Partial state estimation for linear systems with output and input time delays.

This paper deals with the problem of partial state observer design for linear systems that are subject to time delays in the measured output as well as the control input. By choosing a set of appropriate augmented Lyapunov-Krasovskii functionals with a triple-integral term and using the information of both the delayed output and input, a novel approach to design a minimal-order observer is proposed to guarantee that the observer error is ε-convergent with an exponential rate. Existence conditions of such an observer are derived in terms of matrix inequalities for the cases with time delays in both the output and input and with output delay only. Constructive design algorithms are introduced. Numerical examples are provided to illustrate the design procedure, practicality and effectiveness of the proposed observer.

A new fuzzy ratio and its application to the single input rule modules connected fuzzy inference system

The principle of ratios has been applied to many real world problems, e.g. the part-to-part and part-to-whole ratio formulations. As it is difficult for humans to provide an exact ratio in many real situations, we introduce a fuzzy ratio in this paper. We use some notions from fuzzy arithmetic to analyze fuzzy ratios captured from humans. An application of the formulated fuzzy ratio to a Single Input Rule Modules connected Fuzzy Inference System (SIRMs-FIS) is demonstrated. Instead of using a precise weight, fuzzy sets are employed to represent the relative importance of each rule module. The resulting fuzzy weights are explained as a fuzzy ratio on a weight domain. In addition, a new SIRMs-FIS model with fuzzy weights and part-to-whole fuzzy ratio is devised. A simulated example is presented to clarify the proposed SIRM-FIS model.

Reduced order functional observers with application to partial state estimation of linear systems with input delay

Reduced order multi-functional observer design for multi-input multi-utput (MIMO) linear time-invariant (LTI) systems with constant delayed inputs is studied. This research is useful in the input estimation of LTI systems with actuator delay, as well as system monitoring and fault detection of these systems. Two approaches for designing an asymptotically stable functional observer for the system are proposed: delay-dependent and delay-free. The delay-dependent observer is infinite-dimensional, while the delay-free structure is finite-dimensional. Moreover, since the delay-free observer does not require any information on the time delay, it is more practical in real applications. However, the delay-dependent observer contains less restrictive assumptions and covers more variety of systems. The proposed observer design schemes are novel, simple to implement, and have improved numerical features compared to some of the other available approaches to design (unknown-input) functional observers. In addition, the proposed observers usually possess lower order than ordinary Luenberger observers, and the design schemes do not need the observability or detectability requirements of the system. The necessary and sufficient conditions of the existence of an asymptoticobserver in each scenario are explored. The extensions of the proposed observers to systems with multiple delayed-inputs are also discussed. Several numerical examples and simulation results are employed to support our theories.

Adaptive fuzzy multi-surface sliding control of multiple-input and multiple-output autonomous flight systems

In this study, we proposed an adaptive fuzzy multi-surface sliding control (AFMSSC) for trajectory tracking of 6 degrees of freedom inertia coupled aerial vehicles with multiple inputs and multiple outputs (MIMO). It is shown that an adaptive fuzzy logic-based function approximator can be used to estimate the system uncertainties and an iterative multi-surface sliding control design can be carried out to control flight. Using AFMSSC on MIMO autonomous flight systems creates confluent control that can account for both matched and mismatched uncertainties, system disturbances and excitation in internal dynamics. It is proved that the AFMSSC system guarantees asymptotic output tracking and ultimate uniform boundedness of the tracking error. Simulation results are presented to validate the analysis.

New H∞ control design for polytopic systems with mixed time-varying delays in state and input

This paper concerns with the problem of state-feedback H∞ control design for a class of linear systems with polytopic uncertainties and mixed time-varying delays in state and input. Our approach can be described as follows. We first construct a state-feedback controller based on the idea of parameter-dependent controller design. By constructing a new parameter-dependent Lyapunov-Krasovskii functional (LKF), we then derive new delay-dependent conditions in terms of linear matrix inequalities ensuring the exponential stability of the corresponding closed-loop system with a H∞ disturbance attenuation level. The effectiveness and applicability of the obtained results are demonstrated by practical examples.

A delay-dependent functional observer for linear time-invariant systems with input delay

A delay-dependent functional observer is designed for linear time-invariant (LTI) systems with time-varying input delay. Compared to delay-free observers, delay-dependent functional observers are less conservative and cover more systems. The designed functional observer is with minimum possible order (minimal). Necessary and sufficient conditions of the existence of the observer and asymptomatic stability of it are illustrated. The proposed observer is extended to multiple input delayed systems with time-varying delays. An algorithm is developed for designing of the minimal order observer based on the methodology of this paper. Two numerical examples and simulations are used to support our proposed methodology.

Minimal unknown-input functional observers for multi-input multi-output LTI systems

Designing minimum possible order (minimal) disturbance-decoupled proper functional observers for multi-input multi-output (MIMO) linear time-invariant (LTI) systems is studied. It is not necessary that a minimum-order unknown-input functional observer (UIFO) exists in our proposed design procedure. If the minimum-order observer cannot be attained, the observer's order is increased sequentially through a recursive algorithm, so that the minimal order UIFO can be obtained. To the best of our knowledge, this is the first time that this specific problem is addressed. It is assumed that the system is unknown-input functional detectable, which is the least requirement for the existence of a stable UIFO. This condition also is a certificate for the convergence of our observer's order-increase algorithm. Two methodologies are demonstrated to solve the observer design equations. The second presented scheme, is a new design method that based on our observations has a better numerical performance than the first conventional one. Numerical examples and simulation results in the MATLAB/Simulink environment describe the overall observer design procedure, and highlight the efficacy of our new methodology to solve the observer equations in comparison to the conventional one.

On unknown-input functional observability of linear systems

Finding the least possible order of a stable Unknown-Input Functional Observer (UIFO) has always been a challenge in observer design theory. A practical recursive algorithm is proposed in this technical note to design a minimal multi-functional observer for multi-input multi-output (MIMO) linear time-invariant (LTI) systems with unknown-inputs. The concept of unknown-input functional observability is introduced,and it is used as a certificate of the convergence of our algorithm. The proposed procedure looks for a number of additional auxiliary functions to be augmented to the original functions desired for reconstruction. The resulting UIFO is proper, and minimal (of minimum possible order). Moreover, the algorithm does not need the system to be unknown-input observable. A numerical example shows the procedure as well as the effectiveness of the proposed algorithm.

Linear functional observers with guaranteed ε-convergence for discrete time-delay systems with input/output disturbances

The problem of designing linear functional observers for discrete time-delay systems with unknown-but-bounded disturbances in both the plant and the output is considered for the first time in this paper. A novel approach to design a minimum-order observer is proposed to guarantee that the observer error is ϵ-convergent, which means that the estimate converges robustly within an ϵ-bound of the true state. Conditions for the existence of this observer are first derived. Then, by utilising an extended Lyapunov-Krasovskii functional and the free-weighting matrix technique, a sufficient condition for ϵ-convergence of the observer error system is given. This condition is presented in terms of linear matrix inequalities with two parameters needed to be tuned, so that it can be efficiently solved by incorporating a two-dimensional search method into convex optimisation algorithms to obtain the smallest possible value for ϵ. Three numerical examples, including the well-known single-link flexible joint robotic system, are given to illustrate the feasibility and effectiveness of our results.

Unknown input observer design for one-sided Lipschitz discrete-time systems subject to time-delay

In this paper, we address the problem of unknown input observer design, which simultaneously estimates state and unknown input, of a class of nonlinear discrete-time systems with time-delay. A novel approach to the state estimation problem of nonlinear systems where the nonlinearities satisfy the one-sided Lipschitz and quadratically inner-bounded conditions is proposed. This approach also allows us to reconstruct the unknown inputs of the systems. The nonlinear system is first transformed to a new system which can be decomposed into unknown-input-free and unknown-input-dependent subsystems. The estimation problem is then reduced to designing observer for the unknown-input-free subsystem. Rather than full-order observer design, in this paper, we propose observer design of reduced-order which is more practical and cost effective. By utilizing several mathematical techniques, the time-delay issue as well as the bilinear terms, which often emerge when designing observers for nonlinear discrete-time systems, are handled and less conservative observer synthesis conditions are derived in the linear matrix inequalities form. Two numerical examples are given to show the efficiency and high performance of our results.

Measuring output structures of multinational construction industries using the World Input‒Output Database

In the context of international movement towards trade liberalization, increasing technological progress, open competition and social development have impacted deeply on the construction industry in all economies. Using the World Input–Output Database (WIOD), a multinational comparison of the construction industry is estimated from 1995 to 2011 to provide accurate and valid information on the changing patterns of its output structure. The output coefficients for 37 countries and regions are formulated to allow for inter-industry comparisons and to identify the major components of construction output. Changes of output structure are then elaborated over time across countries and regions. The research findings presented in this paper would provide a framework for identifying the output structure of a nation's construction industry and its change trends at an international level, which may help policymakers and enterprises with the formulation of their future development strategies.

Minimum-order filter design for partial state estimation of linear systems with multiple time-varying state delays and unknown input delays

Designing delay-dependent functional observers for LTI systems with multiple known time-varying state delays and unknown time-varying input delays is studied. The input delays are arbitrary, but the state delays should be upper-bounded. In addition, two scenarios of slow-varying and fast-varying state delays are investigated. The results of the paper can also be considered as one of the first contributions considering unknown-input functional observer design for linear systems with multiple time-varying state delays. Based on the Lyapunov Krasovskii approach, delay-dependent sufficient conditions of the exponential stability of the observer in each scenario are established in terms of linear matrix inequalities. Because of using effective techniques, such as the descriptor transformation and an advanced weighted integral inequality, the proposed stability criteria can result in larger stability regions compared with the other papers that study functional observers for time-varying delay systems. Furthermore, to help with the design procedure, a genetic algorithm-based scheme is proposed to adjust a weighting matrix in the established linear matrix inequalities. Two numerical examples illustrate the design procedure and demonstrate the efficacy of the proposed observer in each scenario.

Quality testing and product rationing by input suppliers

Quality testing by suppliers has significant ramifications for downstream supply chain participants and retail consumers. This article focuses on such implications accounting for the fact that suppliers often enjoy discretion in quality testing and reporting. Under a discretionary testing and reporting environment, we show that a supplier can improve the market's perception of product quality by engaging in self-imposed production cuts. Production cuts dampen supplier incentives to engage in excessive quality testing, putting the supplier and the market on a more equal information footing. This reduces the market's need to skeptically discount product quality to protect itself. The improved market perception, then, reduces quality testing demand, introducing cost savings. The result that costly production cuts can improve quality perceptions indicates that the groundwork for influencing market perceptions may have to be laid upfront, even prior to acquiring private information, providing a contrast to routine signaling models.