Unmeasured State Variables Research Articles

State-estimation-based adaptive sliding mode control for a class of uncertain time-delay systems: a new design

In this article, state estimation-based adaptive control problem for a class of uncertain systems subject to time-delay and external disturbance is investigated within sliding mode framework. A simplified state observer without any inputs is designed to reconstruct the unmeasured state variables, from which a novel linear switching surface is provided. By applying a novel adaptive reaching motion controller, the existence and arrival of the defined switching surface are established. It is shown that in the framework of Lyapunov stability theory and linear matrix inequality technique, the proposed control scheme achieves the desirable performance for the closed-loop system. Two illustrative examples are given to substantiate the effectiveness of the proposed method.

Reduced-Order Observer-Based Adaptive Fuzzy Tracking Control Scheme of Stochastic Switched Nonlinear Systems

In this article, an adaptive approximation-based output-feedback tracking control scheme is presented for a class of stochastic switched lower-triangular nonlinear systems with input saturation and unmeasurable state variables. First, to overcome the design obstacle caused by the nondifferential saturation nonlinearity, a carefully selected nonlinear function of the control input signal is applied to estimate the saturation function. Then, a reduced-order state observer is designed to model the unmeasured system states, which also means the error system can be established. Furthermore, the fuzzy-logic systems are utilized to approximate the unknown system nonlinearities in the adaptive backstepping-based controller design procedure. It is ensured that all the closed-loop system variables are bounded in probability and the error signal belongs to a compact set in the mean square sense. Finally, the effectiveness and the practicability of the proposed control scheme are shown by two examples.

Application Study of Newton-Raphson-Type Nonlinear MPC for Hydrostatic Transmissions Under Disturbance and System Uncertainty

Model predictive control is well established and has a huge practical relevance in many industrial applications, especially for chemical or thermal plants. This paper presents the design and the implementation of a nonlinear model predictive control aiming at an accurate tracking control of desired output trajectories under disturbances and uncertainties for a nonlinear hydrostatic transmission system with multiple control inputs, which represents a fast mechatronic system. The benefit of this solution is that it can be easily adapted to either velocity tracking control or torque tracking control -- which is not the case with alternative model-based approaches. The control design is based on a numerical optimization within a moving horizon using the Newton-Raphson method in combination with the optimization-over-some variables technique. The unmeasurable system state variables as well as the system disturbances are reconstructed by an unscented Kalman filter which is well suited for nonlineaer systems subject to process and measurement noise. The proposed control scheme is investigated by simulations and experimentally validated on a test rig at the Chair of Mechatronics, University of Rostock. The results indicates the robustness of the proposed control structure by a high tracking accuracy despite system disturbances and uncertainties.

Event-Triggered/Self-Triggered Leader-Following Control of Stochastic Nonlinear Multiagent Systems Using High-Gain Method.

In this article, the event-triggered and self-triggered leader-following output-feedback control problems are investigated for a class of high-order stochastic nonlinear multiagent systems (MASs) under an undirected graph. First, using the high-gain method, the observer is designed to estimate the unmeasured state variables of the given nonlinear system. Then, by introducing an internal dynamic variable, a distributed Zeno-free dynamic event-triggered controller is constructed. Compared with the static event-triggering results, the interevent time of the proposed dynamic event-triggering mechanism is shown to be prolonged and, thus, the advantages of the event-triggered control approaches can be enhanced. Further, to avoid continuously monitoring the states, a Zeno-free self-triggering mechanism is given. It is shown that the expectations of the output tracking errors converge to an arbitrarily small set if the diffusion terms are different for all agents, and that the expectations of all state tracking errors converge to an arbitrarily small set if the diffusion terms are the same for all agents. Finally, simulation studies are given to illustrate the effectiveness of the proposed methods.

Observer Design and H∞ Performance for Discrete-Time Uncertain Fuzzy-Logic Systems.

The observer design and H∞ algorithm are proposed for the discrete-time fuzzy-logic systems in this article. The considered fuzzy-logic systems are subject to parameter uncertainty and unmeasurable state variables. To appropriately deal with parameter uncertainty and unmeasurable state variables, we first disintegrate the space of premise variables, then the total partitioned regions will be divided into two kinds: 1) crisp regions and 2) fuzzy regions. With the aid of partitioned regions, piecewise fuzzy H∞ observers are presented. Availability of the piecewise fuzzy H∞ observers gives us an accurate picture of the overall evolution of the augmented systems leading therefore to an improved situational awareness for the noncoordination of premise variables and external interference and, hence, the augmented systems achieve the performance conditions: asymptotic convergence and H∞ performance. The simulation results of the proposed approach show the accuracy of the resulting state estimates.

Proportional–Integral Extended State Observer for Monitoring Nuclear Reactors

A proportional-integral extended state observer (PI-ESO) of nuclear reactors is proposed for disturbance estimation, driven by the measurement errors of neutron flux, primary coolant temperatures at reactor inlet and outlet, as well as their integrations. This PI-ESO can provide a globally asymptotically bounded estimation for not only the reactor process variables, including normalized neutron flux and precursor concentrations as well as average temperatures of fuel assemblies and primary coolant, but also the total disturbances in channels of neutron kinetics and coolant thermal hydraulics. Furthermore, the newly built PI-ESO is applied to reconstruct both the unmeasurable state variables and the total disturbances of a nuclear heating reactor (NHR). Numerical simulation results verify the theoretical result, showing both the satisfactory performance and the influence of observer parameters.

Tracking Control of Overhead Crane Using Output Feedback With Adaptive Unscented Kalman Filter and Condition-Based Selective Scaling

Most of the advanced nonlinear control strategies reported in the literature for underactuated mechanisms, such as overhead cranes, require the knowledge of all state variables. For cranes, the state vector includes variables related to the load sway and its velocity. The flatness property of crane-like systems can be exploited to solve both motion planning and tracking problems, so that the load (whose coordinates are included in the set of the flat outputs) exponentially follows a rapid reference trajectory. However, unmodeled friction phenomena and limitations on the direct measurement of sway-related state variables usually impede the practical implementation of flatness-based control laws. This paper proposes the use of an adaptive unscented Kalman filter to estimate friction forces and unmeasured state variables. The convergence of the filter is improved using a novel technique, called condition-based selective scaling. The performance of the suggested scheme is verified through a set of computer simulations on a 2D overhead crane system.

Torque control of new energy four wheel hub motor based on distribution algorithm

Due to the nonlinear, strong coupling and uncertain parameters of the new energy four-wheel hub motor, it is more difficult to control the torque of the motor. In order to solve this problem, a torque control method of the new energy four-wheel hub motor based on the distribution algorithm is proposed. The dynamic model of the new energy four-wheel hub motor is established, and the unmeasurable flux, electric power and other state variables in the motor model are derived according to the degree of freedom of the body. The whole four-wheel hub motor is taken as the research object, and the optimal efficiency of the drive system is taken as the goal, and the distribution algorithm is used to control the electromagnetic torque of the motor. The simulation results show that after the torque control of new energy four wheel hub motor, the driving range of the vehicle is longer, the amplitude of stator flux changes little, the stator current changes and the stability of motor speed are good, and the torque control effect is better.

Predictive control of induction motor drive

The work is devoted to the study of the possibilities of using the predictive torque control system instead of the currently widely used direct torque control system. Aspects of using the system of direct torque control of an induction motor are considered and it is found that its significant disadvantage is the variable frequency of semiconductor switches. As a further development of the direct torque control system, a predictive torque control system is analyzed, which contains blocks for estimating unmeasured state variables, as well as predicting the state of a dynamic system when applying possible control signals. The systems were compared by mathematical modeling in Matlab / Simulink.

Robust State Observers for Electromechanical Control Plants with Sensorless Manipulators

The paper deals with the problem of state observers design for electromechanical control plants with sensorless manipulators in conditions of significant parametric uncertainty. For the estimation of unmeasured state variables, the structure of reduced observers is proposed depending on the set of sensors located on the electrical actuators. Decomposition procedures have been developed for synthesizing piecewise linear control actions of observers that provide a given estimation accuracy. This method does not require additional identification of unknown parameters, since parametrically indefinite differential equations describing the dynamics of unmeasured variables are not used when constructing observers.

Adaptive Control for Systems With Time-Varying Parameters

This article investigates the adaptive control problem for systems with time-varying parameters using the so-called congelation of variables method. First, two scalar examples to illustrate how to deal with time-varying parameters in the feedback path and in the input path, respectively, are discussed. The control problem for an n-dimensional lower triangular system via state feedback is then discussed to show how to combine the congelation of variables method with adaptive backstepping techniques. To achieve output regulation problem via output feedback, problem which cannot be solved directly due to the coupling between the input and the time-varying perturbation, the ISS of the inverse dynamics, referred to as strong minimum-phaseness, is exploited. This allows converting such coupling into the coupling between the output and the time-varying perturbation. A set of filters, resulting in ISS state estimation error dynamics, are designed to cope with the unmeasured state variables. Finally, a controller is designed based on a small-gain-like analysis that takes all subsystems into account. Simulation results show that the proposed controller achieves asymptotic output regulation and outperforms the classical adaptive controller, in the presence of time-varying parameters that are neither known nor asymptotically constant.

Global output feedback tracking control for switched nonlinear systems with deferred prescribed performance

In this paper, the global output feedback tracking control is investigated for a class of switched nonlinear systems with time-varying system fault and deferred prescribed performance. The shifting function is introduced to improve the traditional prescribed performance control technique, remove the constraint condition on the initial value, and make the constraint bounds have more alternative forms. To estimate the unmeasured state variables and compensate the system fault, the switched dynamic gain extended state observer is constructed, which relaxes the traditional Lipschitz conditions on the nonlinear functions. Based on the proposed observer, by constructing the new Lyapunov function and using the backstepping method, the global robust output feedback controller is designed to make the output track the reference signal successfully, and after the adjustment time, the tracking error enters into the prescribed set. The stability of the system is analyzed by the average dwell time method. Finally, simulation results are given to illustrate the effectiveness of the proposed method.

Adaptive prescribed performance neural network control for switched stochastic pure-feedback systems with unknown hysteresis

This paper investigates the problem of neural network (NN) prescribed performance tracking control for a class of switched stochastic nonlinear pure-feedback systems which contain unknown nonlinear functions, unmeasured state variables, and unknown hysteresis input. It provides an adaptive NN controller which is not restricted to a particular type of hysteresis input. A general mathematical model is introduced to describe two kinds of hysteresis nonlinearities and to utilize in the control design producer. Other focus of this paper is on the performance constraint problem to avoid performance degradation and system damage in practical control systems. Prescribed performance control (PPC) and backstepping technique are thus synthesized to develop an adaptive NN output feedback tracking control scheme under deterministic switching signal. Regarding this concern, to cope with the cause of non-differentiable difficulties and complex deductions in traditional PPC, a new asymmetry error transformation is employed. Moreover, radial basis function NNs (RBFNNs) are applied to approximate the unknown nonlinear functions and to construct a NN nonlinear observer to estimate the immeasurable state variables. Based on Lyapunov stability theory, it is demonstrated that the proposed controller can guarantee that all signals in the closed-loop system are semiglobally uniformly ultimately bounded in probability and the tracking error converges to a small neighborhood of the origin with the prescribed performance bounds. Finally, two simulation examples are provided to confirm the advantages of the presented control design approach.

Distributed Adaptive Output Feedback Leader-Following Consensus Control for Nonlinear Multiagent Systems

This paper investigates the problem of the distributed adaptive output feedback leader-following consensus control for a class of high-order nonlinear multiagent systems with unknown parameters and nonlinear terms. First, the reduced order dynamic gain k-filters are built to estimate the unmeasured state variables. The bounds of the unknown parameters are estimated in order to avoid the over-estimation problem. Then, the dynamic surface control technique is used to design the distributed controller, and the computation load of the system is greatly reduced. Finally, a numerical example is shown to verify the effectiveness of the designed controller.

Adaptive output‐feedback stabilization in prescribed time for nonlinear systems with unknown parameters coupled with unmeasured states

SummaryThe prescribed‐time output‐feedback stabilization (ie, regulation of the state and control input to zero within a “prescribed” time picked by the control designer irrespective of the initial state) of a general class of uncertain nonlinear strict‐feedback‐like systems is considered. Unlike prior results, the class of systems considered in this article allows crossproducts of unknown parameters (without any required magnitude bounds on unknown parameters) and unmeasured state variables in uncertain state‐dependent nonlinear functions throughout the system dynamics. We show that prescribed‐time output‐feedback stabilization (ie, both prescribed‐time state estimation and prescribed‐time regulation) is achieved through a novel output‐feedback control design involving specially designed dynamics of an adaptation state variable and a high‐gain scaling parameter in combination with a temporal transformation and a dual high‐gain scaling based observer and controller design. While standard dynamic adaptation techniques cannot be applied due to crossproducts of unknown parameters and unmeasured states, we show that instead, the dynamics of the high‐gain scaling parameter and adaptation parameter can be designed with temporal forcing terms to ensure that unknown parameters in system dynamics are dominated by a particular fractional power of the high‐gain scaling parameter and the adaptation parameter after a subinterval (of unknown length) of the prescribed time interval. We show that the control law can be designed such that the system state and input are regulated to zero in the remaining subinterval of the prescribed time interval.

Application of the Kalman filtering technique for nonlinear state estimation in propulsion system

The estimation of the propulsion system states and especially of the main engine is essential for control, diagnosis and performance evaluation. If all the required sensors were available, providing required measurements, the state and performance monitoring is of no particular difficulty. However, not all the required parameters can be measured directly, or the addition of multiple measurement channels is out of appropriateness. Furthermore, the propulsion plant state dynamics is justified by propeller load torque fluctuation that in turn is caused by fluctuating effective inflow velocity into the propeller, and which cannot be measured directly. Thus, the problem of estimating unmeasured state and disturbance variables of the propulsion system is considered and formulated as the design of an unknown input observer under model uncertainty and nonlinearity. To solve the design problem, this paper introduces a nonlinear engine dynamic model to catch the internal engine states and an unscented Kalman filter for concurrently performing disturbance and state estimation. The effectiveness is verified through the experiments.

Short-term forecasts of the COVID-19 pandemic: a study case of Cameroon.

In this paper, an Ensemble of Kalman filter (EnKf) approach is developed to estimate unmeasurable state variables and unknown parameters in a COVID-19 model. We first formulate a mathematical model for the dynamic transmission of COVID-19 that takes into account the circulation of free coronaviruses in the environment. We provide the basic properties of the model and compute the basic reproduction number that plays an important role in the outcome of the disease. After, assuming continuous measurement of newly COVID-19 reported cases, deceased and recovered individuals, the EnKf approach is used to estimate the unmeasured variables and unknown COVID-19 transmission rates using real data of the current COVID-19 pandemic in Cameroon. We present the forecasts of the current pandemic in Cameroon and explore the impact of non-pharmaceutical interventions such as mass media-based sensitization, social distancing, face-mask wearing, contact tracing and the desinfection and decontamination of infected places by using suitable products against free coronaviruses in the environment in order to reduce the spread of the disease. Through numerical simulations, we find that at that time (i) meaning that the disease will not die out without any control measures, (ii) the infection from COVID-19 infected cases is more important than the infection from free coronaviruses in the environment, (iii) the number of new COVID-19 cases will still increase and there is a necessity to increase timely the surveillance by using contact tracing and sensibilisation of the population to respect social distancing, face-masks wearing through awareness programs and (iv) the eradication of the pandemic is highly dependent on the control measures taken by governments.

Parameter and State Estimation in a Cholera Model with Threshold Immunology: A Case Study of Senegal.

It is often impossible to measure all states affecting spread of a disease. In cholera, asymptomatic and cholera pathogen densities are not practically measurable despite playing a big role in its transmission. They are referred to as inaccessible states of the model and can only be manipulated using the measurable states of the given model. Our interest lies in estimating such states and the parameters catalyzing the spread. A mathematical model for cholera dynamics consisting of five compartments (susceptible, symptomatic, asymptomatic, recovered and bacteria population) with a minimum infection dose (MID) is considered. A method based on observer (from modern control theory) is proposed to estimate the state variables not accessible to measurement and the time-dependent parameters from real data of Senegal. We suppose that the total population of Senegal, the monthly reported cholera-induced deaths and the monthly recovered individuals are known inputs obtainable from real data, and the monthly new cholera cases the system output. An auxiliary system is used, an observer whose solutions converge exponentially to those of an original system and solely utilize known inputs and output of the model. Thus, the estimation of the unmeasured state variables like the pathogen density and the yearly asymptomatic population within the human community playing an important role in the spread of cholera is possible. We derive the expressions for time-dependent infection rate, induced cholera death rate and symptomatic recovery rate and their estimations done using real data. Numerical simulations are then performed for the validation of estimation results. The system together with the observer designed is detectable but is not observable. The observer delivered estimates reflect a close trend already ascertained by other researchers. They indicate the existence of bacteria and asymptomatic individuals in the population of Senegal at any single time for the duration of collection of the data. The ever existence of cholera pathogen explains the endemicity of Cholera in Senegal and other sub-Saharan-African countries owing to role played by the asymptomatic individual in the bacteria density. As such, the heath authorities in Senegal need to educate the general public on hygiene irrespective of observable symptoms to lower the possible number of new infections. We have analytically showed and numerically confirmed the exponential convergence to zero of the estimation errors resulting from the observer model hence the high quality of the estimates.

Parameter estimation of a second order system via nonlinear identification algorithm

In this paper, a parameter estimation for a class of second order nonlinear system is presented. The considered system, can be represented in such way that it is linear respect its parameters. Since the system output is given, only, for the second integrator a state estimation of unmeasured state variables is reconstructed via nonlinear observer based on the terminal sliding mode observer. Therefore, the main contribution of this paper deals with a full order nonlinear observer algorithm design to enhance parameter identification of a nonlinear second order system. Finally, to illustrate the theoretical performance of the proposed identification algorithm, an experimental result of a mechanical system is presented.

Observer-Based Adaptive Fuzzy Tracking Control for Stochastic Nonlinear Multi-Agent Systems with Dead-Zone Input

This paper studies observer-based adaptive fuzzy leader-following tracking control for high-order stochastic nonlinear multi-agent systems with unknown dead-zone input. First, in order to deal with unmeasurable state variables, a reduced-order observer is established for each follower, which could make the computational burden of the systems reduced. Second, the fuzzy logic systems are introduced to approximate the stochastic disturbances and the unknown functions. Then, an adaptive fuzzy tracking controller is designed for high-order multi-agent systems with unknown dead-zone input by using the backstepping approach. Furthermore, it can be proved that all the closed-loop signals are bounded in probability, and the consensus error of the stochastic multi-agent systems can converge to a small region of origin under the Lyapunov stability theory. Finally, a simulation example is given to show the effectiveness of the designed algorithm.