Consensusability and Global Optimality of Discrete-Time Linear Multiagent Systems.

The consensusability and global optimality problems are solved for the discrete-time linear multiagent system (MAS) with marginally stable and strictly unstable dynamics. A unified framework is proposed by capturing the maximal disc-guaranteed gain margin (GGM) of the discrete-time linear quadratic regulator (LQR). Sufficient and necessary conditions on consensusability are established. Two bounds of the consensus region are derived only in terms of the unstable eigenvalues of the agent' dynamics. For the single-input MAS, by proving that the radius of the consensus region exactly equals the reciprocal of the Mahler measure of the agent' dynamics, we incidentally reveal the relation between the maximal GGM and the intrinsic entropy rate of the system dynamics for single-input discrete-time linear systems. By employing the inverse optimal control approach, it is proved that the globally optimal consensus is achieved, if and only if the associated Laplacian matrix is a simple matrix and all its nonzero eigenvalues can be radially projected into a specific subset of the consensus region. Moreover, the limitation on the eigenvalues vanishes for the marginally stable MAS. As an application of the global optimality, the minimum-energy-distributed consensus control problem is solved for the marginally stable MAS. Finally, a numerical example is given to demonstrate the effectiveness of the obtained results.

Analysis and design on intervehicle distance control of autonomous vehicle platoons.

This paper presents an intervehicle distance control (IDC) to solve the problem of autonomous vehicle platooning, motivated by future automated highway system (AHS) or smart road which is proposed as intelligent transportation system (ITS) technology. First the velocity and position control of the single vehicle is studied based on internal model compensator. And then the platooning problem on multiple vehicles is solved in the light of multiagent concept. Moreover, the platoon condition is derived for the corresponding scheme. Further we analyze the influence of controller parameters on the whole system, and propose the guidance for parameter design. Finally some simulations are used to verify the effectiveness of the proposed IDC scheme with an analysis on controller parameters.

Data-Based Optimal Control of Multiagent Systems: A Reinforcement Learning Design Approach.

This paper studies an optimal consensus tracking problem of heterogeneous linear multiagent systems. By introducing tracking error dynamics, the optimal tracking problem is reformulated as finding a Nash-equilibrium solution to multiplayer games, which can be done by solving associated coupled Hamilton-Jacobi equations. A data-based error estimator is designed to obtain the data-based control for the multiagent systems. Using the quadratic functional to approximate every agent's value function, we can obtain the optimal cooperative control by the input-output (I/O) Q -learning algorithm with a value iteration technique in the least-square sense. The control law solves the optimal consensus problem for multiagent systems with measured I/O information, and does not rely on the model of multiagent systems. A numerical example is provided to illustrate the effectiveness of the proposed algorithm.

Distributed Optimal Consensus Control for Nonlinear Multiagent System With Unknown Dynamic.

This paper focuses on the distributed optimal cooperative control for continuous-time nonlinear multiagent systems (MASs) with completely unknown dynamics via adaptive dynamic programming (ADP) technology. By introducing predesigned extra compensators, the augmented neighborhood error systems are derived, which successfully circumvents the system knowledge requirement for ADP. It is revealed that the optimal consensus protocols actually work as the solutions of the MAS differential game. Policy iteration algorithm is adopted, and it is theoretically proved that the iterative value function sequence strictly converges to the solution of the coupled Hamilton-Jacobi-Bellman equation. Based on this point, a novel online iterative scheme is proposed, which runs based on the data sampled from the augmented system and the gradient of the value function. Neural networks are employed to implement the algorithm and the weights are updated, in the least-square sense, to the ideal value, which yields approximated optimal consensus protocols. Finally, a numerical example is given to illustrate the effectiveness of the proposed scheme.

Model-free optimal controller design for continuous-time nonlinear systems by adaptive dynamic programming based on a precompensator.

In this paper, we consider the problem of developing a controller for continuous-time nonlinear systems where the equations governing the system are unknown. Using the measurements, two new online schemes are presented for synthesizing a controller without building or assuming a model for the system, by two new implementation schemes based on adaptive dynamic programming (ADP). To circumvent the requirement of the prior knowledge for systems, a precompensator is introduced to construct an augmented system. The corresponding Hamilton-Jacobi-Bellman (HJB) equation is solved by adaptive dynamic programming, which consists of the least-squared technique, neural network approximator and policy iteration (PI) algorithm. The main idea of our method is to sample the information of state, state derivative and input to update the weighs of neural network by least-squared technique. The update process is implemented in the framework of PI. In this paper, two new implementation schemes are presented. Finally, several examples are given to illustrate the effectiveness of our schemes.