Derivative-free Nonlinear Kalman Filter Research Articles

Flatness-based disturbance observer for condition monitoring of marine power generation units

The article proposes a flatness-based disturbance observer for condition monitoring of the integrated power generation system, which comprises a marine turbine and a synchronous generator. It is proven that this power generation system is differentially flat, thus it can be transformed into an input–output linearized form and into the canonical Brunovsky form. For the linearized state-space description of the system, state estimation can be performed with the use of Kalman Filtering (derivative-free nonlinear Kalman filter). Moreover, by re-designing the Kalman filter as a disturbance observer, it becomes possible to estimate disturbances, model uncertainty terms and fault-induced perturbations that affect the power unit. Consequently, model inconsistencies and faulty conditions in the functioning of the marine power unit can be diagnosed.

A robust damping controller for DFIG based on variable-gain sliding mode and Kalman filter disturbance observer

This paper proposes a sliding mode based inter-area oscillation damping control strategy for the Doubly Fed Induction Generator (DFIG) to enhance the stability of interconnected power systems. The synthesized damping controller is designed based on the variable-gain super-twisting algorithm to deal with the inherent nonlinear behavior in the DFIG and the power system. A Derivative-free nonlinear Kalman Filter is also developed as a disturbance estimator to accurately estimate the disturbance terms in the represented system. Such estimated results make the gains of super-twisting algorithm more efficient. The proposed controller is insensitive to the presence of unmolded system dynamics and the external disturbances acting on the system, and has a fast response speed and robustness with respect to the power system uncertainties. The stability property of the proposed damping controller is proved via the Lyapunov method, and its performance has been verified through numerical simulations considering detailed system model, external disturbances and operation point uncertainty.

Forecasting of Power Corporations’ Default Probability With Nonlinear Kalman Filtering

This paper proposes a systematic method for forecasting default probabilities for financial firms with particular interest in electric power corporations. According to the credit risk theory, a company's closeness to default is determined by the distance of its assets’ value from its debts. The assets’ value depends primarily on the company's market (option) value through a complex nonlinear relation. By forecasting with accuracy the enterprize's option value, it becomes also possible to estimate the future value of the enterprize's asset value and the associated probability of default. This paper proposes a systematic method for forecasting the probability to default for companies (option/asset value forecasting methods) using a new nonlinear Kalman filtering method under the name derivative-free nonlinear Kalman filter. The firm's option value is considered to be described by the Black–Scholes nonlinear partial differential equation (PDE). Using a differential flatness theory, the PDE is transformed into an equivalent state-space model in the so-called canonical form. Using the latter model and by redesigning the derivative-free nonlinear Kalman filter as a m -step-ahead predictor, estimates are obtained of the company's future option values. By forecasting the company's market (option) values, it becomes also possible to forecast the associated asset value and volatility, and finally, to estimate the company's future default risk.

AUV Control and Navigation with Differential Flatness Theory and Derivative-Free Nonlinear Kalman Filtering

The problem of control and navigation for autonomous underwater vessels (AUVs) is solved using differential flatness theory and the Derivative-free nonlinear Kalman Filter. First, differential flatness is proven for the 6-DOF dynamic model of the AUV. This allows for transforming the AUV model into the linear canonical (Brunovsky) form and for designing a state feedback controller. Uncertainty about the parameters of the AUV’s dynamic model, as well external perturbations which affect its motion are issues that have to be taken into account in the controller’s design. To compensate for model imprecision and disturbance terms, it is proposed to use a disturbance observer which is based on the Derivative-free nonlinear Kalman Filter. The considered filtering method consists of the standard Kalman Filter recursion applied on the linearized model of the vessel and of an inverse transformation based on differential flatness theory, which enables to obtain estimates of the state variables of the initial nonlinear model of the vessel. With the use of the the Kalman Filter-based disturbance observer, simultaneous estimation of the non-measurable state variables of the AUV and of the perturbation terms that affect its dynamics is achieved. Moreover, after estimating such disturbances, their compensation is also succeeded. Simulation experiments are performed to confirm the efficiency of the proposed AUV control and estimation scheme.

Control of DC–DC Converter and DC Motor Dynamics Using Differential Flatness Theory

The article proposes a method for nonlinear control of the dynamical system that is formed by a DC–DC converter and a DC motor, making use of differential flatness theory. First it is proven that the aforementioned system is differentially flat which means that all its state vector elements and its control inputs can be expressed as differential functions of primary state variables which are defined to be the system’s flat outputs. By exploiting the differential flatness properties of the model its transformation to a linearized canonical (Brunovsky) form becomes possible. For the latter description of the system one can design a stabilizing feedback controller. Moreover, estimation of the nonmeasurable state vector elements of the system is achieved by applying a new nonlinear Filtering method which is known as Derivative-free nonlinear Kalman Filter. This filter consists of the Kalman Filter recursion applied on the linearized equivalent model of the system and of an inverse transformation that is based on differential flatness theory and which enables to obtain estimates of the initial nonlinear state-space model. Moreover, to compensate for parametric uncertainties and external perturbations the filter is redesigned as a disturbance observer. By estimating the perturbation inputs that affect the joint model of the DC–DC converter and of the DC motor their compensation becomes possible. The efficiency of the proposed control scheme is further confirmed through simulation experiments.

Non-linear feedback control of the p53 protein-mdm2 inhibitor system using the derivative-free non-linear Kalman filter.

It is proven that the model of the p53-mdm2 protein synthesis loop is a differentially flat one and using a diffeomorphism (change of state variables) that is proposed by differential flatness theory it is shown that the protein synthesis model can be transformed into the canonical (Brunovsky) form. This enables the design of a feedback control law that maintains the concentration of the p53 protein at the desirable levels. To estimate the non-measurable elements of the state vector describing the p53-mdm2 system dynamics, the derivative-free non-linear Kalman filter is used. Moreover, to compensate for modelling uncertainties and external disturbances that affect the p53-mdm2 system, the derivative-free non-linear Kalman filter is re-designed as a disturbance observer. The derivative-free non-linear Kalman filter consists of the Kalman filter recursion applied on the linearised equivalent of the protein synthesis model together with an inverse transformation based on differential flatness theory that enables to retrieve estimates for the state variables of the initial non-linear model. The proposed non-linear feedback control and perturbations compensation method for the p53-mdm2 system can result in more efficient chemotherapy schemes where the infusion of medication will be better administered.

Control of Three-Phase Voltage Source Converters with the Derivative-Free Nonlinear Kalman Filter

The paper is concerned with proving differential flatness of the three-phase voltage source converter (VSC) model and its resulting description in the Brunovsky (canonical) form. For the linearized canonical model of the converter a feedback controller is designed. At a second stage, a novel Kalman Filtering method (Derivative-free nonlinear Kalman Filtering) is introduced. The proposed Kalman Filter is redesigned as disturbance observer for estimating additive input disturbances to the VSC model. These estimated disturbance terms are finally used by a feedback controller that enables the DC output voltage track desirable setpoints. The efficiency of the proposed state estimation-based control scheme is tested through simulation experiments.

Control and disturbances compensation in underactuated robotic systems using the derivative-free nonlinear Kalman filter

SUMMARYThe Derivative-free nonlinear Kalman Filter is used for developing a robust controller which can be applied to underactuated MIMO robotic systems. The control problem for underactuated robots is non-trivial and becomes further complicated if the robot is subjected to model uncertainties and external disturbances. Using differential flatness theory it is shown that the model of a closed-chain 2-DOF robotic manipulator can be transformed to linear canonical form. For the linearized equivalent of the robotic system it is shown that a state feedback controller can be designed. Since certain elements of the state vector of the linearized system cannot be measured directly, it is proposed to estimate them with the use of a novel filtering method, the so-called Derivative-free nonlinear Kalman Filter. Moreover, by redesigning the Kalman Filter as a disturbance observer, it is shown that one can estimate simultaneously external disturbance terms that affect the robotic model or disturbance terms which are associated with parametric uncertainty. The efficiency of the proposed Kalman Filter-based control scheme is tested in the case of a 2-DOF planar robotic manipulator that has the structure of a closed-chain mechanism.

Control and Disturbances Compensation for Doubly Fed Induction Generators Using the Derivative-Free Nonlinear Kalman Filter

The paper studies differential flatness properties and an input–output linearization procedure for doubly fed induction generators (DFIGs). By defining flat outputs which are associated with the rotor's turn angle and the magnetic flux of the stator, an equivalent DFIG description in the Brunovksy (canonical) form is obtained. For the linearized canonical model of the generator, a feedback controller is designed. Moreover, a comparison of the differential flatness theory-based control method against Lie algebra-based control is provided. At the second stage, a novel Kalman Filtering method (Derivative-free nonlinear Kalman Filtering) is introduced. The proposed Kalman Filter is redesigned as disturbance observer for estimating additive input disturbances to the DFIG model. These estimated disturbance terms are finally used by a feedback controller that enables the generator's state variables to track desirable setpoints. The efficiency of the proposed state estimation-based control scheme is tested through simulation experiments.

Decentralised control of parallel inverters connected to microgrid using the derivative‐free non‐linear Kalman filter

Decentralised control for parallel inverters connected to the power grid is developed using differential flatness theory and the derivative-free nonlinear Kalman filter. It is proven that the model of the inverters, is a differentially flat one. This means that all its state variables and the control inputs can be written as differential functions of a single algebraic variable which is the flat output. By exploiting differential flatness properties it is shown that the multiple inverters model can be transformed into a set of local inverter models which are decoupled and linearized. For each local inverter the design of a state feedback controller becomes possible. Such a controller processes measurements not only coming from the individual inverter but also coming from other inverters which are connected to the grid. Moreover, to estimate the non-measurable state variables of each local inverter, the derivative-free nonlinear Kalman filter is used. Furthermore, by redesigning the aforementioned filter as a disturbance observer it becomes also possible to estimate and compensate for disturbance terms that affect each local inverter.

Distributed Control of Unmanned Surface Vessels Using the Derivative-free Nonlinear Kalman Filter

Intelligence and autonomy is becoming a prerequisite for maritime transportation systems. In this paper a distributed control problem for unmanned surface vessels (USVs) is formulated as follows: there are N USVs which pursue another vessel (moving target). Each USV can be equipped with various sensors, such as IMU, cameras and non-imaging sensors such as sonar, radar and thermal signature sensors. At each time instant each USV can obtain measurements of the target’s cartesian coordinates. Additionally, each USV is aware of the target’s distance from a reference monitoring station (coastal or satellite monitoring units). The objective is to make the USVs converge in a synchronized manner towards the target, while avoiding collisions between them and avoiding collisions with obstacles in their motion plane. A distributed control law is developed for the USVs which enables not only convergence of the USVs to the goal position, but also makes possible to maintain the cohesion of the multi-USV system. Moreover, distributed filtering is performed, so as to obtain an estimate of the target vessel’s state vector. This provides the desirable state vector to be tracked by each one of the USVs. To this end, a new distributed nonlinear filtering method of improved accuracy and computation speed is introduced. This filtering approach, under the name Derivative-free distributed nonlinear Kalman filter is based on differential flatness theory and on an exact linearization of the target vessel’s dynamic/kinematic model. The performance of the proposed distributed filtering scheme is compared against the Extended and the Unscented Information filter.

Input–Output Linearizing Control of the Underactuated Hovercraft Using the Derivative-Free Nonlinear Kalman Filter

The paper proposes a nonlinear control approach for the underactuated hovercraft model based on differential flatness theory and uses a new nonlinear state vector and disturbances estimation method under the name of derivative-free nonlinear Kalman filter. It is proven that the nonlinear model of the hovercraft is a differentially flat one. It is shown that this model cannot be subjected to static feedback linearization, however it admits dynamic feedback linearization which means that the system's state vector is extended by including as additional state variables the control inputs and their derivatives. Next, using the differential flatness properties it is also proven that this model can be subjected to input–output linearization and can be transformed to an equivalent canonical (Brunovsky) form. Based on this latter description the design of a state feedback controller is carried out enabling accurate maneuvering and trajectory tracking. Additional problems that are solved in the design of this feedback control scheme are the estimation of the nonmeasurable state variables in the hovercraft's model and the compensation of modeling uncertainties and external perturbations affecting the vessel. To this end, the application of the derivative-free nonlinear Kalman filter is proposed. This nonlinear filter consists of the Kalman Filter's recursion on the linearized equivalent model of the vessel and of an inverse nonlinear transformation based on the differential flatness features of the system which enables to compute estimates for the state variables of the initial nonlinear model. The redesign of the filter as a disturbance observer makes possible the estimation and compensation of additive perturbation terms affecting the hovercraft's model. The efficiency of the proposed nonlinear control and state estimation scheme is confirmed through simulation experiments.

SYNCHRONIZATION OF CIRCADIAN OSCILLATORS AND PROTEIN SYNTHESIS CONTROL USING THE DERIVATIVE-FREE NONLINEAR KALMAN FILTER

The paper proposes a new method for synchronization of coupled circadian cells and for nonlinear control of the associated protein synthesis process using differential flatness theory and the derivative-free nonlinear Kalman filter. By proving that the dynamic model of the FRQ protein synthesis is a differentially flat one, its transformation to the linear canonical (Brunovsky) form becomes possible. For the transformed model, one can find a state feedback control input that makes the oscillatory characteristics in the concentration of the FRQ protein vary according to desirable setpoints. To estimate nonmeasurable elements of the state vector, the derivative-free nonlinear Kalman filter is used. The derivative-free nonlinear Kalman filter consists of the standard Kalman filter recursion on the linearized equivalent model of the coupled circadian cells and on computation of state and disturbance estimates using the diffeomorphism (relations about state variables transformation) provided by differential flatness theory. Moreover, to cope with parametric uncertainties in the model of the FRQ protein synthesis and with stochastic disturbances in measurements, the derivative-free nonlinear Kalman filter is redesigned in the form of a disturbance observer. The efficiency of the proposed Kalman filter-based control scheme is tested through simulation experiments.

A chaotic communication system of improved performance based on the Derivative-free nonlinear Kalman filter

The Derivative-free nonlinear Kalman Filter is used for developing a communication system that is based on a chaotic modulator such as the Duffing system. In the transmitter’s side, the source of information undergoes modulation (encryption) in which a chaotic signal generated by the Duffing system is the carrier. The modulated signal is transmitted through a communication channel and at the receiver’s side demodulation takes place, after exploiting the estimation provided about the state vector of the chaotic oscillator by the Derivative-free nonlinear Kalman Filter. Evaluation tests confirm that the proposed filtering method has improved performance over the Extended Kalman Filter and reduces significantly the rate of transmission errors. Moreover, it is shown that the proposed Derivative-free nonlinear Kalman Filter can work within a dual Kalman Filtering scheme, for performing simultaneously transmitter–receiver synchronisation and estimation of unknown coefficients of the communication channel.

Sensorless Control of Distributed Power Generators With the Derivative-Free Nonlinear Kalman Filter

A control method for distributed interconnected power generation units is developed. The power system comprises permanent-magnet synchronous generators (PMSGs), which are connected to each other through transformers and tie-lines. A derivative-free nonlinear Kalman filtering approach is introduced aiming at implementing sensorless control of the distributed power generators. In the proposed derivative-free Kalman filtering method, the generator's model is first subjected to a linearization transformation that is based on differential flatness theory and next state estimation is performed by applying the standard Kalman filter recursion to the linearized model. Unlike Lie algebra-based estimator design methods, the proposed approach provides estimates of the state vector of the PMSG without the need for derivatives and Jacobian calculation. Moreover, by redesigning the proposed derivative-free nonlinear Kalman filter as a disturbance observer, it is possible to estimate at the same time the nonmeasurable elements of each generator's state vector, the unknown input power (torque), and the disturbance terms induced by interarea oscillations. The efficient real-time estimation of the aggregate disturbance that affects each local generator makes possible to introduce a counterdisturbance control term, thus maintaining the power system on its nominal operating conditions.

Detection of parametric changes in the Peyrard-Bishop- Dauxois model of DNA using nonlinear Kalman filtering

The derivative-free nonlinear Kalman filter is proposed for state estimation and fault diagnosis in distributed parameter systems of the wave-type and particularly in the Peyrard-Bishop-Dauxois model of DNA dynamics. At a first stage, a nonlinear filtering approach is introduced for estimating the dynamics of the Peyrard-Bishop-Dauxois 1D nonlinear wave equation, through the processing of a small number of measurements. It is shown that the numerical solution of the associated partial differential equation results in a set of nonlinear ordinary differential equations. With the application of a diffeomorphism that is based on differential flatness theory it is shown that an equivalent description of the system is obtained in the linear canonical (Brunovsky) form. This transformation enables to obtain local estimates about the state vector of the DNA model through the application us of the standard Kalman filter recursion. At a second stage, the local statistical approach to fault diagnosis is used to perform fault diagnosis for this distributed parameter system by processing with statistical tools the differences (residuals) between the output of the Kalman filter and the measurements obtained from the distributed parameter system. Optimal selection of the fault threshold is succeeded by using the local statistical approach to fault diagnosis. The efficiency of the proposed filtering approach in the problem of fault diagnosis for parametric change detection, in nonlinear wave-type models of DNA dynamics, is confirmed through simulation experiments.

Robust control of valves in ship diesel engines with the use of the Derivative-free nonlinear Kalman filter

This article studies robust nonlinear control for gas exchange valves in ship diesel engines, with the use of the derivative-free nonlinear Kalman filter. Robust control of gas exchange valves is important for improving the efficiency in the operation of diesel engines. Due to the relatively wide range of typical internal combustion engine operating conditions imposed on a variable valve timing actuator, the control scheme must compensate for model uncertainties, parametric variations and rapid external disturbances. By applying differential flatness theory, the initial nonlinear model of the system is transformed into the linear canonical (Brunovsky) form. For the latter model, it is possible to design a state feedback controller that enables accurate tracking of the valve’s reference setpoints. To estimate the non-measurable state variables of the model and the unknown external disturbances, the derivative-free nonlinear Kalman filter is used as a disturbance observer. The derivative-free nonlinear Kalman filter consists of the standard Kalman filter recursion on the linearized equivalent model of the valve and of computation of state and disturbance estimates using the diffeomorphism (relations about state variables’ transformation) provided by differential flatness theory. Evaluation tests are performed for assessing the performance of the proposed control scheme.

Estimation of wave-type dynamics in neurons' membrane with the use of the Derivative-free nonlinear Kalman Filter

The paper analyzes wave-type partial differential equations that describe the transmission of neural signals and proposes filtering for estimating the spatiotemporal variations of voltage in the neurons' membrane. It is shown that in specific neuron models the spatiotemporal variations of the membrane's voltage follow partial differential equations (PDEs) of the wave type while in other models such variations are associated with the propagation of solitary waves in the membrane. To compute the dynamics of the membrane PDE model without knowledge of initial conditions and through the processing of noisy measurements, a new filtering method, under the name Derivative-free nonlinear Kalman Filtering, is proposed. The PDE of the membrane is decomposed into a set of nonlinear ordinary differential equations with respect to time. Next, each one of the local models associated with the ordinary differential equations is transformed into a model of the linear canonical (Brunovsky) form through a change of coordinates (diffeomorphism) which is based on differential flatness theory. This transformation provides an extended model of the nonlinear dynamics of the membrane for which state estimation is possible by applying the standard Kalman Filter recursion. The proposed filtering method is tested through numerical simulation tests.

Nonlinear Kalman Filters and Particle Filters for integrated navigation of unmanned aerial vehicles

The paper studies and compares nonlinear Kalman Filtering methods and Particle Filtering methods for estimating the state vector of Unmanned Aerial Vehicles (UAVs) through the fusion of sensor measurements. Next, the paper proposes the use of the estimated state vector in a control loop for autonomous navigation and trajectory tracking by the UAVs. The proposed nonlinear controller is derived according to the flatness-based control theory. The estimation of the UAV’s state vector is carried out with the use of (i) Extended Kalman Filtering (EKF), (ii) Sigma-Point Kalman Filtering (SPKF), (iii) Particle Filtering (PF), and (iv) a new nonlinear estimation method which is the Derivative-free nonlinear Kalman Filtering (DKF). The performance of the nonlinear control loop which is based on these nonlinear state estimation methods is evaluated through simulation tests. Comparing the aforementioned filtering methods in terms of estimation accuracy and computation speed, it is shown that the Sigma-Point Kalman Filtering is a reliable and computationally efficient approach to state estimation-based control, while Particle Filtering is well-suited to accommodate non-Gaussian measurements. Moreover, it is shown that the Derivative-free nonlinear Kalman Filter is faster than the rest of the nonlinear filters while also succeeding accurate, in terms of variance, state estimates.

Derivative-Free Nonlinear Kalman Filtering for MIMO Dynamical Systems: Application to Multi-DOF Robotic Manipulators

The paper proposes derivative-free nonlinear Kalman Filtering for MIMO nonlinear dynamical systems. The considered nonlinear filtering scheme which is based on differential flatness theory extends the class of systems to which Kalman Filtering can be applied without the need for calculation of Jacobian matrices. To deduce if a dynamical system is differentially flat, the following should be examined: (i) the existence of the flat output, which is a variable that can be written as a function of the system's state variables (ii) the system's state variables and the input can be written as functions of the flat output and its derivatives. Nonlinear systems satisfying the differential flatness property can be written in the Brunovsky form via a transformation of their state variables and control inputs. After transforming the nonlinear system to the canonical form it is straightforward to apply the standard Kalman Filter recursion. The performance of the proposed derivative-free nonlinear filtering scheme is tested through simulation experiments on benchmark nonlinear multi-input multi-output dynamical systems, such as robotic manipulators.