Kazunori Sakurama

Distributed Controllers for Multi-Agent Coordination Via Gradient-Flow Approach

This paper provides a unified solution for a general distributed control problem of multi-agent systems based on the gradient-flow approach. First, a generalized coordination is presented as a control objective which represents a wide range of coordination tasks (e.g., consensus, formation and pattern decision) in a unified manner. Second, a necessary and sufficient condition for the gradient-based controllers to be distributed is derived. It turns out that the notion of clique (i.e., complete subgraph) plays a crucial role to obtain any distributed controllers. Furthermore, all such controllers are explicitly characterized with free design parameters. Third, it is shown how to choose an optimal controller in a systematic way among all distributed ones, where an optimality measure is introduced for the generalized coordination. Finally, the effectiveness of the proposed method is demonstrated through simulations, where a distributed pattern decision is discussed as an example of the generalized coordination.

Trajectory tracking control of bimodal piecewise affine systems

This paper deals with a trajectory tracking problem of a class of bimodal piecewise affine systems, which have rarely been discussed so far. This would be very challenging because of the discontinuous changes of their vector fields. First, we introduce an error variable and an error system as a generalization of the tracking error and its system. As an error variable, a function switched by the mode of a piecewise affine system is adopted to overcome an inherent difficulty in trajectory tracking of piecewise affine systems. Next, we design a tracking controller which stabilizes the error system using a Lyapunov-like function, which can be applied to systems including state jumps. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Necessary and sufficient condition for average consensus of networked multi-agent systems with heterogeneous time delays

This paper deals with an average-consensus problem of networked multi-agent systems with heterogeneous time delays. First, a necessary and sufficient condition is derived for multi-agent systems to achieve average consensus. This condition is represented in the form of an algebraic condition by using the delay-transition and the delay-weighted Laplacians. Second, a performance criterion is introduced to evaluate multi-agent systems that do not achieve average consensus. The criterion is represented in terms of the norms with respect to the above Laplacians. These results imply that the introduced Laplacians play important roles in analysing multi-agent systems with heterogeneous time delays. The validity of the analysis results is demonstrated by simulations with six-agent systems.

Trajectory Tracking Control of Nonholonomic Hamiltonian Systems via Generalized Canonical Transformations

This paper is devoted to a unified approach to trajectory tracking control of nonholonomic portcontrolled Hamiltonian systems via generalized canonical transformations. The basic strategy of this approach is to construct an error system, which describes the dynamics of the tracking error, by a passive port-controlled Hamiltonian system. This technique works for both holonomic and nonholonomic port-controlled Hamiltonian systems. A practical design procedure to derive global tracking controllers for those systems is proposed. This method is a natural extension of the conventional passivity based control.

Leader-Following Formation Navigation for Multiple Robots with Collision Avoidance

Abstract This paper deals with a collision avoidance problem in leader-following formation navigation for multiple mobile robots. Because followers should move along a leaders trajectory, we first try to avoid collisions by adjusting their velocities on the trajectory. This strategy causes delays of the followers from the leader, which is often problematic because we cannot predict how late the followers will be from the leader. Moreover, there are situations that the robots cannot avoid collisions only with this strategy. If the leader goes straight and turns back toward the followers suddenly, the followers have to move back along the trajectory where the leader just moved. In this case, the followers would be better off moving around to the back of the leader and recover their delays even if they go away from the specified trajectory. From these viewpoints, this paper proposes a collision avoidance method for leader-following formation navigation taking into account both the tracking errors and the delays of the followers from the leader. This method adjusts the velocity of each follower, as well as modifies the shape of the trajectory if a delay becomes too large. The effectiveness of the proposed method is demonstrated by a simulation with three mobile robots.

Communication-Based Decentralized Demand Response for Smart Microgrids

Demand response (DR) is one of the most promising solutions to efficient control of smart grids with renewable energy resources. Usually, DR programs are implemented by means of centralized control by power supply companies or independent system operators. In contrast, recently, the focus has been on decentralized control to enhance the efficient use of distributed energy resources especially on microgrids. This paper proposes a decentralized control system for DR. The key of the proposed method is a new decentralized algorithm for determining appropriate control signals (corresponding to prices and/or incentives) by using communication networks provided by smart meters. The effectiveness of the proposed method is illustrated by a numerical example.

Average-consensus Problem for Networked Multi-agent Systems with Heterogeneous Time-delays

Abstract This paper deals with an average-consensus problem for networked multi-agent systems with non-uniform and asymmetric (heterogeneous) time-delays. The goal of this paper is to derive a necessary and sufficient condition for average-consensus in the form of an algebraic condition. We deal with two cases according to initial conditions: the state variables before the initial time are constant or not constant. In each case, the necessary and sufficient condition is represented by the eigenvectors of the delay-transition and/or the delay-weighted Laplacians, which are newly introduced in this paper to express the structures of the delayed networks. This is the first paper which shows the strict condition for average-consensus of networked multi-agent systems with heterogeneous time-delays. The validity of the analysis results is demonstrated by simulations with six-agent systems.

Multi-Agent Coordination to High-Dimensional Target Subspaces

In this paper, we consider a coordination problem to high-dimensional target subspaces for networked multi-agent systems. It is a general form of multi-agent coordination which includes a wide range of applications, e.g., rendezvous, alignment, formation and so on. This paper discusses a fundamental issue of this coordination: what kind of network topology enables us to achieve this coordination via distributed and relative control. We derive necessary and sufficient conditions of such network graphs, and show that the connectivity in terms of cliques (i.e., complete subgraphs) plays a crucial role. This result is a natural extension of the well-known result of the consensus control, and provides us with a unified control strategy for various coordination tasks. Numerical examples are given to illustrate the validity of the obtained analysis results.

Adaptive immunity based reinforcement learning

Recently much attention has been paid to intelligent systems which can adapt themselves to dynamic and/or unknown environments by the use of learning methods. However, traditional learning methods have a disadvantage that learning requires enormously long amounts of time with the degree of complexity of systems and environments to be considered. We thus propose a novel reinforcement learning method based on adaptive immunity. Our proposed method can provide a near-optimal solution with less learning time by self-learning using the concept of adaptive immunity. The validity of our method is demonstrated through some simulations with Sutton’s maze problem.

Distributed constraint optimization on networked multi-agent systems

This paper deals with a distributed constraint optimization problem on networked multi-agent systems. First, we propose a distributed algorithm based on the Lagrangian method, where a new update law of the Lagrangian multiplier is designed. This update law enables each agent to estimate the value of the Lagrangian multiplier in a distributed manner. Next, we derive a necessary and sufficient condition that the optimization problem is solvable in a distributed manner over a graph. Finally, we apply the proposed method to power grid control via distributed pricing to maintain the supply-demand balance.