Hu, Jiaming; Trenn, Stephan; Zhu, Xiaojin Funnel control for relative degree one nonlinear system with input saturation Unpublished 2021, (submitted). @unpublished{HuTren21pp,The dilemma between transient behavior and accuracy in tracking control arises in both theoretical research and engineering practice and Funnel Control has showed great potential in solving that problem. Apart from the controlled system, the performance of funnel control strongly depends on the reference signal and the choice of prescribed funnel boundary. In this paper, we will present a new form of funnel controller for systems with control saturation. Compared to former research, the new controller is more reliable, and the closed-loop system can even achieve asymptotic tracking. Besides that, a new concept called constrained funnel boundary is introduced. Together with the new controller and the constrained funnel boundary, the application range of funnel control is extended significantly. |
Chen, Yahao; Trenn, Stephan Stability analysis of switched nonlinear differential-algebraic equations via nonlinear Weierstrass form Unpublished 2021, (submitted). @unpublished{ChenTren21ppd,In this paper, we propose some sufficient conditions for checking the asymptotic stability of switched nonlinear differential-algebraic equations (DAEs) under arbitrary switching signal. We assume that each model of a given switched DAEs is externally equivalent to a nonlinear Weierstrass form. With the help of this form, we can define nonlinear consistency projectors and jump-flow solutions for switched nonlinear DAEs. Then we use a different approach from the paper [12] to study the stability of switched DAEs via a novel notion called the jump-flow explicitation, which attaches a nonlinear control system to a given nonlinear DAE and can be used to simplify the common Lyapunov function conditions for both the flow and the jump dynamics of switched nonlinear DAEs. At last, a numerical example is given to illustrate how to check the stability of a switched nonlinear DAE by constructing a common Lyapunov function. |
Mostacciuolo, Elisa; Trenn, Stephan; Vasca, Francesco An averaged model for switched systems with state jumps applicable for PWM descriptor systems Unpublished 2021, (submitted). @unpublished{MostTren21ppb,Switched descriptor systems with pulse width modulation are characterized by modes whose dynamics are described by differential algebraic equations; this type of models belongs to the more general class of switched impulsive systems, i.e. switched systems with ordinary differential equations as modes dynamics and state jumps at the switching time instants. The presence of possible jumps in the state makes the application of the classical averaging technique nontrivial. In this paper we propose an averaged model for switched impulsive systems. The state trajectory of the proposed averaged model is shown to approximate the one of the original system with an error of order of the switching period. The model reduces to the classical averaged model when there are no jumps in the state. The practical interest of the theoretical averaging results is demonstrated through the analysis of the dynamics of a switched electrical circuit. |
Hossain, Sumon; Trenn, Stephan Reduced realization of switched linear systems with known switching sequence Unpublished 2021, (submitted). @unpublished{HossTren21pp,We propose a novel reduction approach for switched linear systems with a fixed mode sequence based on subspaces related to the (time-varying) reachable and unobservable spaces. These subspaces are defined in such a way that they can be used to construct a switched weak Kalman decomposition, which is then in turn used to define a reduced switched linear system with an identical input-output behavior. The proposed method is illustrated with a low dimensional academic example. |
Lee, Jin Gyu; Berger, Thomas; Trenn, Stephan; Shim, Hyungbo Edge-wise funnel output synchronization of heterogeneous agents with relative degree one Unpublished 2021, (submitted). @unpublished{LeeBerg21pp,In a recent work by three of the authors, in order to enforce synchronization for scalar heterogeneous multi-agent systems with some useful characteristics, a node-wise funnel coupling law was proposed. The emergent dynamics, to which each of the agents synchronizes, was characterized and it was studied how networks can be synthesized which exhibit these emergent dynamics. The advantage of this synthesis is its suitability for plug-and-play operation. However, the aforementioned emergent dynamics under node-wise funnel coupling are determined by an algebraic equation which does not admit an explicit solution in general, and even its pointwise solution proves rather difficult. Furthermore, the contractivity assumption on the emergent dynamics, required to establish the synchronization, is hard to be checked without solving the algebraic equation. To resolve these drawbacks, in the present paper we present a new funnel coupling law that uses edge-wise output differences. Under this novel coupling the benign properties of node-wise funnel coupling are retained, but the emergent dynamics are given explicitly by the blended dynamics of the multi-agent system, which already proved an advantageous tool in the analysis and design of such networks. Additionally, our results are not restricted to scalar systems and treat the case that neighboring agents only communicate their output information, and not their complete state. |
Chen, Yahao; Trenn, Stephan Impulse-free jump solutions of nonlinear differential-algebraic equations Unpublished 2021, (submitted). @unpublished{ChenTren21ppb,In this paper, we propose a novel notion called impulse-free jump solution for nonlinear differential-algebraic equations (DAEs) of the form E(x)x' = F(x) with inconsistent initial values. The term “impulse-free” means that there are no Dirac impulses caused by jumps from inconsistent initial values, i.e., the directions of jumps stay in ker E(x). We find that the existence and uniqueness of impulse-free jumps are closely related to the notion of geometric index-1 and the involutivity of the distribution defined by ker E(x). Moreover, a singular perturbed system approximation is proposed for nonlinear DAEs; we show that solutions of the perturbed system approximate both impulse-free jump solutions and C1-solutions of nonlinear DAEs. Finally, we show by some examples that our results of impulse-free jumps are useful for the problems like consistent initializations of nonlinear DAEs and transient behavior simulations of electric circuits. |
Lee, Jin Gyu; Trenn, Stephan; Shim, Hyungbo Synchronization with prescribed transient behavior: Heterogeneous multi-agent systems under funnel coupling Unpublished 2021, (submitted for publication). @unpublished{LeeTren21pp,In this paper, we introduce a nonlinear time-varying coupling law, which can be designed in a fully decentralized manner and achieves approximate synchronization with arbitrary precision, under only mild assumptions on the individual vector fields and the underlying graph structure. The proposed coupling law is motivated by the funnel control studied in adaptive controls under the observation that arbitrary precision synchronization can be achieved for heterogeneous multi-agent systems by the high-gain coupling, and thus, we follow to call our coupling law as `(node-wise) funnel coupling.' By getting out of the conventional proof technique in the funnel control study, we now can obtain even asymptotic or finite-time synchronization with the same funnel coupling law. More interestingly, the emergent collective behavior that arises for a heterogeneous multi-agent system when enforcing arbitrary precision synchronization by the proposed funnel coupling law, has been analyzed in this paper. In particular, we introduce a single scalar dynamics called `emergent dynamics' that is capable of illustrating the emergent synchronized behavior by its solution trajectory. Characterization of the emergent dynamics is important because, for instance, one can design the emergent dynamics first such that the solution trajectory behaves as desired, and then, provide a design guideline to each agent so that the constructed vector fields yield the desired emergent dynamics. A particular example illustrating the utility of the emergent dynamics is given also in the paper as a distributed median solver. |
Submitted
Funnel control for relative degree one nonlinear system with input saturation Unpublished 2021, (submitted). |
Stability analysis of switched nonlinear differential-algebraic equations via nonlinear Weierstrass form Unpublished 2021, (submitted). |
An averaged model for switched systems with state jumps applicable for PWM descriptor systems Unpublished 2021, (submitted). |
Reduced realization of switched linear systems with known switching sequence Unpublished 2021, (submitted). |
Edge-wise funnel output synchronization of heterogeneous agents with relative degree one Unpublished 2021, (submitted). |
Impulse-free jump solutions of nonlinear differential-algebraic equations Unpublished 2021, (submitted). |
Synchronization with prescribed transient behavior: Heterogeneous multi-agent systems under funnel coupling Unpublished 2021, (submitted for publication). |