Bipartite consensus control for fractional-order nonlinear multi-agent systems: An output constraint approach
TL;DR: A novel fully distributed controller is developed based on backstepping technique and neuro-adaptive update mechanism to ensure bipartite consensus of multiple fractional-order nonlinear systems with output constraints and it is shown that all the closed-loop error signals are uniformly ultimately bounded.
About: This article is published in Neurocomputing.The article was published on 2020-07-15. It has received 58 citations till now. The article focuses on the topics: Bipartite graph & Lyapunov function.
Citations
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TL;DR: All signals, including variables and errors in the closed-loop system are semi-global practical finite-time stability whereas the the tracking errors are asymptotically driven to zero without transgression of the constraints.
Abstract: This article considers the neural adaptive control issues of a category of non-integer-order non-square plants with actuator Nonlinearities and Asymmetric Time-Varying pseudo-State Constraints. First, the original non-square non-affine system with input nonlinearities is transformed into an equivalent affine-in-control square model by defining a set of auxiliary variables and by employing the mean-value theorem. Second, Neural networks and Nussbaum functions are exploited to obviate the requirement of a complete knowledge of the system dynamics and the control directions, respectively. Third, a novel adaptive dynamic surface control method based on Caputo fractional derivative definitions and fractional order filters is developed to overcome the “explosion of complexity” problem in the traditional backstepping design process and to determine the parameter update laws and control signals, concurrently. Then, Asymmetric Barrier Lyapunov Functions with error variables are adopted to ensure the uniform stability of the closed-loop system and to prevent the violation of the full pseudo-State constraints. The novelties and contributions of this article are: (1) through the introduction of new technical Lemmas and corollaries, existing control design and stability theories linked to integer-order square systems are developed and extended to non-square non-integer-order ones. (2) all signals, including variables and errors in the closed-loop system are semi-global practical finite-time stability whereas the the tracking errors are asymptotically driven to zero without transgression of the constraints. Finally, the effectiveness and potential of the proposed control approach are substantiated by two example simulations.
27 citations
01 Jan 2023
TL;DR: In this article , the bipartite consensus tracking control problem for nonlinear networked systems with antagonistic interactions and unknown backlash-like hysteresis is investigated, in which every agent is an independent individual, and this model allows competitive and cooperative interactions to coexist.
Abstract: This article investigates the bipartite consensus tracking control problem for nonlinear networked systems with antagonistic interactions and unknown backlash-like hysteresis. The generalized networked multiagent systems model is considered, in which every agent is an independent individual, and this model allows competitive and cooperative interactions to coexist. A Gaussian function is applied to simulate competition and cooperation among agents. Radial basis function (RBF) neural network (NN) is applied to estimate the unknown nonlinear function. By using backstepping technology, we propose an adaptive neural control protocol, which not only ensures that in the closed-loop system all the signals are bounded but also realizes bipartite consensus control. Finally, we present a simulation example to illustrate the effectiveness of the obtained result.
22 citations
01 Jan 2023
TL;DR: In this article , the bipartite consensus tracking control problem for nonlinear networked systems with antagonistic interactions and unknown backlash-like hysteresis is investigated, in which every agent is an independent individual, and this model allows competitive and cooperative interactions to coexist.
Abstract: This article investigates the bipartite consensus tracking control problem for nonlinear networked systems with antagonistic interactions and unknown backlash-like hysteresis. The generalized networked multiagent systems model is considered, in which every agent is an independent individual, and this model allows competitive and cooperative interactions to coexist. A Gaussian function is applied to simulate competition and cooperation among agents. Radial basis function (RBF) neural network (NN) is applied to estimate the unknown nonlinear function. By using backstepping technology, we propose an adaptive neural control protocol, which not only ensures that in the closed-loop system all the signals are bounded but also realizes bipartite consensus control. Finally, we present a simulation example to illustrate the effectiveness of the obtained result.
17 citations
TL;DR: Simulations with static and dynamic obstacles show that the proposed MPC method can provide significantly better control performance than the traditional logic-based method using less priority switchings.
Abstract: The task priority planning problem is addressed in the task supervisor of null-space behavioral (NSB) control for multi-agent systems. Traditional methods rely on pre-defined logic-based or fuzzy rules to adjust task priority. In this work, a novel task supervisor is proposed using model predictive control (MPC) techniques. At each sampling instant, the task priority planning problem is formulated as a switching mode optimal control problem (OCP), which can be solved by efficient mixed-integer optimal control algorithms. The optimal task priority order is obtained based on current and predictive information of agents, without the need for a pre-defined rule. By explicitly introducing slack variables into constraints, the proposed MPC method is flexible to cope with dynamic obstacles in unknown environments. Simulations with static and dynamic obstacles show that the proposed method can provide significantly better control performance than the traditional logic-based method using less priority switchings.
15 citations
TL;DR: A new scaled disagreement vector is proposed and its properties under switching and undirected graphs are investigated and sufficient conditions in terms of linear matrix inequalities are established in order to guarantee that the multiagent system achieves scaled consensus under DoS attacks.
Abstract: This paper aims to solve scaled consensus problem for general linear multiagent systems under denial-of-service (DoS) attacks. Firstly, we propose a new scaled disagreement vector and investigate its properties under switching and undirected graphs. Secondly, we establish sufficient conditions in terms of linear matrix inequalities in order to guarantee that the multiagent system achieves scaled consensus under DoS attacks. Contrary to most existing studies where DoS attacks on all the channels are same, in this note, we formulate the problem such that the adversary compromises each agent independently. Moreover, the distributed consensus protocol is investigated for networks with time-varying delay. Finally, two simulation examples are given to demonstrate effectiveness of the proposed design methodologies.
15 citations
References
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TL;DR: A distinctive feature of this work is to address consensus problems for networks with directed information flow by establishing a direct connection between the algebraic connectivity of the network and the performance of a linear consensus protocol.
Abstract: In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topology; and 3) undirected networks with communication time-delays and fixed topology. We introduce two consensus protocols for networks with and without time-delays and provide a convergence analysis in all three cases. We establish a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance (or negotiation speed) of a linear consensus protocol. This required the generalization of the notion of algebraic connectivity of undirected graphs to digraphs. It turns out that balanced digraphs play a key role in addressing average-consensus problems. We introduce disagreement functions for convergence analysis of consensus protocols. A disagreement function is a Lyapunov function for the disagreement network dynamics. We proposed a simple disagreement function that is a common Lyapunov function for the disagreement dynamics of a directed network with switching topology. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results.
11,658 citations
Book•
01 Jan 1995
TL;DR: In this paper, the focus is on adaptive nonlinear control results introduced with the new recursive design methodology -adaptive backstepping, and basic tools for nonadaptive BackStepping design with state and output feedbacks.
Abstract: From the Publisher:
Using a pedagogical style along with detailed proofs and illustrative examples, this book opens a view to the largely unexplored area of nonlinear systems with uncertainties. The focus is on adaptive nonlinear control results introduced with the new recursive design methodology--adaptive backstepping. Describes basic tools for nonadaptive backstepping design with state and output feedbacks.
6,923 citations
Book•
01 Jan 1999
TL;DR: In this article, the authors present a method for computing fractional derivatives of the Fractional Calculus using the Laplace Transform Method and the Fourier Transformer Transform of fractional Derivatives.
Abstract: Preface. Acknowledgments. Special Functions Of Preface. Acknowledgements. Special Functions of the Fractional Calculus. Gamma Function. Mittag-Leffler Function. Wright Function. Fractional Derivatives and Integrals. The Name of the Game. Grunwald-Letnikov Fractional Derivatives. Riemann-Liouville Fractional Derivatives. Some Other Approaches. Sequential Fractional Derivatives. Left and Right Fractional Derivatives. Properties of Fractional Derivatives. Laplace Transforms of Fractional Derivatives. Fourier Transforms of Fractional Derivatives. Mellin Transforms of Fractional Derivatives. Existence and Uniqueness Theorems. Linear Fractional Differential Equations. Fractional Differential Equation of a General Form. Existence and Uniqueness Theorem as a Method of Solution. Dependence of a Solution on Initial Conditions. The Laplace Transform Method. Standard Fractional Differential Equations. Sequential Fractional Differential Equations. Fractional Green's Function. Definition and Some Properties. One-Term Equation. Two-Term Equation. Three-Term Equation. Four-Term Equation. Calculation of Heat Load Intensity Change in Blast Furnace Walls. Finite-Part Integrals and Fractional Derivatives. General Case: n-term Equation. Other Methods for the Solution of Fractional-order Equations. The Mellin Transform Method. Power Series Method. Babenko's Symbolic Calculus Method. Method of Orthogonal Polynomials. Numerical Evaluation of Fractional Derivatives. Approximation of Fractional Derivatives. The "Short-Memory" Principle. Order of Approximation. Computation of Coefficients. Higher-order Approximations. Numerical Solution of Fractional Differential Equations. Initial Conditions: Which Problem to Solve? Numerical Solution. Examples of Numerical Solutions. The "Short-Memory" Principle in Initial Value Problems for Fractional Differential Equations. Fractional-Order Systems and Controllers. Fractional-Order Systems and Fractional-Order Controllers. Example. On Viscoelasticity. Bode's Analysis of Feedback Amplifiers. Fractional Capacitor Theory. Electrical Circuits. Electroanalytical Chemistry. Electrode-Electrolyte Interface. Fractional Multipoles. Biology. Fractional Diffusion Equations. Control Theory. Fitting of Experimental Data. The "Fractional-Order" Physics? Bibliography. Tables of Fractional Derivatives. Index.
3,962 citations
TL;DR: This paper presents control designs for single-input single-output (SISO) nonlinear systems in strict feedback form with an output constraint, and explores the use of an Asymmetric Barrier Lyapunov Function as a generalized approach that relaxes the requirements on the initial conditions.
1,999 citations
TL;DR: The question asked in this paper is: is it possible to achieve a form of agreement also in presence of antagonistic interactions, modeled as negative weights on the communication graph?
Abstract: In a consensus protocol an agreement among agents is achieved thanks to the collaborative efforts of all agents, expresses by a communication graph with nonnegative weights. The question we ask in this paper is the following: is it possible to achieve a form of agreement also in presence of antagonistic interactions, modeled as negative weights on the communication graph? The answer to this question is affirmative: on signed networks all agents can converge to a consensus value which is the same for all agents except for the sign. Necessary and sufficient conditions are obtained to describe cases in which this is possible. These conditions have strong analogies with the theory of monotone systems. Linear and nonlinear Laplacian feedback designs are proposed.
1,457 citations