Proposed Observer Design Research Articles

Virtual Sensor: Simultaneous State and Input Estimation for Nonlinear Interconnected Ground Vehicle System Dynamics.

This paper proposes a new observer approach used to simultaneously estimate both vehicle lateral and longitudinal nonlinear dynamics, as well as their unknown inputs. Based on cascade observers, this robust virtual sensor is able to more precisely estimate not only the vehicle state but also human driver external inputs and road attributes, including acceleration and brake pedal forces, steering torque, and road curvature. To overcome the observability and the interconnection issues related to the vehicle dynamics coupling characteristics, tire effort nonlinearities, and the tire-ground contact behavior during braking and acceleration, the linear-parameter-varying (LPV) interconnected unknown inputs observer (UIO) framework was used. This interconnection scheme of the proposed observer allows us to reduce the level of numerical complexity and conservatism. To deal with the nonlinearities related to the unmeasurable real-time variation in the vehicle longitudinal speed and tire slip velocities in front and rear wheels, the Takagi-Sugeno (T-S) fuzzy form was undertaken for the observer design. The input-to-state stability (ISS) of the estimation errors was exploited using Lyapunov stability arguments to allow for more relaxation and an additional robustness guarantee with respect to the disturbance term of unmeasurable nonlinearities. For the design of the LPV interconnected UIO, sufficient conditions of the ISS property were formulated as an optimization problem in terms of linear matrix inequalities (LMIs), which can be effectively solved with numerical solvers. Extensive experiments were carried out under various driving test scenarios, both in interactive simulations performed with the well-known Sherpa dynamic driving simulator, and then using the LAMIH Twingo vehicle prototype, in order to highlight the effectiveness and the validity of the proposed observer design.

Fractional-Order Sliding-Mode Observers for the Estimation of State-of-Charge and State-of-Health of Lithium Batteries

Lithium batteries are widely used in power storage and new energy vehicles due to their high energy density and long cycle life. The accurate and real-time estimation for the state-of-charge (SoC) and the state-of-health (SoH) of lithium batteries is of great significance to improve battery life, reliability, and utilization efficiency. In this paper, three cascaded fractional-order sliding-mode observers (FOSMOs) are designed for the estimation of SoC by observing the terminal voltage, the polarization voltage, and the open-circuit voltage of a lithium cell, respectively. Furthermore, to calculate the value of the SoH, two FOSMOs are developed to estimate the capacity and internal resistance of the lithium cell. The control signals of the observers are continuous by utilizing fractional-order sliding manifolds without low-pass filters. Compared with the existing sliding-mode observers for SoC and SoH, weaker chattering, faster response, and higher estimation accuracy are obtained in the proposed method. Finally, the experiment tests demonstrate the validity and feasibility of the proposed observer design method.

Clustering-based average state observer design for large-scale network systems

This paper addresses the aggregated monitoring problem for large-scale network systems with a few dedicated sensors. Full state estimation of such systems is often infeasible due to unobservability and/or computational infeasibility; therefore, through clustering and aggregation, a tractable representation of a network system, called a projected network system, is obtained for designing a minimum-order average state observer. This observer estimates the average states of the clusters, which are identified under explicit consideration of estimation error. Moreover, given the clustering, the proposed observer design algorithm exploits the structure of the estimation error dynamics to achieve computational tractability. Simulations show that the computation of the proposed algorithm is significantly faster than the usual H2/H∞ observer design techniques. On the other hand, compromise on the estimation error characteristics is shown to be marginal.

Observer-based controller for VTOL-UAVs tracking using direct Vision-Aided Inertial Navigation measurements

This paper proposes a novel observer-based controller for Vertical Take-Off and Landing (VTOL) Unmanned Aerial Vehicle (UAV) designed to directly receive measurements from a Vision-Aided Inertial Navigation System (VA-INS) and produce the required thrust and rotational torque inputs. The VA-INS is composed of a vision unit (monocular or stereo camera) and a typical low-cost 6-axis Inertial Measurement Unit (IMU) equipped with an accelerometer and a gyroscope. A major benefit of this approach is its applicability for environments where the Global Positioning System (GPS) is inaccessible. The proposed VTOL-UAV observer utilizes IMU and feature measurements to accurately estimate attitude (orientation), gyroscope bias, position, and linear velocity. Ability to use VA-INS measurements directly makes the proposed observer design more computationally efficient as it obviates the need for attitude and position reconstruction. Once the motion components are estimated, the observer-based controller is used to control the VTOL-UAV attitude, angular velocity, position, and linear velocity guiding the vehicle along the desired trajectory in six degrees of freedom (6 DoF). The closed-loop estimation and the control errors of the observer-based controller are proven to be exponentially stable starting from almost any initial condition. To achieve global and unique VTOL-UAV representation in 6 DoF, the proposed approach is posed on the Lie Group and the design in unit-quaternion is presented. Although the proposed approach is described in a continuous form, the discrete version is provided and tested.

Robust observer design for LPV systems using Kronecker sum and direct searching

This paper addresses a robust Luenberger observer for an uncertain linear parameter varying (LPV) system based on the concepts of direct searching, Kronecker sum, and small gain theorem. An algorithm is proposed to investigate the situation of the different parts of the initial observer design space, in terms of suitability for being selected as the observer gain or needing elimination due to being an undesirable part. To find the undesirable parts of the design space, the singularity of the Kronecker sum matrix of the estimation error is checked by employing the small gain theorem concept. By excluding undesired parts from the entire design space and checking the remaining parts’ feasibility, a suitable solution can be found, appropriately. The performance of the proposed observer design method is illustrated by using numerical examples and an electric ground vehicle (EGV) system for the estimation of the vehicle sideslip angle and the yaw rate. The results prove the appropriateness of the designed observer using the proposed approach.

Detectability Conditions and State Estimation for Linear Time-Varying and Nonlinear Systems

This work proposes a detectability condition for linear time-varying systems based on the exponential dichotomy spectrum. The condition guarantees the existence of an observer, whose gain is determined only by the unstable modes of the system. This allows for an observer design with low computational complexity compared to classical estimation approaches. An extension of this observer design to a class of nonlinear systems is proposed and local convergence of the corresponding estimation error dynamics is proven. Numerical results show the efficacy of the proposed observer design technique.

On high-gain observer design for nonlinear systems with delayed output measurements

In this paper, we propose a high-gain observer design for nonlinear systems with time-varying delayed output measurements. Based on a recent high-gain like observer design method, called HG/LMI observer, a larger bound of the time-delay is allowed compared to that obtained by using the standard high-gain methodology. Such a HG/LMI observer adopts a lower value of the tuning parameter, which results in the reduction of the value of the observer gain, and an increase in the maximum bound of the delay required to ensure exponential convergence. Indeed, an explicit relation between the maximum bound of the delay and the observer tuning parameter is derived by using a Lyapunov–Krasovskii functional jointly with the Halanay inequality. Such a relation shows clearly the superiority of HG/LMI observer design methodology. An application to nonlinear systems with sampled measurements is provided. Furthermore, the proposed methodology is extended to systems with nonlinear outputs. This extension provides more general synthesis conditions and encompasses the linear case as a particular situation. Finally, two numerical examples are proposed to illustrate the performance of the proposed observer design procedure, and comparison to standard approaches is also provided.

Decentralized Fuzzy Observer Design for Discrete-Time Nonlinear Interconnected Systems with Parametric Uncertainties

This paper presents the decentralized fuzzy observer design technique for discrete-time nonlinear interconnected systems, which are assumed to be composed of fuzzy subsystems with parametric uncertainties and unknown interconnections. To design the decentralized fuzzy observer, the estimation error dynamics is obtained, and the decentralized observer design problem is defined. Based on the observation performance function, the decentralized fuzzy observer design method is proposed to minimize the interconnection bound to attenuation degree ratio. The proposed technique is formulated into linear matrix inequalities with minimization problem. Finally, simulation example shows the validity of the proposed observer design technique.

A Contribution in the Observer Design for a Class of Bilinear Singular Delayed Systems

This paper proposes a functional observer for a bilinear singular systems with constant time delay present in both state and known input vectors. The considered system has transformed to an updated form in order to estimate both a state vector and an unknown inputs functional vector independently from the considered time delay. The necessary conditions for the existence of the functional observer are formulated. The proposed observer design procedure is based on the Lyapunov–Krasovskii theory. Numerical example is given to prove the new approach.

Observer Design in LTI Time-Delay Systems using Partial Pole Placement with Applications

In order to estimate the state of a dynamical system, we address the problem of designing an observer for linear time-invariant (LTI) dynamical systems including a time-delay. Sufficient conditions for the existence of the proposed observer are given using partial placement of the poles for the error. Namely, we exploit the multiplicity-induced-dominance property of the characteristic function corresponding to the system's error. The effectiveness of the proposed observer design is shown in both state lag and input lag respectively through the problems of Mach number control in a wind tunnel and stabilization of the inverted pendulum on a cart by using the delay.

Fault-Tolerant Quantized Sliding Mode Observers Design for a Class of Takagi-Sugeno Fuzzy System With Unmeasurable Premise Variable

This article addresses the state and fault estimation problems for a class of quantized Takagi–Sugeno (T-S) fuzzy systems with sensor and actuator faults. Two types of observer design methods are developed for two different network transmission environments. In the first case, the signal quantization effect is only considered on the channel between sensor and controller, and a sliding mode observer is designed, which can reconstruct the actuator faults. In the second case, the quantization effects are considered in both the sensor-controller side and the controller-actuator side, which is more difficult to be dealt with compared to the first case, and the sliding mode observer method cannot be effective now since the discontinuous term is difficult to be designed. A descriptor reduced-order observer is presented to solve this problem, where the jumping behavior that resulted from the signal quantization is considered in the observer, which is novel and effective to compensate the quantization effects. Finally, simulation examples of rigid-body satellite attitude control T-S fuzzy system are presented to verify the effectiveness of the proposed observer design approaches.

State Estimation for a Class of Linear Systems with Quadratic Output

This paper deals with the problem of state estimation for a class of linear time-invariant systems with quadratic output measurements. An immersion-type approach is presented that transforms the system into a state-affine system by adding a finite number of states to the original system. Under suitable persistence of excitation conditions on the input and its higher derivatives, global state estimation is exhibited by means of a Kalman-type observer. A numerical example is provided to illustrate the applicability of the proposed observer design for the problem of position and velocity estimation for a vehicle navigating in the n— dimensional Euclidean space using a single position range measurement.

ℓ2–ℓ∞ proportional–integral observer design for systems with mixed time‐delays under round–robin protocol

AbstractIn this article, the design problem of ℓ2–ℓ∞ proportional–integral observer (PIO) is investigated for a class of discrete‐time systems with mixed time‐delays. The mixed time‐delays comprise both the discrete time‐varying delays and infinitely distributed delays. The round–robin protocol (RRP) is employed to schedule the data transmissions from the sensors to the observer so as to mitigate the communication burden and prevent the data collisions. A novel PIO is developed whose observer gain is dependent on the data transmission order as a reflection of the effects induced by the RRP scheduling. By resorting to the token‐dependent Lyapunov functional and the matrix inequality technique, the desired PIO is designed with exponentially stable error dynamics of the state estimation and guaranteed ℓ2–ℓ∞ disturbance attenuation/resistance capacity. Finally, a simulation example is exploited to verify the validity of the proposed observer design method.

Design of tracking observers for locally jointly observable systems

This paper considers distributed state estimation of continuous-time linear system monitored by a network of multiple sensors. Each sensor can only access locally partial measurement output of the system and effectively communicates with its neighbors to cooperatively achieve the asymptotic estimation of the target full system state. For a constructive design, we shall incorporate the concept of system immersions and propose a class of distributed tracking observers for the problem under a reasonable condition of the locally joint observability. Moreover, as a direct application of the proposed observer design, we further present an interesting leader-following consensus design for multi-agent system.

Finite-Time State Estimation for an Inverted Pendulum under Input-Multiplicative Uncertainty

A sliding mode observer is presented, which is rigorously proven to achieve finite-time state estimation of a dual-parallel underactuated (i.e., single-input multi-output) cart inverted pendulum system in the presence of parametric uncertainty. A salient feature of the proposed sliding mode observer design is that a rigorous analysis is provided, which proves finite-time estimation of the complete system state in the presence of input-multiplicative parametric uncertainty. The performance of the proposed observer design is demonstrated through numerical case studies using both sliding mode control (SMC)- and linear quadratic regulator (LQR)-based closed-loop control systems. The main contribution presented here is the rigorous analysis of the finite-time state estimator under input-multiplicative parametric uncertainty in addition to a comparative numerical study that quantifies the performance improvement that is achieved by formally incorporating the proposed compensator for input-multiplicative parametric uncertainty in the observer. In summary, our results show performance improvements when applied to both SMC- and LQR-based control systems, with results that include a reduction in the root-mean square error of up to 39% in translational regulation control and a reduction of up to 29% in pendulum angular control.

측정 잡음을 고려한 1기 무한모선 시스템의 고장 판별을 위한 DQN 기반 외란 관측기 설계

Increasing demand on electric power supply results in a need of an intelligent method for fast detection of various failures in the power system. This paper presents a reinforcement learning-based disturbance observer (DOB) design for the determination and protection against a line fault occurred in the single-machine infinite bus (SMIB) power system. Whilst a high gain disturbance observer could estimate the system states and the external disturbance successfully, the high gain of the observer can cause problems in the presence of the measurement noise. When measurement noise exists in the output, fault detection methods based on the estimated states may often result in false alarms. To solve the problem, this paper designs an adaptive DOB using Deep Q-Network (DQN) which is one of reinforcement learning algorithms. For the proposed observer design, this paper explains the definitions of the state, the action, and the reward for the reinforcement learning. Matlab simulations have been conducted based on the observer gains trained using the power angle data from the swing equation. The results show that the estimation performance of the proposed DQN-based observer can be satisfactory against both an external disturbance and the measurement noise.

A Novel Approach to State and Unknown Input Estimation for Takagi–Sugeno Fuzzy Models With Applications to Fault Detection

In this paper, a novel approach is proposed for state and unknown input estimation of Takagi-Sugeno fuzzy systems. By introducing an augmented state vector, containing both system state and the unknown input, a functional observer is proposed to estimate this vector, and the proposed observer provides a highly flexible estimation output. Through casting the observer design problem into an equivalent solvability problem of a linear matrix equation with respect to the observer gains, the existence condition for the proposed observer is explicitly derived in terms of matrix rank. Furthermore, a parameterization methodology of the observer gain matrices is provided as well, which avoids directly solving the Sylvester equation. The proposed observer design scheme is further applied to the $H\_{}/H_\infty $ fault detection problem, and the effectiveness of the proposed approach is demonstrated by state and unknown input estimation for a tunnel diode circuit and fault detection for a continuously stirred tank reactor system.

Observer-based Economic Model Predictive Control for Direct Contact Membrane Distillation

In this work, we present an Observer-based Economic Model Predictive Control (OEMPC) scheme for Direct Contact Membrane Distillation (DCMD). To compute control actions via MPC strategy, full knowledge of the system states is necessary to predict the future evolution of the system. However, the full state measurement for DMCD is either difficult or costly. In this work, an integrated framework of an observer design and EMPC paradigm is proposed for the DMCD process. Numerical simulations are presented to illustrate the performance of the proposed observer design. Closed-loop simulations show that the proposed OEMPC scheme was able to operate the process economically while satisfying process and input constraints.

Design of a Fault Tolerant Sampled-Data Fuzzy Observer With Exponential Time-Varying Gains

This paper deals with the sampled-data fuzzy observer design problem with time-varying gains under the sensor fault consideration. To this end, a nonlinear system with sensor fault is represented by a Takagi-Sugeno fuzzy model with immeasurable premise variables. The sensor fault considered in this paper is assumed to be a time-varying uncertain matrix included in measurements. The observer is designed to consist of gains varying exponentially between two consecutive sampling instants, by which the equilibrium point of the estimation error dynamics is asymptotically exponentially stabilized. In addition, the observer considered in this paper is assumed not to share the same premise variable with a system. Unlike previous studies, this paper proposes a method handling this mismatched premise problem by using an H-infinity criterion. The proposed observer design condition is formulated in terms of linear matrix inequalities, which is relaxed based on a novel fuzzified Lyapunov-Krasovskii functional and a matrix inequality. Finally, two simulation examples are given to validate the effectiveness of the proposed method.

Designing Fuzzy Descriptor Observer with Unmeasured Premise Variables for Head-Two-Arms-Trunk System

Abstract Using the technique of unknown input observer, this paper aims at estimating internal variables of people living with a complete spinal cord injury (SCI). The goal is to provide a better understanding on the sitting control strategy of SCI people. The observer design is based on a Head-Two-Arms-Trunk (H2AT) model, belonging to a class of nonlinear descriptor systems. For observer design, this model is represented in a specific Takagi-Sugeno (TS) fuzzy form with nonlinear consequents. In contrast to previous fuzzy estimation results based on conventional TS fuzzy modeling, the new TS formulation allows separating all unmeasured premise variables in the nonlinear consequent parts. This contributes to reduce the computational burden of the observer design and the structural complexity of the designed fuzzy observer. In particular, the new formulation enables a more effective way to deal with unmeasured premise variables. Using Lyapunov stability theorem, sufficient conditions to design the unknown input observer are derived in the form of linear matrix inequalities, conveniently solved by convex optimization techniques. Simulation results demonstrate the effectiveness of the proposed observer design.