observer/Kalman Filter Identification Method Research Articles

National innovation systems and dynamic impact of institutional structures on national innovation capability: A configurational approach with the OKID method

Understanding the national innovation capability involves the consideration of a variety of evolving institutional structures within the national innovation system (NIS). The variety of and interactions among institutional structures requires a systemic and dynamic approach to the NIS. In this respect, a configurational approach generates specific configurational conditions of the institutional structures, and offers a comprehensive and integrated approach to deal with the inherently complex and evolving nature of the NIS. In this research, using the Global Innovation Index (GII) data, we employ a fuzzy model with the Observer Kalman filter identification (OKID) method to develop configurational combinations. Our analysis provides a characterization of the impact of specific institutional structures on national innovation capability, while accounting for time and the innovation level of the countries. By explaining which specific institutional structures impact national innovation capability, this study contributes to the design of the innovation systems with a systemic approach and our understanding of which institutional structures to support innovation.

A Modified Functional Observer-Based EID Estimator for Unknown Continuous-Time Singular Systems

This paper presents the design of a linear quadratic analog tracker (LQAT) based on the observer–Kalman-filter identification (OKID) method and the design of a modified functional observer-based equivalent input disturbance (EID) estimator for unknown square–non-square singular analog systems with unknown input and output disturbances. First, an equivalent mathematical model of the singular analog system is presented to simulate the time response of continuous-time linear singular analog systems to arbitrary inputs via the model conversion method. Then, for the unknown singular analog system, it constructs a linear quadratic analog tracker with state feedback and feed-forward gains based on the off-line OKID method. Furthermore, it extends the design methodology of the EID estimator for strictly proper regular systems with unknown matched–mismatched input and output disturbances to proper regular systems. It is important to mention that the newly developed modified functional observer for proper systems is used to estimate the unknown EID of singular analog systems and that the constraints on the dimensions of unknown disturbances can be eliminated by using the newly proposed EID estimation method. The contributions of this paper can be listed as follows: (1) based on both the OKID method and the discrete-to-continuous model conversion, the simulation of the time responses of the continuous-time linear singular models (which are not feasible using existing MATLAB toolboxes) become feasible; (2) for effective control of the unknown singular analog system, an off-line OKID method is proposed to design an LQAT with state feedback and feed-forward gains; and (3) based on the newly developed modified functional observer for the reduced-order proper regular system, the original EID estimator in the literature is newly extended to estimate the EID from the unknown strictly proper singular analog system, without the original dimensional constraints of the disturbances. It is important to mention that the disturbances of interest can be unknown matched–mismatched input and output disturbances.

A modified functional observer-based EID estimator for unknown sampled-data singular systems

This paper presents both an observer/Kalman filter identification (OKID) method-based linear quadratic digital tracker (LQDT) and a new functional observer-based discrete equivalent input disturbance (EID) estimator, for unknown square/non-square singular sampled-data systems with unknown input and output disturbances. Initially, it is shown that even if the solution of the impulsive mode-free singular linear quadratic tracker problem exists, under some quite general conditions the tracker-based generalised algebraic Riccati equation (GARE) might have no solution. To overcome this issue, an innovative methodology that involves an introduced reduced-order equivalent proper regular model (EPRM) of the singular system is presented, to make the tracker-based GARE solvable for a wide class of servo control problems for a singular system. Furthermore, a new functional observer-based design methodology for the discrete EID estimator of the discrete EPRM is proposed in this paper, for a proper sampled-data system with unknown matched/mismatched input and output disturbances. Finally, a discrete-time EPRM of the unknown singular sampled-data system is constructed using the off-line OKID method and the robust prediction-based state-estimate optimal LQDT, associated with the (plug-in) discrete EID estimator, is developed for the singular sampled-data system.

Modeling and tracker for unknown nonlinear stochastic delay systems with positive input constraints

An approach for universal modeling and tracker design for input-constrained unknown nonlinear input time-delay stochastic sampled-data systems is newly proposed in this paper. First, the improved observer/Kalman filter identification (OKID) method, which uses the current output measurement to estimate the current state, is newly proposed in this paper and it is shown that it outperforms the traditional OKID method. In addition, it is shown that the newly proposed current output-based Kalman filter is a well-performed output estimator in the extreme case, in which it is not a filter anymore, becoming a universal way of formulating an artificial system model of a real physical process without disturbing its normal operation. Consequently, the proposed artificial system model has the following advantages: (i) It is capable of quantifying the stochastic and deterministic characteristics of the dynamical system of interest; (ii) It is capable of carrying out the analyses of various control-design methodologies to achieve the performance specifications in the pre-study phase; and (iii) It is capable of estimating missing and/or abnormal output measurements during the testing and/or practical operating phases. Furthermore, an alternative re-designed current output-based observer is newly proposed in this paper, in order to develop a modified observer-based model predictive control (MPC) with input constraints to improve the performance of the unknown nonlinear time-delay stochastic system. When the proposed artificial system model is used together with the proposed constrained MPC, a long-time prediction of future input–output sets in a closed-loop setting can be carried out. Finally, the operation of a temperature controlled real nonlinear input time-delay blast furnace process is presented as a case study in this paper, to show the effectiveness of the proposed mechanism.

Fault-tolerant tracker for a class of unknown interconnected large-scale sampled-data nonlinear systems with input constraint and actuator failure

Based on the model predictive control (MPC), the soft switching method, and the observer/Kalman filter identification (OKID) method, this paper presents the decentralized fault-tolerant trackers for a class of unknown interconnected large-scale multi-input multi-output sampled-data nonlinear systems with input constraint, actuator failure, and closed-loop decoupling properties. The off-line OKID method is utilized to determine decentralized appropriate (low-) order discrete-time linear models for the class of unknown interconnected large-scale sampled-data systems by using known input–output sampled data. Then, to overcome the effect of modeling error on the identified linear model of each subsystem, an improved observer with the high-gain property based on the digital redesign approach will be presented. So, decentralized multiple MPC controllers are designed beforehand by using the identified linear models. Once a fault is detected in each decentralized controller, one of the backup control configurations in each decentralized subsystem is switched to using the soft switching approach. Thus, the decentralized fault-tolerant control with the closed-loop decoupling property can be achieved through the above approach with a high-gain property decentralized observer/tracker.

Detection of Sensor Faults in Small Helicopter UAVs Using Observer/Kalman Filter Identification

Reliability is a critical issue in navigation of unmanned aerial vehicles (UAVs) since there is no human pilot that can react to any abnormal situation. Due to size and cost limitations, redundant sensor schemes and aeronautical‐grade navigation sensors used in large aircrafts cannot be installed in small UAVs. Therefore, other approaches like analytical redundancy should be used to detect faults in navigation sensors and increase reliability. This paper presents a sensor fault detection and diagnosis system for small autonomous helicopters based on analytical redundancy. Fault detection is accomplished by evaluating any significant change in the behaviour of the vehicle with respect to the fault‐free behaviour, which is estimated by using an observer. The observer is obtained from input‐output experimental data with the Observer/Kalman Filter Identification (OKID) method. The OKID method is able to identify the system and an observer with properties similar to a Kalman filter, directly from input‐output experimental data. Results are similar to the Kalman filter, but, with the proposed method, there is no need to estimate neither system matrices nor sensor and process noise covariance matrices. The system has been tested with real helicopter flight data, and the results compared with other methods.

Observer Kalman filter identification and multiple-model adaptive estimation technique for classifying animal behaviour using wireless sensor networks

The identification of a mathematical model capable of describing the behaviour of animals given input such as feed has great potential for behavioural control purposes. Such models will allow to make predictions which are fundamental to any closed loop control such as control of the feeding. This paper investigates the problem of mathematically modelling animal behaviour. An observer Kalman filter identification method was successfully applied to input–output data and two models representing the hypotheses that animals are actively feeding and the hypotheses that animals are inactive were identified. The input and output of each of the identified models were feed dry matter offer and the pitch angle of the neck, respectively. The pitch angle of the neck of the animal was successfully measured and aggregated by a ZigBee-based wireless sensor network. Two fourth-order models describing the dynamics of an animal in the active and inactive behaviour modes showed good performance in terms of prediction error, cross-correlation between the residual and the output as well as cross-correlation between the residual and the input with 99% confidence interval. A multiple-model adaptive estimation approach was applied to determine the likelihood of each of the two models being the correct model for a specific input of dry matter feed. The average classification success rate was 87.2% for the whole experiment.

Low-order self-tuner for fault-tolerant control of a class of unknown nonlinear stochastic sampled-data systems

Based on the modified state-space self-tuning control (STC) via the observer/Kalman filter identification (OKID) method, an effective low-order tuner for fault-tolerant control of a class of unknown nonlinear stochastic sampled-data systems is proposed in this paper. The OKID method is a time-domain technique that identifies a discrete input–output map by using known input–output sampled data in the general coordinate form, through an extension of the eigensystem realization algorithm (ERA). Then, the above identified model in a general coordinate form is transformed to an observer form to provide a computationally effective initialization for a low-order on-line “auto-regressive moving average process with exogenous (ARMAX) model”-based identification. Furthermore, the proposed approach uses a modified Kalman filter estimate algorithm and the current-output-based observer to repair the drawback of the system multiple failures. Thus, the fault-tolerant control (FTC) performance can be significantly improved. As a result, a low-order state-space self-tuning control (STC) is constructed. Finally, the method is applied for a three-tank system with various faults to demonstrate the effectiveness of the proposed methodology.

Lower-order state-space self-tuning control for a stochastic chaotic hybrid system

In this paper, subject to acceptable closed-loop performance, an effective lower-order tuner for a stochastic chaotic hybrid system is designed using the observer/Kalman filter identification (OKID) method, in which the system state in a general coordinate form is transformed to one in an observer form. The OKID method is a time-domain technique that identifies a discrete input–output map by using known input–output sampled data in the general coordinate form, through an extension of the eigensystem realization algorithm. Moreover, it provides a lower-order realization of the tracker, with computationally effective initialization, for on-line “auto-regressive moving average process with exogenous model” -based identification and a lower-order state-space self-tuning control technique. Finally, the chaotic Chen's system is used as an illustrative example to demonstrate the effectiveness of the proposed methodology.

State-Space Self-Tuning Control for Stochastic Fractional-Order Chaotic Systems

Based on the modified state-space self-tuning control (STC), a novel low-order tuner via the modified observer/Kalman filter identification (OKID) is proposed for stochastic fractional-order chaotic systems. The OKID method is a time-domain technique that identifies a discrete input-output map by using known input-output sampled data in the general coordinate form, through an extension of the eigensystem realization algorithm (ERA). First, the estimated system in the general coordinate based on the conventional OKID method is transformed to the one in an observer form to fit the state-space innovation form for the STC. Then, in stead of the conventional recursive least squares (RLS) identification algorithm used for STC, the Kalman filter as a parameter estimator with the state-space innovation form is presented for effectively estimating the time-varying parameters. Besides, taking the advantage of the digital redesign approach, the derivation of the current-output-based observer is proposed for the modified STC. As a result, the low-order state-space self-tuner with the high-gain controller property is then proposed for stochastic fractional-order chaotic systems, which the fractional operators are well approximated using the standard high integer-order operators. Finally, the fractional-order Chen and Roumlssler systems with stochastic system process and measurement noises are used as illustrative examples to demonstrate the effectiveness of the proposed methodology

Vibration control of piezoelectric smart structures based on system identification technique: Numerical simulation and experimental study

The aim of this study is to investigate the efficiency of a system identification technique known as observer/Kalman filter identification (OKID) technique in the numerical simulation and experimental study of active vibration control of piezoelectric smart structures. Based on the structure responses determined by finite element method, an explicit state space model of the equivalent linear system is developed by employing OKID approach. The linear quadratic Gaussian (LQG) algorithm is employed for controller design. The control law is then incorporated into the ANSYS finite element model to perform closed loop simulations. Therefore, the control law performance can be evaluated in the context of a finite element environment. Furthermore, a complete active vibration control system comprising the cantilever plate, the piezoelectric actuators, the accelerometers and the digital signal processor (DSP) board is set up to conduct the experimental investigation. A state space model characterizing the dynamics of the physical system is developed from experimental results using OKID approach for the purpose of control law design. The controller is then implemented by using a floating point TMS320VC33 DSP. Numerical examples by employing the proposed numerical simulation method, together with the experimental results obtained by using the active vibration control system, have demonstrated the validity and efficiency of OKID method in application of active vibration control of piezoelectric smart structures.