Robust graph coloring based on the matrix semi-tensor product with application to examination timetabling

This paper investigates the robust graph coloring problem with application to a kind of examination timetabling by using the matrix semi-tensor product, and presents a number of new results and algorithms. First, using the matrix semi-tensor product, the robust graph coloring is expressed into a kind of optimization problem taking in an algebraic form of matrices, based on which an algorithm is designed to find all the most robust coloring schemes for any simple graph. Second, an equivalent problem of robust graph coloring is studied, and a necessary and sufficient condition is proposed, from which a new algorithm to find all the most robust coloring schemes is established. Third, a kind of examination timetabling is discussed by using the obtained results, and a method to design a practicable timetabling scheme is presented. Finally, the effectiveness of the results/algorithms presented in this paper is shown by two illustrative examples.

PARALLEL SIMULTANEOUS STABILIZATION OF A SET OF PORT-CONTROLLED HAMILTONIAN SYSTEMS SUBJECT TO ACTUATOR SATURATION

This paper investigates parallel simultaneous stabilization （PSS） of a set of multi-input nonlinear Port-Controlled Hamiltonian （PCH） systems subject to actuator saturation （AS）, and proposes a number of results on the design of PSS controllers for the PCH systems with AS. Firstly, the case of two PCH systems with AS is studied. Exploring the special property of the saturation nonlinearity and the structural properties of dissipative Hamiltonian system, the two systems are combined to generate an augmented PCH system, with which some results on the control design are then obtained. When there are external disturbances in the two systems, a robust PSS controller is designed for the systems. Secondly, the case of more than two PCH systems with AS is investigated, and several new results are proposed for the PSS problem. Finally, two illustrative examples are presented to show that the stabilization controllers obtained in this paper work very well.

On estimation of attraction domain for port-controlled Hamiltonian systems subject to actuator saturation

This paper investigates the estimation of domain of attraction for nonlinear port controlled Hamiltonian （PCH） systems with actuator saturation （AS）. Several conditions are established under which an ellipsoid is contractively invariant, and thus can be employed to find the biggest ellipsoid contained in the domain of attraction. It is shown that the proposed conditions can be expressed in the form of the linear matrix inequalities （LMIs） optimization problem with constraints. Study of an illustrative example shows that the proposed method works very well in estimating the domain of attraction for some classes of nonlinear PCH systems with AS.

H_(∞)output feedback control for large-scale nonlinear systems with time delay in both state and input

The H_(∞)output feedback control problem for a class of large-scale nonlinear systems with time delay in both state and input is considered in this paper.It is assumed that the interconnected nonlinearities are limited by constant multiplied by unmeasured states,delayed states and external disturbances.Different from existing methods to study the H_(∞)control of large-scale nonlinear systems,the static gain control technique is utilized to obtain an observer-based output feedback control strategy,which makes the closed-loop system globally asymptotically stable and attenuates the effect of external disturbances.An example is finally carried out to show the feasibility of the proposed control strategy.