Yingmin Jia

H ∞ consensus control of multi-agent systems with switching topology: a dynamic output feedback protocol

This article is devoted to the consensus control for switching networks of multiple agents with linear coupling dynamics and subject to external disturbances, which is transformed into an H ∞ control problem by defining an appropriate controlled output. On this basis, a distributed dynamic output feedback protocol is proposed with an undetermined system matrix, and a condition in terms of linear matrix inequalities (LMIs) is derived to ensure consensus of the multi-agent system with a prescribed H ∞ level. Furthermore, system matrix of the protocol is designed by solving two LMIs. A numerical example is included to illustrate the effectiveness of the proposed consensus protocol.

Robust control of state delayed systems with polytopic type uncertainties via parameter-dependent Lyapunov functionals

Abstract This paper considers the problem of robust stability and robust stabilization for linear systems with a constant time-delay in the state and subject to real convex polytopic uncertainty. First of all, for robust stability problem, we exploit new matrix inequalities characterization of delay-dependent quadratic stability results, demonstrate that it allows the use of parameter-dependent Lyapunov functionals, and develop control design methods based on linear matrix inequalities (LMIs) for solving the robust control problem. Next, the problem of determining the maximum time-delay under which the system remains stable is cast into a generalized eigenvalue problem and thus solved by LMI techniques. Finally, illustrative examples are given to demonstrate the advantage of these new representations.

Finite-time observers for multi-agent systems without velocity measurements and with input saturations

Abstract This paper is devoted to the distributed finite-time observers for multi-agent systems, where the control inputs are required to be bounded and the velocities are assumed to be not available for feedback. An effective framework through defining a class of coordinated saturation functions is introduced, under which both a first-order finite-time observer and a high-order finite-time observer are constructed. By applying the homogeneous theory for stability analysis, it is proven that all the states of the followers can converge to that of the leader in finite time under our proposed observers. With mild modifications of our control strategies, the foregoing results are then extended to the distributed finite-time containment control problem, where the states of the followers converge to the convex hull spanned by the multiple dynamic leaders. Numerical simulations are presented to demonstrate the efficiency of our methods.

Packet-loss dependent controller design for networked control systems via switched system approach

The stabilization problem of networked control systems with bounded packet loss is addressed. We model such networked control systems as a class of switched systems, and present sufficient conditions for the stabilization by using a packet-loss dependent Lyapunov function. Moreover, different from existing results, we propose the design for packet-loss dependent stabilizing controllers for two types of packet-loss processes: one is a arbitrary packet-loss process, and the other is a Markovian packet-loss process. Several numerical examples and simulations are worked out to demonstrate the effectiveness of the proposed design technique.

Delay-dependent H ∞ control for LPV systems with time delays

In this paper, the delay-dependent Hinfin control problem is considered for linear parameter-varying (LPV) systems with time-varying delays. By using new Lyapunov-Krasovskii functionals, some sufficient conditions on Hinfin performance analysis are given in terms of linear matrix inequalities (LMIs). Based on these conditions the state-feedback controller and the dynamical output-feedback controller are designed. A numerical example is included to illustrate the proposed method.

LPV Control With Decoupling Performance of 4WS Vehicles Under Velocity-Varying Motion

In this paper, a new control strategy with robustness for four-wheel steering vehicles is proposed, which has the decoupling performance while vehicles are steering with varying velocity. To get velocity-varying model, it is considered for the first time, that longitudinal velocity as a state and output is decoupled with lateral velocity and yaw rate while the driving force is taken as the control input in the longitudinal subsystem. Based on this completed decoupling result, the subsystem with lateral velocity and yaw rate as states is transferred into a typical linear-parameter varying (LPV) system for the first time, where varying parameters are longitudinal velocity and its functions. Then to this LPV system, lateral velocity and yaw rate are decoupled into lower triangular structure with steering angles using a suitable distribution coefficient of total longitudinal force while the cornering stiffness coefficients are considered as uncertain parameters. To improve the robustness of the above decoupled system, a new LPV controller is designed at last. In this new control strategy, feedback signals are longitudinal velocity, the yaw rate and lateral velocity. However, lateral velocity need not be designed the observer or measured precisely. Simulation results show that, even though with a large velocity-varying range, the handling characteristics, safety and comfort of the vehicle driving are improved significantly.

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.

H2 control of discrete-time periodic systems with Markovian jumps and multiplicative noise

This paper addresses the problem of optimal and robust H2 control for discrete-time periodic systems with Markov jump parameters and multiplicative noise. To analyse the system performance in the presence of exogenous random disturbance, an H2 norm is firstly established on the basis of Gramian matrices. Further, under the condition of exact observability, a necessary and sufficient condition is presented for the solvability of H2 optimal control problem by means of a generalised Riccati equation. When the transition probabilities of jump parameter are incompletely measurable, an H2-guaranteed cost norm is exploited and the robust H2 controller is designed through a linear matrix inequality (LMI) optimisation approach. An example of a networked control system is supplied to illustrate the proposed results.

Robust strict positive real stabilization criteria for SISO uncertain systems

Abstract This paper is devoted to the study of robust strict positive real stabilization criteria for SISO uncertain systems, i.e., considering the problem of when a single controller not only robustly stabilizes a plant with uncertainty under unity-feedback but also enables the closed-loop system to be robustly strictly positive real. The uncertain system models with both parameter variation and unstructured perturbation are considered and some necessary and sufficient conditions for the problem are derived.

Robust H∞ control for spacecraft formation flying with coupled translational and rotation dynamics

In this paper, the problem on robust H∞ control for 6-DOF spacecraft formation flying in the presence of parameter uncertainties and external disturbances is addressed. Firstly, the model of coupled translation and rotation motion of spacecraft formation is established. Subsequently, a robust H∞ controller is proposed, which is constructed by the solution to the Hamilton-Jacobi-Inequality (HJI). It is proved that the 6-DOF coupled system is asymptotically stable and robust in respect to parameter uncertainties, and the H∞ norm between external disturbances and regulated output is ensured to be no more than a prescribed attenuation level. Since it is hard to solve the HJI analytically, a modified θ-D method is proposed, which is an effective approach to find an approximate solution to the HJI. It is illustrated that the modified θ-D method is feasible and convenient to implement onboard in the practical situation. Finally, numerical simulations are performed to demonstrate the effectiveness of the robust H∞ controller based on the modified θ-D method.