A new set of orthogonal functions and its application to the analysis of dynamic systems

The present work proposes a complementary pair of orthogonal triangular function (TF) sets derived from the well-known block pulse function (BPF) set. The operational matrices for integration in TF domain have been computed and their relation with the BPF domain integral operational matrix is shown. It has been established with illustration that the TF domain technique is more accurate than the BPF domain technique as far as integration is concerned, and it provides with a piecewise linear solution.As a further study, the newly proposed sets have been applied to the analysis of dynamic systems to prove the fact that it introduces less mean integral squared error (MISE) than the staircase solution obtained from BPF domain analysis, without any extra computational burden. Finally, a detailed study of the representational error has been made to estimate the upper bound of the MISE for the TF approximation of a function f(t) of Lebesgue measure.     

Numerical solutions of optimal control for linear time-varying systems with delays via hybrid functions

By applying hybrid functions of general block-pulse functions and Legendre polynomials, the linear-quadratic problem of linear time-varying systems with delays are transformed into the optimization problem of multivariate functions. The approximate solutions of the optimal control and state as well as the optimal value of the objective functional are derived. The numerical examples illustrate that the algorithms are valid.     

Parameter fault detection and estimation of a class of nonlinear systems using observers

The focus of this paper is on the detection and estimation of parameter faults in nonlinear systems with nonlinear fault distribution functions. The novelty of this contribution is that it handles the nonlinear fault distribution function; since such a fault distribution function depends not only on the inputs and outputs of the system but also on unmeasured states, it causes additional complexity in fault estimation. The proposed detection and estimation tool is based on the adaptive observer technique. Under the Lipschitz condition, a fault detection observer and adaptive diagnosis observer are proposed. Then, relaxation of the Lipschitz requirement is proposed and the necessary modification to the diagnostic tool is presented. Finally, the example of a one-wheel model with lumped friction is presented to illustrate the applicability of the proposed diagnosis method.     

Dissipativity analysis and synthesis of a class of nonlinear systems with time-varying delays

In this paper, new results are established for the delay-independent and delay-dependent problems of dissipative analysis and state-feedback synthesis for a class of nonlinear systems with time-varying delays with polytopic uncertainties. This class consists of linear time-delay systems subject to nonlinear cone-bounded perturbations. Both delay-independent and delay-dependent dissipativity criteria are established as linear matrix inequality-based feasibility tests. The developed results in this paper for the nominal system encompass available results on H_∞ approach, passivity and positive realness for time-delay systems as special cases. All the sufficient stability conditions are cast. Robust dissipativity as well as dissipative state-feedback synthesis results are also derived. Numerical examples are provided to illustrate the theoretical developments.     

一类具有动态领导者和时滞的多主体系统的一致性

研究了一类具有动态领导者并且存在时变耦合时滞的多主体系统的一致性问题．在所考虑的模型中,领导者的速度不能被精确量测．为了跟踪这样一个领导者主体,将对每个跟随者主体构造分散式状态估计器以及设计基于邻居的控制器;同时,由于耦合时滞的存在,基于邻居的控制器和状态估计器均包含了时变时滞的作用．当多主体系统的耦合拓扑是固定的或切换的有向图时,跟随者与领导者之间的跟踪误差得到了估计．特别地,可以证明,当动态领导者的速度可以被精确量测时,每一个跟随者都能够跟踪上领导者．