A finite-time consensus algorithm with simple structure for fixed networks

In this paper, a continuous-time consensus algorithm with guaranteed finite-time convergence is proposed. Using homogeneity theory, finite-time consensus is proved for fixed topologies. The proposed algorithm is computationally simpler than other reported finite-time consensus algorithms, which is an important feature in scenarios of energy efficient nodes with limited computing resources such as sensor networks. Additionally, the proposed approach is compared on simulations with existing consensus algorithms, namely, the standard asymptotic consensus algorithm and the finite-time and fixed-time convergent algorithms, showing, in cycle graph topology, better robustness features on the convergence with respect to the network growth with less control effort. Indeed, the convergence time of other previously proposed consensus algorithms grows faster as the network grows than the one herein proposed whereas the control effort of the proposed algorithm is lower

Equivalence of nonlinear systems to triangular form: the singular case

The problem of state equivalence of a given nonlinear system to a triangular form is considered here. The solution of this problem has been known for the regular case, i.e. when there exists a certain nested sequence of regular and involutive distributions. It is also known that in this case the corresponding system is linearizable using a smooth coordinate change and static state feedback. This paper deals with the singular case, i.e. when the nested sequence of involutive distributions of the system contains singular distributions. Special attention is paid to the so-called bijective triangular form. Geometric, coordinates-free criteria for the solution of the above problem as well as constructive, verifiable procedures are given. These results are used to obtain a result in the nonsmooth stabilization problem

Chaos Theory for Evolutionary Algorithms Researchers

This chapter deals with chaotic systems. Based on the characterization of deterministic chaos, universal features of that kind of behavior are explained. It is shown that despite the deterministic nature of chaos, long term behavior is unpre- dictable. This is called sensitivity to initial conditions. We further give a concept of quantifying chaotic dynamics: the Lyapunov exponent. Moreover, we explain how chaos can originate from order by period doubling, intermittence, chaotic transients and crises. In the second part of the chapter we discuss different examples of sys- tems showing chaos, for instance mechanical, electronic, biological, meteorological, algorithmical and astronomical systems.P(GA102/08/0186), P(GA102/09/1680), Z(AV0Z10750506), Z(MSM7088352101

Embedding the Generalized Acrobot into the N-Link with an Unactuated Cyclic Variable and Its Application to Walking Design

International audienceThe Acrobot is the well-known and widely studied underactuated mechanical system having two links and one actuated joint between them. It may be also viewed as the simplest possible walking like mechanism without knees and the ankle-joint actuation, alternatively also referred to as the underactuated Compass gait walker. To extend techniques used to control the Acrobot to a more general underactuated n-link having an unactuated cyclic variable, this paper defines the so-called generalized Acrobot. Further, it is shown that for every set of virtual constraints there exists a generalized Acrobot that is linearly embedded into this n-link. Based on this property and results valid for the Acrobot, walking strategies for the n-link are provided. Important achievement here is that the exponentially stable tracking during the swing phase only is possible, i.e. the stabilizing effect of the impact map is not needed. Computer simulations of the 4-link case are provided

Analysis and control of underactuated mechanical systems with application to walking robots

L objet de cette thèse est de placer l analyse et la commande des robots marcheurs dans le contexte des systèmes mécaniques sous-actionnés plus généraux. Nous avons développé un nouveau cadre pour la commande d une classe de systèmes mécaniques sous-actionnés. L analyse de la structure des systèmes mécaniques sous-actionnés simples nous permet de définir cette classe de systèmes qui représentent les robots marcheurs. La transformation exacte de coordonnées proposée linéarise (partiellement) le système de manière exacte. Cette forme linéarisante est associée à une commande linéaire. Nous montrons que ce cadre permet d engendrer de manière efficace des trajectoires de référence ainsi que la commande qui assure la poursuite de ces trajectoires. En raison des deux échelles de temps de la commande, ce nouveau cadre est appelé Commande composite . On a montré ici que notre nouvelle approche utilise deux systèmes de coordonnées. Ces deux systèmes de coordonnées sont adaptés soit la planification de trajectoire, soit à la résolution du problème de poursuiteA novel framework for modeling and control of underactuated mechanical systems has been developed. Structural analysis of the mechanical system is used to define the subclass of the underactuated systems representing the walking structures that are studied in sequel. The basic methodology of the proposed approach consists of various types of the partial exact linearization of the model that can be also viewed as a part of modelling process. First, based on a suitable exact linearization combined with the so-called composite control the asymptotic stabilization of several underactuated systems is achieved, including a general nlink. The composite principle combined with specific linear control method is a novel idea of the thesis combining certain fast and slow feedbacks in different coordinates systems to compensate the above-mentioned lack of actuation. It is applicable to walking trajectory planning and its asymptotic tracking design. In particular, a so-called pseudopassive walking strategy has been proposed showing a good capacity for designing walking trajectories with various step parameters, e.g. step length, velocity of walking, etc. The proposed coordinate system choice greatly facilitates efficient feedback strategy design to achieve stable walking trajectory tracking. Numerous experimental simulation results have been achieved confirming the success of the above design strategyNANTES-BU Sciences (441092104) / SudocNANTES-Ecole Centrale (441092306) / SudocSudocFranceF

Damping a pendulum's swing by string length adjustment - design and comparison of various control methods

status: publishe

Quantized nonlinear model predictive control for a building

© 2015 IEEE. In this paper, the task of quantized nonlinear predictive control is addressed. In such case, values of some inputs can be from a continuous interval while for the others, it is required that the optimized values belong to a countable set of discrete values. Instead of very straightforward a posteriori quantization, an alternative algorithm is developed incorporating the quantization aspects directly into the optimization routine. The newly proposed quaNPC algorithm is tested on an example of building temperature control. The results for a broad range of number of quantization steps show that (unlike the naive a posteriori quantization) the quaNPC is able to maintain the control performance close to the performance of the original continuous-valued nonlinear predictive controller and at the same time it significantly decreases the undesirable oscillations of the discrete-valued input