Algebraic criteria for consensus problems of continuous-time networked systems

This article addresses algebraic criteria for consensus problems of continuous-time networked systems with fixed and switching topology. A special eigenvector ω of the Laplacian matrix is first constructed and correlated with the connectivity of digraph. And then, some necessary and/or sufficient algebraic conditions are presented by employing the vector ω, which can directly determine whether the consensus problem can be solved. More importantly, for the switching topology case, the obtained algebraic conditions for the average consensus problem are necessary and sufficient. Furthermore, the presented results clearly show that only the agents corresponding to the positive elements of ω contribute to the group decision value and decide the collective behaviour of the system. Particularly for the fixed topology case, the role of each agent is exactly measured by the value of the corresponding element of ω. Based on these results, some extended protocols are further proposed to solve the average consensus problem, in which the interaction digraphs are not needed to be balanced. Numerical examples are included to illustrate the obtained results.     

Conditions for the equivalence between IQC and graph separation stability results

This paper provides a link between time-domain and frequency-domain stability results in the literature. Specifically, we focus on the comparison between stability results for a feedback interconnection of two nonlinear systems stated in terms of frequency-domain conditions. While the integral quadratic constrain (IQC) theorem can cope with them via a homotopy argument for the Lurye problem, graph separation results require the transformation of the frequency-domain conditions into truncated time-domain conditions. To date, much of the literature focuses on ‘hard’ factorisations of the multiplier, considering only one of the two frequency-domain conditions. Here it is shown that a symmetric, ‘doubly-hard’ factorisation is required to convert both frequency-domain conditions into truncated time-domain conditions. By using the appropriate factorisation, a novel comparison between the results obtained by IQC and separation theories is then provided. As a result, we identify under what conditions the IQC theorem may provide some advantage.     

An augmented model for robust stability analysis of time-varying delay systems

Stability analysis of linear systems with time-varying delay is investigated. In order to highlight the relations between the variation of the delay and the states, redundant equations are introduced to construct a new modelling of the delay system. New types of Lyapunov–Krasovskii functionals are then proposed allowing to reduce the conservatism of the stability criterion. Delay-dependent stability conditions are then formulated in terms of linear matrix inequalities. Finally, several examples show the effectiveness of the proposed methodology.     

Leader-following consensus of high-order multi-agent linear systems with bounded transmission channels

The leader-following consensus of high-order multi-agent linear systems with bounded transmission channels is considered. Agents modelled as LTI dynamics exchange information according to a network which can be described as a graph with agents as its vertices and information transmission channels as its edges. The transmission channels are bounded. The objective is leader-following in the sense that the state of all agents should converge to that of the leader vehicle. Detailed analysis of the leader-following consensus under bounded transmission channels is investigated for both fixed and switching network topologies.     

An improved fuzzy Kalman filter for state estimation of non-linear systems

The extended fuzzy Kalman filter (EFKF) of non-linear systems which can deal with fuzzy uncertainty effectively has been developed recently. But it seems to be inapplicable to the cases where the states change abruptly or there exist model mismatches in non-linear systems. Therefore, based on the EFKF, a new concept of the improved fuzzy Kalman filter (IFKF) is proposed in this article. Due to the introduction of the extension orthogonality principle given as a criterion to design the new algorithm, the IFKF can track the abrupt changes of the states and has definite robustness against the model mismatches. Finally, computer simulations with a MIMO non-linear model are presented, which illustrate that the proposed IFKF has the strong tracking ability and robustness against the model mismatches.     

A fuzzy record-to-record travel algorithm for solving rough set attribute reduction

Attribute reduction can be defined as the process of determining a minimal subset of attributes from an original set of attributes. This paper proposes a new attribute reduction method that is based on a record-to-record travel algorithm for solving rough set attribute reduction problems. This algorithm has a solitary parameter called the DEVIATION, which plays a pivotal role in controlling the acceptance of the worse solutions, after it becomes pre-tuned. In this paper, we focus on a fuzzy-based record-to-record travel algorithm for attribute reduction (FuzzyRRTAR). This algorithm employs an intelligent fuzzy logic controller mechanism to control the value of DEVIATION, which is dynamically changed throughout the search process. The proposed method was tested on standard benchmark data sets. The results show that FuzzyRRTAR is efficient in solving attribute reduction problems when compared with other meta-heuristic approaches.     

Optimal control of LQG problem with an explicit trade-off between mean and variance

For discrete-time linear-quadratic Gaussian (LQG) control problems, a utility function on the expectation and the variance of the conventional performance index is considered. The utility function is viewed as an overall objective of the system and can perform the optimal trade-off between the mean and the variance of performance index. The nonlinear utility function is first converted into an auxiliary parameters optimisation problem about the expectation and the variance. Then an optimal closed-loop feedback controller for the nonseparable mean–variance minimisation problem is designed by nonlinear mathematical programming. Finally, simulation results are given to verify the algorithm's effectiveness obtained in this article.     

Limit cycles induced in type-1 linear systems with PID-type of relay feedback

This article investigates the limit cycles within type-1 linear systems under PID-type of relay feedback. The problem is generalised from the identification of friction models of servo mechanical systems via limit-cycle experiments under dual-channel relay feedback. Locations of limit cycles are given so that the exact durations between two consecutive switchings of relays can be determined via numerical computation. After this, local stability of limit cycles can be checked via the Jacobian of Poincaré map. Examples are analysed using proposed theorems.     

Mixed time- and frequency-domain robust eigenstructure assignment

This paper considers robust eigenstructure assignment for multivariable systems. The time-domain performance specifications provided by eigenstructure assignment and robust performance specifications in the frequency domain considered by H infinity control are combined to realize joint optimal robust control design. A parametric expression for state-feedback eigenstructure assignment is introduced on the basis of a set of free parameters. The mixed performance index used as the cost function consists of two parts: robustness in the frequency domain; and system eigenstructure constraints in the time domain. The analytical gradient calculation of the cost function with respect to the free parameters is derived for optimal robust eigenstructure assignment using gradientbased optimization. The mixed time- and frequency-domain robust eigenstructure assignment is demonstrated in the design of a mode-decoupled roll-yaw autopilot.