Cooperative Line Formation Control of Multi-Agent Systems Based on Least Squares Estimation

In this chapter, we focus on introducing a distributed online optimization problem for a set of nodes communicating on a time-varying unbalanced directed network, while considering the problem of how to preserve the privacy of their local cost functions. The main goal of this set of nodes is to cooperatively minimize the sum of all locally known convex cost functions (global cost function). We propose a differentially private distributed stochastic subgradient-push algorithm, named DP-DSSP, to solve such an optimization problem in a collaborative and distributed manner. The algorithm ensures that nodes interact with their in-neighbors and collectively optimize the global cost function. Unlike most existing distributed algorithms that do not consider privacy issues, DP-DSSP successfully protects the privacy of participating nodes through a differential privacy strategy, which is more practical in applications involving sensitive information, such as military affairs or medical treatment. An important feature of DP-DSSP is that it handles distributed online optimization problems in the context of time-varying unbalanced directed networks. Theoretical analysis shows that DP-DSSP can effectively protect differential privacy and can achieve sublinear regret. The tradeoff between the level of privacy and accuracy of DP-DSSP is also revealed. Moreover, DP-DSSP is able to handle arbitrarily large but uniformly bounded delays in the communication link. Finally, simulation experiments confirm the usefulness of DP-DSSP and the findings of this chapter.KeywordsDistributed online optimizationDifferential privacyStochastic subgradient-push algorithmTime-varying directed networksCommunication delays

The distributed optimal coordinated control problem of heterogeneous linear multi-agent systems is studied in this paper. Specifically, each agent in the system under consideration has a local private cost function, which is assumed to be strongly convex with a Lipschitz continuous gradient. The agents aim to achieve output consensus on the optimal solution of a global cost function, which is the sum of local cost functions. The communication topology among agents is assumed to be a weight-unbalanced and strongly connected directed graph. To solve such a control problem, a tracking-based approach is suggested and utilized, where an auxiliary system is designed to seek the optimal solution. Based on the output regulation technique, distributed tracking control inputs are proposed for the agents, which ensure that the outputs of the agents track the trajectories generated by the auxiliary system. Under the assumptions on the local cost functions, the communication topology and system matrices, it is proved that with the proposed control scheme, the outputs of all agents can achieve consensus on the optimal solution. Finally, two numerical simulation examples are presented to illustrate the effectiveness of the proposed tracking control scheme.

Formation control and obstacle avoidance for multi-agent systems have attracted more and more attention. In this paper, the problems of formation control and obstacle avoidance are investigated by means of a consensus algorithm. A novel distributed control model is proposed for the multi-agent system to form the anticipated formation as well as achieve obstacle avoidance. Based on the consensus algorithm, a distributed control function consisting of three terms (formation control term, velocity matching term, and obstacle avoidance term) is presented. By establishing a novel formation control matrix, a formation control term is constructed such that the agents can converge to consensus and reach the anticipated formation. A new obstacle avoidance function is developed by using the modified potential field approach to make sure that obstacle avoidance can be achieved whether the obstacle is in a dynamic state or a stationary state. A velocity matching term is also put forward to guarantee that the velocities of all agents converge to the same value. Furthermore, stability of the control model is proven. Simulation results are provided to demonstrate the effectiveness of the proposed control.

Various distributed optimization methods have been developed for solving problems which have simple local constraint sets and whose objective function is the sum of local cost functions of distributed agents in a network. Motivated by emerging applications in smart grid and distributed sparse regression, this paper studies distributed optimization methods for solving general problems which have a coupled global cost function and have inequality constraints. We consider a network scenario where each agent has no global knowledge and can access only its local mapping and constraint functions. To solve this problem in a distributed manner, we propose a consensus-based distributed primal-dual perturbation (PDP) algorithm. In the algorithm, agents employ the average consensus technique to estimate the global cost and constraint functions via exchanging messages with neighbors, and meanwhile use a local primal-dual perturbed subgradient method to approach a global optimum. The proposed PDP method not only can handle smooth inequality constraints but also non-smooth constraints such as some sparsity promoting constraints arising in sparse optimization. We prove that the proposed PDP algorithm converges to an optimal primal-dual solution of the original problem, under standard problem and network assumptions. Numerical results illustrating the performance of the proposed algorithm for a distributed demand response control problem in smart grid are also presented.

Hierarchical optimization for task-space bipartite coordination of multiple uncertain Lagrange plants

This paper proposes an adaptive supper twisting sliding mode strategy for formation control of multi-agent systems evolving on the Special Euclidean group. The proposed controller is deemed decentralized and deals with actuator fault and matched uncertainties in the agents’ inertia parameters. The introduced control is designed based on the local neighboring information of each agent. The formation convergence is studies using the Lyapunov’s stability theorem. A simulation example is provided to evaluate the performance of the proposed approach.

The current paper investigates the active disturbance rejection time-varying formation control for second-order multi-agent systems subjected to external disturbances. Firstly, a robust time-varying formation control protocol with the disturbance compensation is proposed. Then, an extended state observer is designed to estimate the disturbance compensation by the active disturbance rejection control method. Moreover, sufficient conditions for robust time-varying formation feasibility analysis and protocol design are shown, respectively. Finally, a numerical simulation is presented to verify the theoretical results.

In this paper, the distributed optimization problem for multi-agent system (MAS) formation control of unmanned aerial vehicles (UAVs) is suggested here. The situation that the internal states of a single UAV can be made fully available was aimed at, the internal optimal control law of a single UAV is designed using the optimal control theory. To cope with the obstacle that each agent in the system can only communicate with its neighbor agents, the distributed formation control law of the system is introduced based on the communication topology of the system, and further the stability of the system is analyzed in helps of graph theory. The validity of the suggested scheme is verified by both the numerical simulation and UAV platform.

This paper considers distributed nonconvex optimization with the cost functions being distributed over agents. Noting that information compression is a key tool to reduce the heavy communication load for distributed algorithms as agents iteratively communicate with neighbors, we propose three distributed primal–dual algorithms with compressed communication. The first two algorithms are applicable to a general class of compressors with bounded relative compression error and the third algorithm is suitable for two general classes of compressors with bounded absolute compression error. We show that the proposed distributed algorithms with compressed communication have comparable convergence properties as state-of-the-art algorithms with exact communication. Specifically, we show that they can find first-order stationary points with sublinear convergence rate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(1/T)$</tex-math></inline-formula> when each local cost function is smooth, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T$</tex-math></inline-formula> is the total number of iterations, and find global optima with linear convergence rate under an additional condition that the global cost function satisfies the Polyak–Łojasiewicz condition. Numerical simulations are provided to illustrate the effectiveness of the theoretical results.

The Asia Pacific Information and Communication Technology Alliance (APICTA) Awards has been held for 12 years, rewarding the most innovative solutions in different categories of Information and Communication Technology (ICT). To maintain professionalism, judges are nominated from each economy, and appointed to panels of different categories. Judge assignment is a difficult task, since it has to optimize between expertise, distribution of workloads, fairness and sometimes even political correctness. In this paper, we describe our experience in analyzing and automating the APICTA judge assignment process using Soft Constraint Programming for the 13 th APICTA hosted in Hong Kong on November, 2013. We chose the weighted constraint satisfaction (WCSP) framework since both hard constraints and preferences can be modeled by cost functions. Consistency algorithms can effect strong propagation by redistributing costs among cost functions. We observe that a number of restrictions in the judge assignment problem involves counting. In our first attempt, we utilized the Soft_Among var global cost function for these counting conditions but we could not solve the problem within a day. Soft_GCC val is another possible global cost function to model counting, which is what we used in the second attempt. We can compute the optimum in a few hours, which is far from practical.We apply similar techniques as Régin to show that the combination of Soft_GCC val and Soft_Among var is flow-based. We further prove that the combination results in a flow-based projection-safe cost function, meaning that soft arc consistencies can be enforced efficiently. By using this combination in our final model, we can solve the judge assignment problem within a few minutes. We consider this a success story where theory and practice meet.

Event-triggered formation control of linear continuous-time multiagent systems is studied in this article. A complex-valued Laplacian is adopted by the local information of desired formation. For each agent, an event-triggering mechanism based on the neighboring information at event-triggering time instants is presented and continuous communications between neighboring agents are avoided. Furthermore, an event-triggered control strategy using the idea of dynamic state observer is designed. It is shown that any desired formation shape can be achieved. Moreover, the Zeno-behavior is strictly excluded. Finally, effectiveness of the obtained theoretical results is validated by two simulation examples.

This article studies formation control for multiagent systems in the presence of denial-of-service (DoS) attacks. The challenge is to address secure formation tracking and communication bandwidth-saving issues simultaneously. To tackle this, we propose a switching-like event-triggered mechanism that reduces excessive bandwidth consumption during interactions among multiple followers under DoS attacks. The triggering condition is allowed to be switched during the intervals when attacks are activated, ensuring that triggering can normally occur throughout the overall time interval by introducing an auxiliary variable depending on the success of the latest trigger moment. Based on this approach, we construct an event-based time-varying formation control scheme. In addition, we establish sufficient conditions that reveal the relationship between exponential stability and the frequency/duration of the DoS attacks. Unlike other single-leader methods, a significant feature of the formation control scheme is its ability to achieve the desired formation tracking for multiagent systems with multiple leaders. Finally, the validity of the proposed method is demonstrated through simulation and experimental results.

This paper presents the theoretical basis and some practical applications of the simulation program DAISY (Activated Sludge DYnamic simulator) version 2.0 with the aim of optimizing the design of complex activated sludge plants for wastewater treatment. The software, developed by CEIT, was designed for the Spanish firm CADAGUA S.A. and is currently used as design tool by the engineering department of the company. The new version of the simulator introduces an optimization module that estimates automatically the optimum dimensions and of an activated sludge plant to reduce the global cost function that could include effluent quality, construction cost and plant restrictions. This global cost function can combine continuous cost and penalty functions. The automatic optimization is based on a direct search algorithm introduced in the simulation software previously developed. This algorithm determines the path towards an optimum by evaluating the objective function at several points without calculating derivatives. The paper includes some examples to illustrate the vast possibilities of these kind of optimization procedures in the design of complex wastewater treatment plants including organic matter and nutrient removal.

This paper investigates the time-varying formation control problem for multi-agent systems and uses algebraic graph theory to abstract topological relationships between agents. Unlike conventional time-varying topologies, we consider a more challenging situation where agents may be destroyed during the maneuvering process. To cope with this problem, firstly we propose the time-varying target formation based on the rigidity graph theory. Then the double-integrator dynamics are addressed and the distributed multi-agent control laws based on the consistency theory and stress matrix are developed during at different stages of formation. Finally, the stability of the system is given and simulation results demonstrate the validity of the proposed formation control algorithm under time-varying topology.

This paper addresses a formation control problem for multi-agent systems with heterogeneous drift velocities and time-varying attitudes. Each agent is assumed to be able to measure relative states of neighbor agents in its local frame. We propose a distributed and relative feedback controller consisting of formation error among neighbors and its integral value, called proportional-integral (PI) formation controller. We show that the proposed controller can completely eliminate the formation error in spite of the existence of time-varying disturbances, caused by the variations of the agent attitudes. The effectiveness of the proposed controller is illustrated by a simulation result.