arXiv subjects

Yahao Chen

Publications and source records attributed to Yahao Chen.

7 recordsLinked to original sources

arXiv2026

Structural Methods for handling mode changes in multimode DAE systems

Hybrid systems are an important concept in Cyber-Physical Systems modeling, for which multiphysics modeling from first principles and the reuse of models from libraries are key. To achieve this, DAEs must be used to specify the dynamics in each discrete state (or mode in our context). This led to the development of DAE-based equational languages supporting multiple modes, of which Modelica is a popular standard. Mode switching can be time- or state-based. Impulsive behaviors can occur at mode changes. While mode changes are well understood in particular physics (e.g., contact mechanics), this is not the case in physics-agnostic paradigms such as Modelica. This situation causes difficulties for the compilation of programs, often requiring users to manually smooth out mode changes. In this paper, we propose a novel approach for the hot restart at mode changes in such paradigms. We propose a mathematical meaning for hot restarts (such a mathematical meaning does not exist in general), as well as a combined structural and impulse analysis for mode changes, generating the hot restart even in the presence of impulses. Our algorithm detects at compile time if the mode change is insufficiently specified, in which case it returns diagnostics information to the user.

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arXiv2022

Implicit function theorem for nonlinear time-delay systems with algebraic constraints

In this note, we discuss a generalization of the well-known implicit function theorem to the time-delay case. We show that the latter problem is closely related to the bicausal changes of coordinates of time-delay systems. An iterative algorithm is proposed to check the conditions and to construct the desired bicausal change of coordinates for the proposed implicit function theorem. Moreover, we show that our results can be applied to delayed differential-algebraic equations (DDAEs) to reduce their indices and to get their solutions. Some numerical examples are given to illustrate our results.

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arXiv2021

Feedback linearization of nonlinear differential-algebraic control systems

In this paper, we study feedback linearization problems for nonlinear differential-algebraic control systems (DACSs). We consider two kinds of feedback equivalences, namely, the external feedback equivalence, which is defined (locally) on the whole generalized state space, and the internal feedback equivalence, which is defined on the locally maximal controlled invariant submanifold (i.e., on the set where solutions exist). Necessary and sufficient conditions are given for the locally internal and the locally external feedback linearizability of DACSs with the help of a notion called the explicitation with driving variables, which attaches a class of ordinary differential equation control systems (ODECSs) to a given DACS. We show that the feedback linearizability of a DACS is closely related to the involutivity of the linearizability distributions of the explicitation systems. Finally, we apply our results of feedback linearization of DACSs to an academical example and a constrained mechanical system.

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arXiv2021

Geometric analysis of nonlinear differential-algebraic equations via nonlinear control theory

For nonlinear differential-algebraic equations (DAEs), we define two kinds of equivalences, namely, the external and internal equivalence. Roughly speaking, the word "external" means that we consider a DAE (locally) everywhere and "internal" means that we consider the DAE on its (locally) maximal invariant submanifold (i.e., where its solutions exist) only. First, we revise the geometric reduction method in DAEs solution theory and formulate an implementable algorithm to realize that method. Then a procedure named explicitation with driving variables is proposed to connect nonlinear DAEs with nonlinear control systems and we show that the driving variables of an explicitation system can be reduced under some involutivity conditions. Finally, due to the explicitation, we will use some notions from nonlinear control theory to derive two nonlinear generalizations of the Weierstrass form.

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arXiv2021

From Morse Triangular Form of ODE Control Systems to Feedback Canonical Form of DAE Control Systems

In this paper, we relate the feedback canonical form \textbf{FNCF} of differential-algebraic control systems (DACSs) with the famous Morse canonical form \textbf{MCF} of ordinary differential equation control systems (ODECSs). First, a procedure called an explicitation (with driving variables) is proposed to connect the two above categories of control systems by attaching to a DACS a class of ODECSs with two kinds of inputs (the original control input $u$ and a vector of driving variables $v$). Then, we show that any ODECS with two kinds of inputs can be transformed into its extended \textbf{MCF} via two intermediate forms: the extended Morse triangular form and the extended Morse normal form. Next, we illustrate that the \textbf{FNCF} of a DACS and the extended \textbf{MCF} of the explicitation system have a perfect one-to-one correspondence. At last, an algorithm is proposed to transform a given DACS into its \textbf{FBCF} via the explicitation procedure and a numerical example is given to show the efficiency of the proposed algorithm.

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arXiv2021

An approximation for nonlinear differential-algebraic equations via singular perturbation theory

In this paper, we study jumps of nonlinear DAEs caused by inconsistent initial values. First, we propose a simple normal form called the index-1 nonlinear Weierstrass form (INWF) for nonlinear DAEs. Then we generalize the notion of consistency projector for linear DAEs to the nonlinear case. By an example, we compare our proposed nonlinear consistency projectors with two existing consistent initialization methods to show that the two existing methods are not coordinate-free, i.e., the consistent points calculated by the two methods are not invariant under nonlinear coordinates transformations. Next we propose a singular perturbed system approximation for nonlinear DAEs, which is an ordinary differential equation (ODE) with a small perturbation parameter, we show that the solutions of the proposed perturbation system approximate both the jumps resulting from the nonlinear consistency projectors and the $\mathcal C^1$-solutions of the DAE. At last, we use a numerical simulation of a nonlinear DAE model arising from an electric circuit to illustrate the effectiveness of the proposed singular perturbed system approximation of DAEs.

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arXiv2020

Geometric analysis of differential-algebraic equations via linear control theory

We consider linear differential-algebraic equations DAEs and the Kronecker canonical form KCF of the corresponding matrix pencils. We also consider linear control systems and their Morse canonical form MCF. For a linear DAE, a procedure named explicitation is proposed, which attaches to any linear DAE a linear control system defined up to a coordinates change, a feedback transformation and an output injection. Then we compare subspaces associated to a DAE in a geometric way with those associated (also in a geometric way) to a control system, namely, we compare the Wong sequences of DAEs and invariant subspaces of control systems. We prove that the KCF of linear DAEs and the MCF of control systems have a perfect correspondence and that their invariants are related. In this way, we connect the geometric analysis of linear DAEs with the classical geometric linear control theory. Finally, we propose a concept named internal equivalence for DAEs and discuss its relation with internal regularity, i.e., the existence and uniqueness of solutions.

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