi^{\varepsilon}(0,t)=\varphi^{\varepsilon}(1,t)=0 \quad t\in (0,T)
\]
\[
\varphi^{\varepsilon}(x.T)=\varphi^{\varepsilon}_T(x)\quad x\in (0,1),
\]
where \(\varphi_T^{\varepsilon}\) is a function of the form \(\varphi^{\varepsilon}_T=\sum\limits^{m}_{k=0}\varepsilon^k\varphi^k_T\), the functions \(\varphi^0_T,\varphi^1_T,\ldots,\varphi^m_T\) being given.
The authors show that under some conditions on the functions \(v^k\) and on the initial condition \(y_0\) one can pass to the limit as \(m\to \infty\) and establish a convergence result of the sequence \((w^{\varepsilon}_m)_{(m\ge 0)}\).
Then they use the asymptotic results to discuss the controllability properties of the solution for \(T\ge 1/M\).
Reviewer: Artyom Andronov (Saransk)Exit time asymptotics for dynamical systems with fast random switching near an unstable equilibrium.https://www.zbmath.org/1456.601392021-04-16T16:22:00+00:00"Bakhtin, Yuri"https://www.zbmath.org/authors/?q=ai:bakhtin.yuri-yu"Gaál, Alexisz"https://www.zbmath.org/authors/?q=ai:gaal.alexisz-tamasIndirect boundary observability of semi-discrete coupled wave equations.https://www.zbmath.org/1456.650642021-04-16T16:22:00+00:00"El Akri, Abdeladim"https://www.zbmath.org/authors/?q=ai:el-akri.abdeladim"Maniar, Lahcen"https://www.zbmath.org/authors/?q=ai:maniar.lahcenSummary: This work concerns the indirect observability properties for the finite-difference space semi-discretization of the 1-d coupled wave equations with homogeneous Dirichlet boundary conditions. We assume that only one of the two components of the unknown is observed. As for a single wave equation, as well as for the direct (complete) observability of the coupled wave equations, we prove the lack of the numerical observability. However, we show that a uniform observability holds in the subspace of solutions in which the initial conditions of the observed component is generated by the low frequencies. Our main proofs use a two-level energy method at the discrete level and a Fourier decomposition of the solutions.A compact form dynamics controller for a high-DOF tetrapod-on-wheel robot with one manipulator via null space based convex optimization and compatible impedance controllers.https://www.zbmath.org/1456.700212021-04-16T16:22:00+00:00"Du, Wenqian"https://www.zbmath.org/authors/?q=ai:du.wenqian"Benamar, Faïz"https://www.zbmath.org/authors/?q=ai:benamar.faizSummary: This paper develops a compact form dynamics controller to generate multi-compliant behaviors for a new designed tetrapod-on-wheel robot with one manipulator. The whole-body compliant torque controller is stated through one null-space-based convex optimization and compatible null-space-based impedance controllers. Different from fixed contact points of conventional quadruped robots, the kinematic wheel contact constraints are derived for our legged-on-wheel robot, which serves as the basis for each task reference extraction and each compliance controller. The compact relationships between task references and optimization control variables are extracted using null-space-based inverse dynamics, which is used to build the cost function in the operational space and/or in the joint space. The whole-body control frame is developed and several null-space-based feed-back impedance controllers are integrated into the compact relationships to allow the robot to achieve compliance and compensate the model impreciseness, especially the wheel contact model. Then the detailed algorithm is presented whose output combines the feed-forward and feedback torque. The validation of our approach is performed via advanced numerical simulations for a virtual legged-on-wheel robot with one manipulator.Bias of particle approximations to optimal filter derivative.https://www.zbmath.org/1456.930062021-04-16T16:22:00+00:00"Tadić, Vladislav Z. B."https://www.zbmath.org/authors/?q=ai:tadic.vladislav-z-b"Doucet, Arnaud"https://www.zbmath.org/authors/?q=ai:doucet.arnaudMeasurement of network complexity and capability in command and control system.https://www.zbmath.org/1456.900362021-04-16T16:22:00+00:00"Song, Xiao"https://www.zbmath.org/authors/?q=ai:song.xiao"Zhang, Shaoyun"https://www.zbmath.org/authors/?q=ai:zhang.shaoyun"Shi, Xuecheng"https://www.zbmath.org/authors/?q=ai:shi.xuechengSummary: A concept of complexity of the Command and Control (C2) information system is introduced and an innovative approach of measuring network complexity is proposed compared with traditional network complexity computation methods. Complexity measurements, including connectivity, collaboration and redundancy, are proposed and computed. Then the complexity-based capability is discussed and studied. Finally, two case studies of an anti-aircraft defence C2 network and partial tank division network are carried out to illustrate the computation processes of the proposed network complexity and capability.Hybrid projective combination-combination synchronization in non-identical hyperchaotic systems using adaptive control.https://www.zbmath.org/1456.340632021-04-16T16:22:00+00:00"Khan, Ayub"https://www.zbmath.org/authors/?q=ai:khan.ayub"Chaudhary, Harindri"https://www.zbmath.org/authors/?q=ai:chaudhary.harindriSummary: In this paper, we investigate a hybrid projective combination-combination synchronization scheme among four non-identical hyperchaotic systems via adaptive control method. Based on Lyapunov stability theory, the considered approach identifies the unknown parameters and determines the asymptotic stability globally. It is observed that various synchronization techniques, for instance, chaos control problem, combination synchronization, projective synchronization, etc. turn into particular cases of combination-combination synchronization. The proposed scheme is applicable to secure communication and information processing. Finally, numerical simulations are performed to demonstrate the effectivity and correctness of the considered technique by using MATLAB.