Estimates of agents in a distributed consensus control are aligned with a particular value through interacting on communication graphs, which are of particular interest for researchers in the field of multi-agent coordination. Following this pattern, a discrete-time constrained consensus issue with generalized time delays is first established in this article, which is manipulated into an optimization problem via a quadratic performance index introduced as a global objective function. Then, a novel consensus scheme is investigated and proposed for handling this problem, enabling the consensus to approach the desired state globally and rapidly with optimal system property ensured. Besides, to advance the convergence speed and stability in resisting constant bias or oscillation, an adjustment control method is explored to construct a modified consensus scheme; further, to enhance the scene adaptability, fix topologies are extended to switching ones, and the latter is involved to develop another scheme on this basis. Moreover, the convergence and robustness of these three proposed consensus schemes are substantiated by theoretical analysis and numerical simulations. To highlight the practical implementations, the proposed consensus schemes are incorporated with a winner-take-all operation to accomplish multi-agent competitive coordination in a distributed way, and the results embody their effectiveness and superior consensus control ability, along with strong plasticity.Note to Practitioners—This paper is dedicated to investigating and optimizing distributed consensus schemes with time delays and output saturation with application to the competitive coordination of multi-agent systems. On the one hand, the consensus problem with output saturation receives limited attention, and few consensus algorithms consider both saturation limitation and channel gain. On the other hand, most existing studies on consensus with saturation consider simply the dynamic behaviour of agents without employing optimization, thus limiting further improvement of system performance. In this paper, a consensus algorithm is built from an optimization perspective that guarantees the state consensus of a multi-agent system with output constraints and generalized time delays. In addition, a consensus scheme is designed in a discrete-time framework and further modified and perfected along with the idea of considering time delays and expanding diverse topologies. Finally, experiments are conducted by applying the consensus scheme to a winner-take-all operation, with contributions of this paper verified.

Enlightened by competitive and collaborative coordination behaviors widely observed in natural swarm systems, this work emphasizes these coordinating modes in multirobot systems and optimizes system stability along with resource utilization. Then, schemes are constructed to describe and model these two modes, where a$k$-winner-take-all concept is introduced as the driving principle of multirobot competition. In addition, a distributed coordination approach is established to effectively handle the above schemes aided with optimality theory, which is developed by a fusion of a recurrent neural dynamics solver and a distributed solver. The former is a single-layer neural dynamics model with a simple structure, and the latter transforms the involved global information to a distributed type via consensus. Both of them are carried out in the discrete-time domain to fit the actual application. Finally, the convergence and stability of the proposed coordination approach are proved via theoretical analysis and further demonstrated through simulations and experiments.

This paper investigates a distributed competition behavior in multi-robot coordination under variable communication topology and switching one. In terms of multi-robot competition-based coordination, a winner-take-all (WTA) strategy is leveraged to address this issue with inevitable environmental barriers incorporated. Moreover, an innovative control theory stimulated gradient neural network (CTSGNN) algorithm is proposed to realize the WTA with prominent robustness and convergence over the traditional ones. Besides, to adapt to diversified local communication modes among multi-robot systems, fast variable and low switching topologies are constructed to establish two dynamic consensus estimators, accompanied by the proposed distributed control schemes. Traditional algorithms are introduced and served as a contrast. Afterward, the global convergence of the proposed algorithm in dealing with multi-robot competitive coordination, the universality of the application scenario, as well as the weaknesses of traditional methods are substantiated theoretically. The effectiveness and superiority of the proposed CTSGNN algorithm and the resultant distributed control schemes by integrating consensus estimators are further sustained via simulations. Note to Practitioners—The motivation of this paper is the coordination operation of multi-robot systems, but it is also applicable to other fields adopting multi-agent systems. Most of the existing researches on multi-robot coordination only exploit their collaborative behavior, which usually leads to the system redundancy and overflow of control costs. To this end, an innovative control algorithm is proposed for this competitive coordination and remains to be perfect in terms of stability and accuracy. Then, this paper establishes new distributed control schemes for multi-robot systems to compete for optimal dynamic task allocation. In this sense, under the premise of ensuring a successful task execution, only a few individuals with strong abilities and advantages are assigned. It is promising to maximize resource utilization, increase efficiency, and be extended to multi-objective scenarios. Note that the design of this scheme takes into account the environmental constraints and physical constraints of the robot itself. Theoretical analysis and preliminary simulation experiments prove the high efficiency of the control scheme. In ongoing research, the competitive coordination tasks of the mobile robot systems and communication delays or fault in control scheme design are explored to expand the operation scope and system extensibility.

In this article, a robust k -winner-take-all ( k -WTA) neural network employing the saturation-allowed activation functions is designed and investigated to perform a k -WTA operation, and is shown to possess enhanced robustness to disturbance compared to existing k -WTA neural networks. Global convergence and robustness of the proposed k -WTA neural network are demonstrated through analysis and simulations. An application studied in detail is competitive multiagent coordination and dynamic task allocation, in which k active agents [among ] are allocated to execute a tracking task with the static m-k ones. This is implemented by adopting a distributed k -WTA network with limited communication, aided with a consensus filter. Simulation results demonstrating the system's efficacy and feasibility are presented.

Recent decades have witnessed a trend that control-theoretical techniques are widely leveraged in various areas, e.g., design and analysis of computational models. Computational methods can be modeled as a controller and searching the equilibrium point of a dynamical system is identical to solving an algebraic equation. Thus, absorbing mature technologies in control theory and integrating it with neural dynamics models can lead to new achievements. This work makes progress along this direction by applying control-theoretical techniques to construct new recurrent neural dynamics for manipulating a perturbed nonstationary quadratic program (QP) with time-varying parameters considered. Specifically, to break the limitations of existing continuous-time models in handling nonstationary problems, a discrete recurrent neural dynamics model is proposed to robustly deal with noise. This work shows how iterative computational methods for solving nonstationary QP can be revisited, designed, and analyzed in a control framework. A modified Newton iteration model and an improved gradient-based neural dynamics are established by referring to the superior structural technology of the presented recurrent neural dynamics, where the chief breakthrough is their excellent convergence and robustness over the traditional models. Numerical experiments are conducted to show the eminence of the proposed models in solving perturbed nonstationary QP.

In this article, the existing approaches, including numerical algorithms as well as neural networks to solve dynamic linear matrix equations, have been presented and reviewed. Specifically, the conventional gradient recurrent neural networks (CGRNNs) and the conventional zeroing neural networks (CZNNs) are successively provided to solve the dynamic problems and linear matrix equations, both of which manifest inherent limitations during the solving procedures. To remedy the drawbacks on convergence time, nonzero residual error, and large computational load of the traditional models, an adaptive gradient recurrent neural network (AGRNN) to solve dynamic linear matrix equations is proposed. This proposed inversion-free model possesses rapid convergence rate and accurate calculated solutions. Moreover, theoretical analyses guarantee the advantages of the AGRNN compared with the CGRNN and the CZNN to solve dynamic linear matrix equations. Finally, three numerical experiments, and applications to a PUMA 560 robot motion planning and a mobile subject localization based on angle-of-arrival technique are implemented to testify the advantages of the AGRNN.

In this article, a neural dynamics model is constructed and investigated for solving time-dependent Sylvester equation with matrix inversion involved in the solving process. Besides, to eliminate the matrix inversion in the model, the quasi-Newton Broyden-Fletcher-Goldfarb-Shanno method is leveraged to construct a new model. Moreover, the global convergence performance and the effectiveness of the two discrete computational models are testified by providing theoretical analyses and numerical experiments with comparisons to the existing solutions, respectively. Two applications to robotics and the multiple-input multiple-output system are given to elucidate the feasibility of the proposed models for solving time-dependent Sylvester equation.

It has been reported that some specially designed recurrent neural networks and their related neural dynamics are efficient for solving quadratic programming (QP) problems in the real domain. A complex-valued QP problem is generated if its variable vector is composed of the magnitude and phase information, which is often depicted in a time-dependent form. Given the important role that complex-valued problems play in cybernetics and engineering, computational models with high accuracy and strong robustness are urgently needed, especially for time-dependent problems. However, the research on the online solution of time-dependent complex-valued problems has been much less investigated compared to time-dependent real-valued problems. In this article, to solve the online time-dependent complex-valued QP problems subject to linear constraints, two new discrete-time neural dynamics models, which can achieve global convergence performance in the presence of perturbations with the provided theoretical analyses, are proposed and investigated. In addition, the second proposed model is developed to eliminate the operation of explicit matrix inversion by introducing the quasi-Newton Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. Moreover, computer simulation results and applications in robotics and filters are provided to illustrate the feasibility and superiority of the proposed models in comparison with the existing solutions.