3,463 research outputs found
Consensus Tracking for Multiagent Systems Under Bounded Unknown External Disturbances Using Sliding-PID Control
This paper is devoted to the study of consensus tracking for multiagent systems under unknown but bounded external disturbances. A consensus tracking protocol which is a combination between the conventional PID controller and sliding mode controller named sliding-PID protocol is proposed. The protocol is applied to the consensus tracking of multiagent system under bounded external disturbances where results showed high effectiveness and robustness
Generalized Homogeneous Rigid-BodyAttitude Control
The attitude tracking problem for a full-actuated rigid body in 3D is studied
using a impulsive system model based on Lie algebra so(3). A nonlinear
homogeneous controller is designed to globally track a smooth attitude
trajectory in a finite or a (nearly) fixed time. A global settling time
estimate is obtained, which is easily adjustable by tuning the homogeneity
degree. The local input-to-state stability is proven. Simulations illustrating
the performance of the proposed algorithm are presented
Homogeneous control design using invariant ellipsoid method
The invariant ellipsoid method is aimed at minimization of the smallest
invariant and attractive set of a linear control system operating under bounded
external disturbances. This paper extends this technique to a class of the
so-called generalized homogeneous system by defining the \dn-homogeneous
invariant/attractive ellipsoid. The generalized homogeneous optimal (in the
sense of invariant ellipsoid) controller allows further improvement of the
control system providing a faster convergence and better precision. Theoretical
results are supported by numerical simulations and experiments
Homogeneous finite-gain Lp-stability analysis on homogeneous systems
In dieser Arbeit wird gezeigt, dass die klassische Lp-StabilitĂ€t und Lp-VerstĂ€rkung fĂŒr beliebige stetige, gewichtete homogene Systeme nicht wohldefiniert ist. Indem die klassische Lp-Norm von Signalen zu einer homogenen Lp-Norm so angepasst wird, dass diese bezĂŒglich der Gewichtsvektoren homogen ist, ist es möglich zu zeigen, dass jedes intern stabile homogene System fĂŒr hinreichend groĂe p eine global definierte endliche homogene Lp-VerstĂ€rkung besitzt. Mit Hilfe einer homogenen Lyapunov-Funktion kann die homogene Lp-StabilitĂ€t durch eine homogene partielle Differentialungleichung charakterisiert werden, die sich im eingangsaffinen Fall in eine homogene Hamilton-Jacobi-Ungleichung transformieren lĂ€sst. Des Weiteren werden in dieser Arbeit detaillierte Methoden zur AbschĂ€tzung von oberen Schranken fĂŒr homogene Lp-VerstĂ€rkungen aus diesen Ungleichungen abgeleitet. Dies schlieĂt die homogene Lâ-VerstĂ€rkung und die homogene Eingangs-Zustands-VerstĂ€rkung ebenfalls ein. Bei rĂŒckgekoppelten homogenen Systemen, bei denen die Gewichtsvektoren zwischen den Systemen zueinander passend sind, erlaubt die additive Ungleichung fĂŒr die homogene Lp-Norm die EinfĂŒhrung des homogenen Small-Gain Theorems fĂŒr beliebige p, wodurch eine StabilitĂ€tsanalyse des geschlossenen Regelkreises ermöglicht wird. Weiterhin können homogene Hâ-Regler entworfen werden, wenn das System eingangsaffin ist. Da die konventionellen Werkzeuge der linearen Systemtheorie nicht zur VerfĂŒgung stehen, können solche homogenen Hâ-Regler nur garantieren, dass der geschlossene Regelkreis eine homogene Lp-VerstĂ€rkung hat, die kleiner als ein bestimmbarer Wert ist. Ihre OptimalitĂ€t kann hingegen nicht garantiert werden. In jedem Kapitel werden mehrere kurze Beispiele vorgestellt, um zu veranschaulichen, wie eine solche homogene Lp-VerstĂ€rkung berechnet werden kann. Insbesondere ist eine detaillierte Analyse des âContinuous Super-Twisting Like Algorithm" mit tieferen Einblicken fĂŒr interessierte Leser enthalten.In this thesis, it is shown that the classical Lp-stability and Lp-gain is not well-defined for arbitrary continuous weighted homogeneous systems. By modifying the classical Lp-norm of signals to be homogeneous w.r.t. some weight vectors, which is called homogeneous Lp-norm, it is possible to show that every internally stable homogeneous system has a globally defined finite homogeneous Lp-gain, for p sufficiently large. With the help of a homogeneous Lyapunov function, homogeneous Lp-stability can be characterized by a homogeneous partial differential inequality, which in the input affine case can be transformed to a homogeneous Hamilton-Jacobi inequality. Furthermore, in this thesis some detailed methods to calculate upper estimates for the homogeneous Lp-gain are provided from theses inequalities. This also includes the homogeneous Lâ-gain and homogeneous Input-to-State gain. For feedback interconnected systems, if the weight vectors between plants are matched, the additive inequality for homogeneous Lp-norm allows the introduction of the homogeneous small gain theorem for each p, enabling stability analysis on the closed loop system. Finally, some homogeneous Hâ-controllers can be designed, if the system is affine in the control input. Without the convenient tools for the linear systems, such homogeneous Hâ-controllers can only guarantee that the closed loop system has homogeneous Lp-gain less than some derivable numbers, its optimality can not be guaranteed. Several short examples are presented within each chapter to illustrate how such homogeneous Lp-gain can be calculated. In particular a detailed analysis on the Continuous Super-Twisting Like Algorithm is included with deeper insight for interested readers
Antifragile Control Systems: The case of an oscillator-based network model of urban road traffic dynamics
Existing traffic control systems only possess a local perspective over the
multiple scales of traffic evolution, namely the intersection level, the
corridor level, and the region level respectively. But luckily, despite its
complex mechanics, traffic is described by various periodic phenomena. Workday
flow distributions in the morning and evening commuting times can be exploited
to make traffic adaptive and robust to disruptions. Additionally, controlling
traffic is also based on a periodic process, choosing the phase of green time
to allocate to opposite directions right of the pass and complementary red time
phase for adjacent directions. In our work, we consider a novel system for road
traffic control based on a network of interacting oscillators. Such a model has
the advantage to capture temporal and spatial interactions of traffic light
phasing as well as the network-level evolution of the traffic macroscopic
features (i.e. flow, density). In this study, we propose a new realization of
the antifragile control framework to control a network of interacting
oscillator-based traffic light models to achieve region-level flow
optimization. We demonstrate that antifragile control can capture the
volatility of the urban road environment and the uncertainty about the
distribution of the disruptions that can occur. We complement our
control-theoretic design and analysis with experiments on a real-world setup
comparatively discussing the benefits of an antifragile design for traffic
control
Fixed-time Stabilization with a Prescribed Constant Settling Time by Static Feedback for Delay-Free and Input Delay Systems
A static non-linear homogeneous feedback for a fixed-time stabilization of a
linear time-invariant (LTI) system is designed in such a way that the settling
time is assigned exactly to a prescribed constant for all nonzero initial
conditions. The constant convergence time is achieved due to a dependence of
the feedback gain of the initial state of the system. The robustness of the
closed-loop system with respect to measurement noises and exogenous
perturbations is studied using the concept of Input-to-State Stability (ISS).
Both delay-free and input delay systems are studied. Theoretical results are
illustrated by numerical simulations
On Finite-Time Stabilization of Evolution Equations: A Homogeneous Approach
International audienceGeneralized monotone dilation in a Banach space is introduced. Classical theorems on existence and uniqueness of solutions of nonlinear evolution equations are revised. A universal homogeneous feedback control for a finite-time stabilization of linear evolution equation in a Hilbert space is designed using homogeneity concept. The design scheme is demonstrated for distributed finite-time control of heat and wave equations
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