In this paper, a new subspace identification approach based on principal component analysis (PCA) and noise estimation is developed for multivariable dynamic process modeling. In contrast to typical subspace identification methods based on standard PCA with instrumental variables, the noise term is first estimated and naturally eliminated in the proposed approach, and then a PCA procedure is used to determine system observability subspace and extract system matrices A, B, C, and D from the estimated observability subspace. For comparison with other typical subspace identification methods based on PCA, numerical simulation and activated sludge process benchmark modeling are included to demonstrate the superiority of the proposed approach and reveal the probable reason for unsatisfied B and D estimations derived by some subspace identification methods based on PCA.
In this paper, the formation control problem has been considered for second-order multiagent system with time delay. The involved controller is divided into two parts. The first part is to design the leader-following and adaptive control strategies that are utilized to achieve the specified formation shape. Based on a potential field function, the second part is applied to realizing the collision avoidance of the agents communicating with each other. By using the Lyapunov theory, some sufficient criteria are derived to ensure the specified formation shape of all agents and collision avoidance of any pair of agents. The derived criteria are formulated in terms of algebraic conditions, in which the control gains play an important role. Finally, a numerical simulation is given to illustrate the effectiveness of the derived results.
This paper studies the synchronization of general linear multi‐agent systems with measurement noises in mean square. It shows that the conventional consensus protocol is efficient and robust to the additive and multiplicative measurement noises in mean square. For the additive measurement noises which are independent of the relative‐states, it shows that the multi‐agent systems can achieve synchronization in practical mean square. For the multiplicative measurement noises which are dependent of the relative‐states, it shows that the multi‐agent systems can achieve synchronization in (strict) mean square. Furthermore, the new consensus protocol is better than the conventional one at some specific situations, i.e., the multi‐agent systems with additive measurement noises can also achieve synchronization in (strict) mean square. Numerical simulations are also provided and the results show highly consistent with the theoretical results.
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