In this paper, we mainly review the topics in consensus and coordination of multi-agent systems, which have received a tremendous surge of interest and progressed rapidly in the past few years. Focusing on different kinds of constraints on the controller and the self-dynamics of each individual agent, as well as the coordination schemes, we categorize the recent results into the following directions: consensus with constraints, event-based consensus, consensus over signed networks, and consensus of heterogeneous agents. We also review some applications of the very well developed consensus algorithms to the topics such as economic dispatch problem in smart grid and k -means clustering algorithms.

Recent Advances in Consensus of Multi-Agent Systems: A Brief Survey

Guidance laws based on a conventional sliding mode ensures only asymptotic convergence. However, convergence to the desired impact angle within a finite time is important in most practical guidance applications. These finite time convergent guidance laws suffer from singularity leading to control saturation. In this paper, guidance laws to intercept targets at a desired impact angle, from any initial heading angle, without exhibiting any singularity, are presented. The desired impact angle, which is defined in terms of a desired line-of-sight angle, is achieved in finite time by selecting the interceptor's lateral acceleration to enforce nonsingular terminal sliding mode on a switching surface designed using nonlinear engagement dynamics. Numerical simulation results are presented to validate the proposed guidance laws for different initial engagement geometries and impact angles. Although the guidance laws are designed for constant speed interceptors, its robustness against the time-varying speed of interceptors is also evaluated through extensive simulation results.

Nonsingular Terminal Sliding Mode Guidance with Impact Angle Constraints

In this paper, sliding-mode-control-based guidance laws to intercept stationary, constant-velocity, and maneuvering targets at a desired impact angle are proposed. The desired impact angle, which is defined in terms of a desired line-of-sight angle, is achieved in finite time by selecting the missile's lateral acceleration to enforce terminal sliding mode on a switching surface designed using nonlinear engagement dynamics. The conditions for capturability are also presented. In addition, by considering a three-degree-of-freedom linear-interceptor dynamic model and by following the procedure used to design a dynamic sliding-mode controller, the interceptor autopilot is designed as a simple static controller to track the lateral acceleration generated by the guidance law. Numerical simulation results are presented to validate the proposed guidance laws and the autopilot design for different initial engagement geometries and impact angles.

Sliding-Mode Guidance and Control for All-Aspect Interceptors with Terminal Angle Constraints

The bipartite consensus problem for a group of homogeneous generic linear agents with input saturation under directed interaction topology is examined. It is established that if each agent is asymptotically null controllable with bounded controls and the interaction topology described by a signed digraph is structurally balanced and contains a spanning tree, then the semi-global bipartite consensus can be achieved for the linear multiagent system by a linear feedback controller with the control gain being designed via the low gain feedback technique. The convergence analysis of the proposed control strategy is performed by means of the Lyapunov method which can also specify the convergence rate. At last, the validity of the theoretical findings is demonstrated by two simulation examples.

On the Bipartite Consensus for Generic Linear Multiagent Systems With Input Saturation

Truncated predictor feedback for linear systems with long time-varying input delays

https://cyberleninka.org/article/n/550948.pdf

Integrated Guidance and Control of Homing Missiles Against Ground Fixed Targets

Low gain feedback has found several applications in constrained control systems, robust control and nonlinear control Low gain feedback refers to a family of stabilizing state feedback gains that are parameterized in a scalar and go to zero as the scalar decreases to zero Such feedback gains can be constructed either by an eigenstructure assignment algorithm or through the solution of a parametric algebraic Riccati equation (ARE) The eigenstructure assignment approach leads to feedback gains in the form of a matrix polynomial in the parameter, while the ARE approach requires the solution of an ARE for each value of the parameter This paper proposes an alternative approach to low gain feedback design based on the solution of a parametric Lyapunov equation Such an approach possesses the advantages of both the eigenstructure assignment approach and the ARE based approach It also avoids the possible numerical stiffness in solving a parametric ARE and the structural decomposition of the open loop system that is required by the eigenstructure assignment approach

A Parametric Lyapunov Equation Approach to the Design of Low Gain Feedback

The author deals with eigenstructure assignment in the second--order linear system q- Aq - Cq = Bu using the proportional - plus - derivative feedback controller. Under the controllability condition of the matrix pair [A B], very simple, general, and complete parametric expressions in direct closed forms for both the closed--loop eigenvector matrix and the feedback gains are established. The approach utilises directly the original system data A, B and C, and involves manipulations on only n - dimensional matrices. Two examples illustrate the effect of the proposed approach.

Complete parametric approach for eigenstructure assignment in a class of second-order linear systems

Fully-actuated second-order systems occur in many applications, such as robotics systems, aircraft systems, mechanical systems etc. Yet what does a fully-actuated system offer? This paper proposes a direct parametric approach which solves the control of a fully-actuated second-order system completely. It is revealed that, with this proposed approach, fully-actuated systems, no matter linear or nonlinear, can actually be turned into a constant linear system with desire eigenstructure by state proportional plus derivative feedback. What is more, in such a realization the approach also provides all the degrees of freedom which may be further utilized to improve the system performance. Direct general complete parametrization of such a controller is proposed based on the solution to a type second-order Sylvester matrix equations, application to a robotic system shows the great convenience of the proposed direct parametric approach.

Direct parametric control of fully-actuated second-order nonlinear systems—The normal case

This paper considers the solution to a class of the second-order Sylvester matrix equation EVF2&#x2212;AVF&#x2212;CV=BW. Under the controllability of the matrix triple (E,A,B), a complete, general, and explicit parametric solution to the second-order Sylvester matrix equation, with the matrix F in a diagonal form, is proposed. The results provide great convenience to the analysis of the solution to the second-order Sylvester matrix equation, and can perform important functions in many analysis and design problems in control systems theory. As a demonstration, an illustrative example is given to show the effectiveness of the proposed solution.

/pdf/on-the-parametric-solution-to-the-second-order-sylvester-3t3c2y68bl.pdf

Duan Guang-ren

Papers

Integrated Guidance and Control of Homing Missiles Against Ground Fixed Targets

A Parametric Lyapunov Equation Approach to the Design of Low Gain Feedback

Complete parametric approach for eigenstructure assignment in a class of second-order linear systems

Direct parametric control of fully-actuated second-order nonlinear systems—The normal case

On the Parametric Solution to the Second-Order Sylvester Matrix Equation EVF2−AVF−CV=BW