LMI‐based adaptive output feedback fault‐tolerant controller design for nonlinear systems

This paper presents 2‐novel linear matrix inequality (LMI)‐based adaptive output feedback fault‐tolerant control strategies for the class of nonlinear Lipschitz systems in the presence of bounded matched or mismatched disturbances and simultaneous occurrence of actuator faults, including failure, loss of effectiveness, and stuck. The constructive algorithms based on LMI with creatively using Lyapunov stability theory and without the need for an explicit information about mode of actuator faults or fault detection and isolation mechanism are developed for online tuning of adaptive and fixed output‐feedback gains to stabilize the closed‐loop control system asymptotically. The proposed controllers guarantee to compensate actuator faults effects and to attenuate disturbance effects. The resulting control methods have simpler structure, as compared with most existing recent methods and more suitable for practical systems. The merits of the proposed fault‐tolerant control scheme have been verified by the simulation on nonlinear Boeing 747 lateral motion dynamic model subjected to actuator faults.     

Variational inequality in classical plasticity. Applications to Armstrong–Frederick elasto-plastic model

In this paper the quasi-static initial and boundary value problem for an elasto-plastic mixed hardening material is reformulated within the constitutive framework of small strains. The plastic factor plays the basic role in describing the rate independent evolution equations for the plastic strain and hardening variables. The plastic factor is equivalently represented as the solution of an appropriate local inequality involving the yield function. The main idea was to introduce the variational inequality at any time $t$ to be solved for the velocity field and the complementary plastic factor. There is the plastic factor in a strain-driven process. The solution procedure proposed here to solve the initial and boundary value problem is based on the solutions of the variational inequality at time $t$, coupled with an update algorithm in order to evaluate the current state of the material for an incremental deformation process. This time the return mapping algorithm is avoided as the values of the plastic factor and the velocity are known at time $t.$ As we developed a procedure to simultaneously solve the equilibrium equation coupled with the rate-independent evolution equations, no necessity to compute the algorithmic elasto-plastic tangent moduli occurs. The numerical simulations are done for the mixed hardening elasto-plastic model involving Armstrong–Frederick kinematic hardening. To validate the proposed numerical algorithms, we compare the solutions based on the variational inequality and those based on return mapping algorithm, computed for the same Prager kinematic hardening law.     

Semirigid inclusions in elastic bodies: Mechanical interplay and optimal control

The paper concerns an analysis of an equilibrium problem for 2D elastic body with two semirigid inclusions. It is assumed that inclusions have a joint point, and we investigate a junction problem for these inclusions. The existence of solutions is proved, and different equivalent formulations of the problem are proposed. We investigate a convergence to infinity of a rigidity parameter of the semirigid inclusion. It is proved that in the limit, we obtain an equilibrium problem for the elastic body with a rigid inclusion and a semirigid one. A parameter identification problem is investigated. In particular, the existence of a solution to a suitable optimal control problem is proved.     

Optimal lot-sizing policy for a manufacturer with defective items in a supply chain with up-stream and down-stream trade credits

In this paper, we establish an economic production quantity model for a manufacturer (or wholesaler) with defective items when its supplier offers an up-stream trade credit M while it in turn provides its buyers (or retailers) a down-stream trade credit N. The proposed model is in a general framework that includes numerous previous models as special cases. In contrast to the traditional differential calculus approach, we use a simple-to-understand and easy-to-apply arithmetic–geometric inequality method to find the optimal solution. Furthermore, we provide some theoretical results to characterize the optimal solution. Finally, several numerical examples are presented to illustrate the proposed model and the optimal solution.     

The Generalized Jackknife Statistic

This paper shows how tabulated exact factors for prediction intervals for all k future observations, under the assumption of normality, readily provide conservative factors for some values of k beyond the range of the tabulations.     

Robust disturbance rejection in modified repetitive control system

This study concerns disturbance rejection for a modified repetitive control system (MRCS) that contains a strictly proper plant with time-varying uncertainties. Since an MRCS is affected by both periodic and aperiodic disturbances, and since the disturbances are often unknown, an equivalent-input-disturbance (EID)-based estimator was added to an MRCS to yield an EID-based MRCS that compensates for all types of disturbances. In this system, the repetitive controller ensures tracking of a periodic reference input, and the incorporation of an EID estimate into the control input enables rejection of unknown periodic and aperiodic disturbances. A robust stability condition for the MRCS was established in the form of a linear matrix inequality, and the condition was used to design the parameters of the controller. This design method handles uncertainties and enables the preferential adjustment of the tracking and control performance of the MRCS. Simulation results demonstrate the validity of the method.     

New stability and stabilization conditions for nonlinear systems with time-varying delay based on delay-partitioning approach

This paper focuses on stability analysis and stabilization of nonlinear systems with interval time-varying delay, modeled by Takagi-Sugeno (T-S) fuzzy approach. To achieve more relaxation in the feasibility region, delay-partitioning approach is used for all integral terms in the Lyapunov-Krasovskii functional (LKF). A fuzzy Lyapunov function is proposed instead of non-integral term in LKF, and moreover, some slack matrices variables are offered to enlarge the design space. By doing this, new delay-dependent stability criteria are obtained. During the derivation of stability conditions, Jensen’s integral inequality is applied to deal with integral terms. Furthermore, in this paper the problem of controller design via the parallel distributed compensation (PDC) scheme is studied. Stability and stabilization conditions with less conservative are achieved in terms of linear matrix inequality (LMI). Finally, two numerical examples are presented to show the effectiveness of the proposed results.     

A new approach to static output feedback stabilization of linear dynamic systems

The topic of this study is output feedback control of linear control system with output. Use of condensed forms of the linear system under static output feedback (SOF) control is made to derive sufficient conditions for stabilization. A minimal-order control-free observer is presented.     

The effects of government subsidies on decentralised reverse supply chains

This paper examines the impacts of exogenous government subsidies on recycled material flows in decentralised reverse supply chains where players behave according to their own interests. We present a four-tiered network equilibrium model consisting of the sources of electronic scrap products and the collectors, processors and demand markets. We mathematically transform the players’ optimality conditions governing players’ behaviours into a variational inequality formulation. We investigate the impact of alternate schemes of government subsidies on the equilibrium amount, subsidy effectiveness and subsidy elasticity. The real-world case study shows that subsidising the tier of processors demonstrates the superiority of the investigated performance measures.