arXiv subjects

Yajuan Sun

Publications and source records attributed to Yajuan Sun.

25 records · Page 2Linked to original sources

arXiv2013

Multiple invariants conserving Runge-Kutta type methods for Hamiltonian problems

In a recent series of papers, the class of energy-conserving Runge-Kutta methods named Hamiltonian BVMs (HBVMs) has been defined and studied. Such methods have been further generalized for the efficient solution of general conservative problems, thus providing the class of Line Integral Methods (LIMs). In this paper we derive a further extension, which we name Enhanced Line Integral Methods (ELIMs), more tailored for Hamiltonian problems, allowing for the conservation of multiple invariants of the continuous dynamical system. The analysis of the methods is fully carried out and some numerical tests are reported, in order to confirm the theoretical achievements.

math.NA↗

arXiv2013

Enhanced HBVMs for the numerical solution of Hamiltonian problems with multiple invariants

Recently, the class of energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs), has been proposed for the efficient solution of Hamiltonian problems, as well as for other types of conservative problems. In this paper, we report further advances concerning such methods, resulting in their enhanced version (Enhanced HBVMs, or EHBVMs). The basic theoretical results are sketched, along with a few numerical tests on a Hamiltonian problem, taken from the literature, possessing multiple invariants.

math.NA↗

arXiv2012

An Input-Output Simulation Approach to Controlling Multi-AffineSystems for Linear Temporal Logic Specifications

This paper presents an input-output simulation approach to controlling multi-affine systems for linear temporal logic (LTL) specifications, which consists of the following steps. First, we partition the state space into rectangles, each of which satisfies atomic LTL propositions. Then, we study the control of multi-affine systems on rectangles including the control of driving all trajectories starting from a rectangle to exit through a facet and the control of stabilizing the system towards a desired point. With the proposed controllers, a finitely abstracted transition system is constructed which is shown to be input-output simulated by the rectangular transition system of the multi-affine system. Since input-output simulation preserves LTL properties, the controller synthesis of the multi-affine system for LTL specifications is achieved by designing a nonblocking supervisor for the abstracted transition system and by continuously implementing the resulting supervisor for the original multi-affine system.

eess.SY↗

arXiv2012

The minimal stage, energy preserving Runge-Kutta method for polynomial Hamiltonian systems is the Averaged Vector Field method

No Runge-Kutta method can be energy preserving for all Hamiltonian systems. But for problems in which the Hamiltonian is a polynomial, the Averaged Vector Field (AVF) method can be interpreted as a Runge-Kutta method whose weights $b_i$ and abscissae $c_i$ represent a quadrature rule of degree at least that of the Hamiltonian. We prove that when the number of stages is minimal, the Runge-Kutta scheme must in fact be identical to the AVF scheme.

math.NA↗

arXiv2012

Bisimilarity Enforcing Supervisory Control for Deterministic Specifications

This paper investigates the supervisory control of nondeterministic discrete event systems to enforce bisimilarity with respect to deterministic specifications. A notion of synchronous simulation-based controllability is introduced as a necessary and sufficient condition for the existence of a bisimilarity enforcing supervisor, and a polynomial algorithm is developed to verify such a condition. When the existence condition holds, a supervisor achieving bisimulation equivalence is constructed. Furthermore, when the existence condition does not hold, two different methods are provided for synthesizing maximal permissive sub-specifications.

eess.SY↗

arXiv2011

Decentralized Supervisory Control of Discrete Event Systems for Bisimulation Equivalence

In decentralized systems, branching behaviors naturally arise due to communication, unmodeled dynamics and system abstraction, which can not be adequately captured by the traditional sequencing-based language equivalence. As a finer behavior equivalence than language equivalence, bisimulation not only allows the full set of branching behaviors but also explicitly specifies the properties in terms of temporal logic such as CTL* and mu-calculus. This observation motivates us to consider the decentralized control of discrete event systems (DESs) for bisimulation equivalence in this paper, where the plant and the specification are taken to be nondeterministic and the supervisor is taken to be deterministic. An automata-based control framework is formalized, upon which we develop three architectures with respect to different decision fusion rules for the decentralized bisimilarity control, named a conjunctive architecture, a disjunctive architecture and a general architecture. Under theses three architectures, necessary and sufficient conditions for the existence of decentralized bisimilarity supervisors are derived respectively, which extend the traditional results of supervisory control from language equivalence to bisimulation equivalence. It is shown that these conditions can be verified with exponential complexity. Furthermore, the synthesis of bisimilarity supervisors is presented when the existence condition holds.

eess.SY↗

arXiv2011

Computation for Supremal Simulation-Based Controllable and Strong Observable Subautomata

Bisimulation relation has been successfully applied to computer science and control theory. In our previous work, simulation-based controllability and simulation-based observability are proposed, under which the existence of bisimilarity supervisor is guaranteed. However, a given specification automaton may not satisfy these conditions, and a natural question is how to compute a maximum permissive subspecification. This paper aims to answer this question and investigate the computation of the supremal simulation-based controllable and strong observable subautomata with respect to given specifications by the lattice theory. In order to achieve the supremal solution, three monotone operators, namely simulation operator, controllable operator and strong observable operator, are proposed upon the established complete lattice. Then, inequalities based on these operators are formulated, whose solution is the simulation-based controllable and strong observable set. In particular, a sufficient condition is presented to guarantee the existence of the supremal simulation-based controllable and strong observable subautomata. Furthermore, an algorithm is proposed to compute such subautomata.

eess.SY↗