Distributed neuro‐adaptive controller for output consensus of uncertain multi‐agent systems with a high‐dimensional leader

Optimized backstepping consensus control using adaptive observer-critic–actor reinforcement learning for strict-feedback multi-agent systems

Based on PD and PI control methods, the lag output consensus problem for second-order nonlinear multiagent systems (MASs) without and with external disturbances is addressed, which generalizes the existing lag consensus results for MASs. Firstly, a lag output consensus condition is derived for the MAS by designing a proper PD control scheme. Furthermore, a PI control strategy is developed to ensure that the MAS realizes the lag output consensus. In addition, two lag <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal {H}}_{\infty } $ </tex-math></inline-formula> output consensus criteria are also established on the basis of PD and PI control schemes for the MAS with external disturbances. Lastly, two examples are utilized to verify the correctness and effectiveness of the devised control schemes. Note to Practitioners—Recently, virtual leader-based approach has been widely utilized to address the output consensus control problem for various MASs. Practically, each agent receiving its own output information may be later than the virtual leader. Therefore, it is more reasonable and meaningful to discuss the lag output consensus for MASs. Furthermore, considering that PID control is very simple and easy to implement, some PD and PI control strategies are developed to tackle the lag output consensus for MASs. In addition, since external disturbances are ubiquitous and may destroy the lag output consensus, the lag <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal {H}}_{\infty } $ </tex-math></inline-formula> output consensus for MASs is also investigated. Multiple single-link robot systems experiments verify that the approaches given in this paper are feasible and valid.

Distributed adaptive output consensus control of a class of heterogeneous multi-agent systems under switching directed topologies

Leader-following almost output consensus for discrete-time heterogeneous multi-agent systems in the presence of external disturbances

This paper suggests frequency-domain stability criteria for homogeneous multiconnected automatic control systems that allow an easy stability analysis of high-order systems of a large dimension. The results are confirmed by mathematical modeling.

In two recent papers, Brayton and Tong developed some significant results which are the basis of a constructive approach in the stability analysis of dynamical systems. Although their algorithm is powerful, it taxes the capabilities of most modern computers when the dimension of a system is high or even when the dimension is moderate in size. In this paper we remove these difficulties to a certain extent by generalizing the work of Brayton and Tong to interconnected dynamical systems. In our approach, the analysis of complex dynamical systems (which may be of high dimension) is accomplished in terms of the qualitative properties of the free subsystems and the interconnections of such systems.

Output consensus problem is investigated for the mixed-order multi-agent system, which is composed of two types agents with one and two poles at the origin respectively. According to generalized Nyquist stability criterion, consensus conditions are gained for the mixed-order multi-agent systems to achieve an asymptotic stationary consensus. Besides, output consensus is also analyzed for a simplest mixed-order multiagent system, which is composed of single and double integrators. Numerical examples demonstrate the correctness of the results.

Bipartite event-triggered impulsive output consensus for switching multi-agent systems with dynamic leader

Distributed consensus of heterogeneous multi-agent systems subject to switching topologies and delays

Leader–follower output consensus of multiagent systems over finite fields

GTS-based communication task scheduling for quantized output consensus over IEEE 802.15.4 wireless networks

Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an open and challenging research frontier, with a spectrum of applications ranging from stochastic thermodynamics to biophysics and data science. Among these, the design of nanoscale electronic components motivates the study of underdamped dynamics, leading to practical and conceptual difficulties. In this work, we develop analytic techniques to determine protocols steering finite time transitions at a minimum thermodynamic cost for stochastic underdamped dynamics. As cost functions, we consider two paradigmatic thermodynamic indicators. The first is the Kullback–Leibler divergence between the probability measure of the controlled process and that of a reference process. The corresponding optimization problem is the underdamped version of the Schrödinger diffusion problem that has been widely studied in the overdamped regime. The second is the mean entropy production during the transition, corresponding to the second law of modern stochastic thermodynamics. For transitions between Gaussian states, we show that optimal protocols satisfy a Lyapunov equation, a central tool in stability analysis of dynamical systems. For transitions between states described by general Maxwell-Boltzmann distributions, we introduce an infinite-dimensional version of the Poincaré-Lindstedt multiscale perturbation theory around the overdamped limit. This technique fundamentally improves the standard multiscale expansion. Indeed, it enables the explicit computation of momentum cumulants, whose variation in time is a distinctive trait of underdamped dynamics and is directly accessible to experimental observation. Our results allow us to numerically study cost asymmetries in expansion and compression processes and make predictions for inertial corrections to optimal protocols in the Landauer erasure problem at the nanoscale.

On the convergence of two-step methods generated by point-to-point operators

We analyze the stability of a class of thin-shell wormholes with spherical symmetry evolving in flat FRW spacetimes. The wormholes considered here are supported at the throat by a perfect fluid with equation of state [Formula: see text] and have a physical radius equal to aR, where a is a time-dependent function describing the dynamics of the throat and R is the background scale factor. The study of wormhole stability is done by means of the stability analysis of dynamic systems.

Introduction. Minimization of ravine convex functions, both smooth and non-smooth, arises in many problems of planning, control, stability analysis of dynamic systems, artificial intelligence, and machine learning. Therefore, the development of new and improvement of existing methods is an important task, taking into account the fact that more and more frequently the functions to be minimized depend on a large number of variables. Special attention should be paid to the methods using the operation of linear transformation of space, which allow to improve the properties of the objective function and significantly accelerate its minimization. Known methods of this type, in particular, ellipsoid methods and r-algorithms, require recalculation of the transformation matrix at each iteration. Therefore, the development of methods with a one-time transformation of space, which have a lower cost of iteration, is definitely an urgent task. The purpose of the article is to review modifications of subgradient method with Polyak’s step that use a scalar parameter m(1 and one-time space transformation operation. Supplement the justification of the convergence and convergence rate of the modifications described. Give recommendations regarding determination of parameter m and space transformation matrix B. Results. Subgradient method with Polyak’s step in transformed space and parameter m&gt;1 is an effective method for minimizing smooth and non-smooth convex functions that have a ravine structure. Determination of an appropriate value of the parameter m(1 and space transformation matrix B allows to significantly accelerate this method and use it for minimization functions that depend on a large number of variables. Conclusions. The development of fast methods for minimization of non-smooth convex functions of many variables with a ravine structure makes it possible to effectively solve modern problems of artificial intelligence, in particular, the problems of machine learning, image recognition, big data analysis, etc. Keywords: subgradient method, space transformation, ravine functions.