Simultaneous Estimation of Innovation Variance and States in a Dynamic System

International audience

The combination of the automatic control theory courses, simulation verification and practical implementation of the designed controller algorithms in real-time conditions is very important for training of the control engineers.This contribution present structure and usage of Self-tuning Controllers Simulink Library (STCSL) for real time control.The STCSL was created for design, simulation verification and especially realtime implementation of single input -single output (SISO) digital self-tuning controllers.The proposed adaptive controllers, which are included in the library, can be divided into three groups (PID controllers, controllers based on the polynomial approach and the controllers derived on the other approaches (minimum variance etc.).This Library is very successfully used in Adaptive Control Course in education practice for design and verification of self-tuning control systems in simulation and real-time conditions.It is suitable also for design and verification of industrial digital controllers.The highly nonlinear laboratory model, the DR300 Speed Control with Variable Load, has been chosen as example for real-time control.

State estimation is an important topic in the study of dynamical systems. The problem of estimation can be structured into three categories: 1 centralised scheme; 2 decentralised scheme; 3 distributed scheme. Distributed estimation is a compromise between completely centralised and decentralised versions of estimation. In this paper, we will provide an assessment of distributed estimation based on Kalman filtering techniques for large-scale or sensor networks. In simulation, a second order dynamical system is employed in a scenario of ten sensor nodes. The sensor nodes attempt to estimate the states of the dynamical system with embedded consensus filters. The results show that the distributed estimation algorithm effectively approximates the central Kalman filter. It is concluded that the distributed estimation techniques for distributed dynamical system requires further extensive research.

Guest Editorial: Situational awareness of integrated energy systems

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.

In this paper, the set-membership state and parameter estimation problems are considered for linear time-varying systems. The noises in the system are unknown but bounded and the variation of parameters is considered as a bounded expansion. The entire estimator is an interactive estimation of parameters and states. In parameter estimation, the exact set of parameter estimates may be non-convex because of the uncertain states. A polytopic linear parameter varying (LPV) enclosure of the system regression expression is constructed as a convex relaxation. The result of parameter estimation is a set to include the true parameter of the model. Meanwhile, in the state estimation, a similar LPV enclosure of the state-space model is also used to bound the state matrix uncertainties. This LPV enclosure in the state estimation is narrowed by the parameter estimation, and then the set of state estimates is computed to include the true state. The constrained zonotope (CZ) is used to describe sets of interest and the necessary set operations are expanded to LPV mapping. Because of the highly adjustable accuracy of CZ, the proposed algorithm can make a better trade-off between computational accuracy and efficiency. Finally, a numerical example is given to illustrate the effectiveness of the proposed algorithm.

A kernel functional representation of linear time-varying systems is employed in conjunction with B-spline functional approximation techniques to construct non-asymptotic state and parameter estimators for LTV systems. Total observability of the estimated system must be assumed. Practical identifiability conditions for parametric estimation are also stated. In the absence of output measurement noise the observer provides almost exact reconstruction of the system state and delivers high fidelity functional estimates of the time varying system parameters. It also shares the usual superior features of algebraic observers such as independence of the initial conditions of the system and good noise attenuation properties. Other advantages of the kernel and B-spline based identification of linear time-varying systems are elucidated.

For nonlinear discrete systems with dual unknown inputs, there are many limitations regarding previous nonlinear filters. This paper proposes two new, improved square-root cubature Kalman filtering (ISRCKF) algorithms to estimate system states and dual unknown inputs. Improved square-root cubature Kalman filtering 1 (ISRCKF1) introduces an innovation that first obtains the unknown input estimates from the measurement equation, then updates the innovation to derive the unknown input estimates from the state equation, then uses the already obtained estimates of the dual unknown inputs to correct the one-step estimate of the state, and finally the minimum variance unbiased estimate of the state is obtained. Improved square-root cubature Kalman filtering 2 (ISRCKF2) builds a unified innovation feedback model, then applies the minimum variance unbiased estimation (MVUE) criterion to obtain the estimates of system states and dual unknown inputs, refining a more concise recursive filter but requiring stronger assumptions. Finally, simulation results demonstrate that the above two algorithms can achieve the optimal estimates of system states and dual unknown inputs simultaneously, and ISRCKF2 further enhances the accuracy of both state and dual unknown inputs estimation, which verifies the validity of the proposed algorithms.

Adaptive disturbance rejection neural output feedback control of hydraulic manipulator systems

The work conducted in this thesis is a part of an EU Horizon 2020 research initiative project known as DigiArt. This part of the DigiArt project presents and explores the design, formulation and implementation of probabilistically orientated state estimation algorithms with focus towards unmanned system positioning and three-dimensional (3D) mapping. State estimation algorithms are considered an influential aspect of any dynamic system with autonomous capabilities. Possessing the ability to predictively estimate future conditions enables effective decision making and anticipating any possible changes in the environment. Initial experimental procedures utilised a wireless ultra-wide band (UWB) based communication network. This system functioned through statically situated beacon nodes used to localise a dynamically operating node. The simultaneous deployment of this UWB network, an unmanned system and a Robotic Total Station (RTS) with active and remote tracking features enabled the characterisation of the range measurement errors associated with the UWB network. These range error metrics were then integrated into an Range based Extended Kalman Filter (R-EKF) state estimation algorithm with active outlier identification to outperform the native approach used by the UWB system for two-dimensional (2D) pose estimation.The study was then expanded to focus on state estimation in 3D, where a Six Degreeof-Freedom EKF (6DOF-EKF) was designed using Light Detection and Ranging (LiDAR) as its primary observation source. A two step method was proposed which extracted information between consecutive LiDAR scans. Firstly, motion estimation concerning Cartesian states x, y and the unmanned system’s heading (ψ) was achieved through a 2D feature matching process. Secondly, the extraction and alignment of ground planes from the LiDAR scan enabled motion extraction for Cartesian position z and attitude angles roll (θ) and pitch (φ). Results showed that the ground plane alignment failed when two scans were at 10.5◦ offset. Therefore, to overcome this limitation an Error State Kalman Filter (ES-KF) was formulated and deployed as a sub-system within the 6DOF-EKF. This enabled the successful tracking of roll, pitch and the calculation of z. The 6DOF-EKF was seen to outperform the R-EKF and the native UWB approach, as it was much more stable, produced less noise in its position estimations and provided 3D pose estimation.

Efficient Spectral-Chaos Methods for Uncertainty Quantification in Long-Time Response of Stochastic Dynamical Systems

Smart grid is built by combination of electric and information technologies and achieves the two-way interaction between power utilization and power generation. Unfortunately, new security threats appears together with cyber-physical communication systems. In order to properly monitor power network, an effective cyber attack detection and state estimation method are required to know attack and system states. This article considers the problem of robust grid state estimation and suggests a technique for distributed state estimation in power networks. First, the distribution power system incorporating multiple synchronous generators is modeled as a state-space framework, where attack occurs in measurements. Basically, the false data injection attacks can interfere with state estimation process by tampering with sensor measurements. Using mean squared error principle, the distributed dynamic state estimation algorithm is designed where local and neighboring gains are obtained using optimal filter and graph theory. For local gain computation, the attack parameter is obtained using the Bayesian learning process. The convergence condition of the proposed approach is derived. Extensive simulation results show that the proposed approach is able to estimate the system state within a short period of time. Hopefully, the proposed methodology can be used to tolerate the cyber attacks for improving the confidence of the grid state estimation process.

This paper presents a new approach to dynamic system state estimation under bounded noises via the Evidential Reasoning(£K) rule. This method regards the dynamic system equations and the actual observations of the system states as two information sources. The random set description of evidence and the extension principle of random set are used to recursively generate state evidence and observation evidence respectively from the two information sources and to propagate them in system equations. At each time step, the ER rule is used to fuse the two pieces of evidence in observation domain and then the fused result is transformed to state domain by the extension principles. Pignistic expectation of the fused result is calculated as state estimation value. Compared with the estimation method using interval analysis and evidence theory given by Nassreddine, the proposed approach makes estimation results more accurate by using fusion mechanism of the ER rule considering weight and reliability of evidence. The method is shown to have better performances in an application to liquid level estimation of industrial level apparatus than does the Nassreddine's method.

This paper presents a technique for failure detection and diagnosis (FDD) for on-board vehicle applications. Failures are represented by abrupt changes in the characteristic parameters of a system that occur at random instants of time. This representation facilitates the formulation of the FDD problem as a combined state and parameter estimation problem of a system with uncertain parameters. This non-linear estimation problem is solved using a Bayesian approach and implementing a suboptimal filter. The performance of the FDD system is demonstrated in simulations of an active suspension subjected to sensor failures. In the simulations, the system diagnosed failures correctly within .05 seconds from their occurrence.

In some real practical and industrial applications, output signal sampling and input signal updating are performed with different rates because of technological constraints. Thus, a large number of existing systems are dual-rate or multi-rate. Identifying parameters of such systems is of great importance. In this paper, we identify parameters of a dual-rate observable canonical system. Since parameters and system states are not known simultaneously, Kalman filter and least squares error method are combined. Parameters are identified with least squares error method and states are estimated using Kalman filter. In this paper, two different algorithms are proposed. In the first algorithm, interpolation is employed to calculate output at instants which are not accessible. In the second algorithm, an auxiliary model is used to obtain output. Finally, in a simulation, parameters of a system are estimated using these algorithms and their results are compared.