Unmeasured State Variables Research Articles

Multivariable extension of global finite‐time HOSM based differentiator for output‐feedback unit vector and smooth binary control

AbstractIn this paper, we propose a unit vector control law by output feedback to solve the problem of global exact output tracking for a class of multivariable uncertain plants with nonlinear disturbances. In order to face the nonuniform arbitrary relative degree obstacle, we extend our earlier estimation scheme based on global finite‐time differentiators using dynamic gains to a multivariable architecture. A diagonally stable condition over the system high‐frequency gain (HFG) matrix has to be assumed. Preserving the simplicity of its mono variable framework, variable gain super‐twisting algorithm (STA) is employed to obtain the robust and exact multivariable differentiator. Moreover, state‐norm observers for the unmeasured state variables are constructed to upper bound the disturbances as well as to update the differentiator gains, being both state dependent. Uniform global exponential stability and ultimate exact tracking are proved. As an alternative to chattering alleviation, we appeal to the Emelyanov's concept of binary control in order to obtain a continuous control signal replacing the unit vector function in the controller by a high‐gain gradient adaptive law with parameter projection. As shown in the existing literature for mono variable systems, the proposed multiparameter binary‐adaptive formulation tends to the unit vector control as the adaptation gain increases to infinity, also smoothing the transition from adaptive to sliding mode control. A numerical example is portrayed to illustrate the potentialities of the developed multivariable techniques.

A Comparison of Methods for Quantifying Prediction Uncertainty in Systems Biology

The parameters of dynamical models of biological processes always possess some degree of uncertainty. This parameter uncertainty translates into an uncertainty of model predictions. The trajectories of unmeasured state variables are examples of such predictions. Quantifying the uncertainty associated with a given prediction is an important problem for model developers and users. However, the nonlinearity and complexity of most dynamical models renders it nontrivial. Here, we evaluate three state-of-the-art approaches for prediction uncertainty quantification using two models of different sizes and computational complexities. We discuss the trade-offs between applicability and statistical interpretability of the different methods, and provide guidelines for their application.

State-feedback control with a full-state estimator for a cart-inverted pendulum system

A Cart Inverted Pendulum System is an unstable, nonlinear and underactuated system. This makes a cart inverted pendulum system used as a benchmark for testing many control method. A cart must occupy the desired position and the angle of the pendulum must be in an equilibrium point. System modeling of a cart inverted pendulum is important for controlling this system, but modeling using assumptions from state-feedback control is not completely valid. To minimize unmeasured state variables, state estimators need to be designed. In this paper, the state estimator is designed to complete the state-feedback control to control the cart inverted pendulum system. The mathematical model of the cart inverted pendulum system is obtained by using the Lagrange equation which is then changed in the state space form. Mathematical models of motors and mechanical transmissions are also included in the cart inverted pendulum system modeling so that it can reduce errors in a real-time application. The state gain control parameter is obtained by selecting the weighting matrix in the Linear Quadratic Regulator (LQR) method, then added with the Leuenberger observer gain that obtained by the pole placement method on the state estimator. Simulation is done to determine the system performance. The simulation results show that the proposed method can stabilize the cart inverted pendulum system on the cart position and the desired pendulum angle.

Decentralized Adaptive Output Feedback Fault Detection and Control for Uncertain Nonlinear Interconnected Systems.

This paper studies the problem of decentralized adaptive output feedback fault detection and control for a class of uncertain nonlinear interconnected systems. The K-filters are designed to estimate the unmeasured state variables of the system. Moreover, the built-in noise dampening filters are introduced to attenuate the influence caused by the measurement noises. Then the fault detection scheme is proposed by designing the residual and threshold signals. Subsequently, by using the backstepping design method, the decentralized switched control strategies are proposed with the help of the neural network approximation technique. Based on the Lyapunov stability theory, it is proved strictly that all signals of the resulting closed-loop system are bounded. Finally, a simulation example is presented to verify the effectiveness of the theoretical result.

Event-Based Dynamic Output Feedback Adaptive Fuzzy Control for Stochastic Nonlinear Systems

This paper focuses on the problem of decentralized event-based dynamic output feedback adaptive fuzzy control for a class of interconnected stochastic nonlinear systems. In order to relax the Lipschitz condition for the nonlinearity, a novel dynamic gain observer is constructed to estimate the unmeasured state variables. The funnel-like control technique is proposed to ensure that the output of each subsystem satisfies the prescribed performance requirement. To save energy in signal transmission, the controller and its triggered mechanism are codesigned based on backstepping method. By using the approximation theory of fuzzy logic systems, an unknown continuous function is approximated, and the difficulty caused by unmodeled dynamics is removed with the aid of changing supply function idea. By applying the Lyapunov stability theory, it is proved that all the signals of the resulting closed-loop system with the designed controller are bounded in probability. Finally, simulation results are given to verify the effectiveness of the theoretical results.

Sliding mode observers for a network of thermal and hydroelectric power plants

This paper deals with the design of a novel sliding mode observer-based scheme to estimate and reconstruct the unmeasured state variables in power networks including hydroelectric power plants and thermal power plants. The proposed approach reveals to be flexible to topological changes to power networks and can be easily updated only where changes occur. The discussed numerical simulations validate the effectiveness of the proposed estimation scheme.

Generalized dynamic observers for quasi‐LPV systems with unmeasurable scheduling functions

SummaryThis paper presents a generalized dynamic observer design for polytopic quasi–linear parameter‐varying systems where the parameters are depending on unmeasured state variables. It generalizes the existing results on the proportional observers and proportional‐integral observers. Conditions of existence and stability are given through the Lyapunov approach. Its design is obtained in terms of a set of linear matrix inequalities. A semiactive suspension example illustrates the performance and effectiveness of the proposed approach.

Robust High-Gain Observers Based Liquid Levels and Leakage Flow Rate Estimation

The paper aims to solve the problem of liquid level and leakage flow rate estimations for a state coupled four-tank process, that is why an UIO is developed to simultaneously estimate the unmeasured state variables and the perturbations considered as unknown inputs. We have proposed a state repartition that allows putting the model of the quadruple tank system to the canonical form for which the design of the observer is more easier. The observation scheme that uses a combination of high-gain observers and sliding mode observers allows improving robustness in the state estimation quality and a perfect reconstruction of the disturbance waveforms.

Observer and Adaptive Fuzzy Control Design for Nonlinear Strict-Feedback Systems With Unknown Virtual Control Coefficients

This paper considers the problems of designing a robust observer and developing a backstepping-based adaptive fuzzy control scheme for a class of strict-feedback systems, in which the virtual control coefficients are unknown. By using convex combination method, a robust fuzzy observer has been constructed to estimate the unmeasurable system state variables. Further, an observer-based adaptive fuzzy control scheme has been proposed. During the controller design procedure, fuzzy logic systems are used to model the unknown nonlinear functions, adaptive technique and backstepping are combined to construct the ideal virtual and the real laws. The proposed adaptive fuzzy output feedback controller guarantees that the tracking error converges to a small neighborhood of the origin and all the signals in the adaptive closed-loop system are bounded. Simulation results are provided to demonstrate the effectiveness of the presented approach.

Output-feedback control design for switched nonlinear systems: Adaptive neural backstepping approach

The tracking control is addressed for switched nonlinear systems with arbitrary switchings by adaptive neural approach via output feedback. The switched systems under consideration are composed of some subsystems in non-strict -feedback form. It is assumed that all the system state variables are unavailable, but the output variable is measurable. A switched nonlinear observer is set up to estimate those unmeasurable state variables. Convex combination method is utilized to determine the observer gain matrix so that the effect from those nonlinear terms can be well compensated for. By the feature of the basis vector functions of radial basis neural networks (RBF NN), a new observer-based adaptive neural backstepping control design scheme is presented for the switched nonlinear non-strict feedback systems. The multiple Lyapunov method is used to show the stability of the adaptive closed-loop systems. It is also proven that the tracking error converges to a small neighborhood around the original point under the action of the suggested controllers. Finally, a simulation example is studied to test the efficacy of the suggested control strategies.

Filter-Driven-Approximation-Based Control for a Class of Pure-Feedback Systems With Unknown Nonlinearities by State and Output Feedback

This paper presents a new approximation-based control approach for uncertain nonlinear pure-feedback systems. The main idea of this paper is to estimate unknown continuous nonlinear functions through a linear combination of first-order filtered signals of state variables and a control input in the nonadaptive control framework, instead of using conventional adaptive neural or fuzzy function approximators. Based on the proposed filter-driven approximation technique, we first present a state-feedback control scheme for pure-feedback systems with unknown nonaffine nonlinearities and a dead-zone input. Then, a filter-driven-approximation-based output-feedback control scheme is proposed via a system transformation and an observer to estimate unmeasurable state variables. Based on the Lyapunov stability theorem, the control errors and the filter-driven approximation errors are considered to prove that the controlled closed-loop system is semi-globally uniformly ultimately bounded. Finally, simulation results are provided to show that the proposed filter-driven-approximation-based controller and the existing function-approximation-based adaptive controllers have similar control performance for nonlinear pure-feedback systems.

Output feedback control for stochastic nonlinear time delay systems using dynamic gain technique

This paper investigates the output feedback control for a class of stochastic nonlinear time delay systems based on dynamic gain technique. The nonlinear terms of the stochastic system satisfy linear growth condition on unmeasured state variables with the output dependent incremental rate, which makes the studied time delay stochastic system more general than the exiting results. Firstly, the full order dynamic gain observer is constructed. Then, the linear-like controller is designed without using recursive design method. Next, the stability analysis is given and a useful corollary is obtained. Finally, a simulation is given to illustrate the effectiveness of the proposed method.

Sufficiently Exciting Inputs for Structurally Identifiable Systems Biology Models

A parameter is structurally identifiable if its value can theoretically be estimated by observing the model output. Structural identifiability is a desirable property in biological modelling: if a parameter is structurally unidentifiable, its estimated numerical value is meaningless, and model predictions of unmeasured state variables can be wrong, compromising the ability of the model to provide biological insight. Structural identifiability depends on the system dynamics, observation function (model output), initial conditions, and external inputs. In this paper we focus on the last factor. Methods for structural identifiability analysis typically classify a model as identifiable provided that it is fed with sufficiently exciting inputs. For example, a given model may require a time-varying input to be structurally identifiable, while for another model a constant non-zero input may be enough. Here we present a method that determines how sufficiently exciting an input should be. The approach builds on the STRIKE-GOLDD toolbox, which considers structural identifiability as generalized observability. The approach incorporates extended Lie derivatives, which correctly assess structural identifiability in the case of time-varying inputs. The procedure can also be used to determine the type of input profile that is required to make the parameters identifiable. This capability is helpful when designing new experiments for the purpose of parameter estimation.

Desired Compensation Nonlinear Cascade Control of High-Response Proportional Solenoid Valve Based on Reduced-Order Extended State Observer

With the gradual improvement of microprocessor, various nonlinear controllers are successfully applied in the electronic hydraulic system (EHS). The high-response proportional solenoid valve (HPSV), as the key component of many middle-end and high-end EHS, attracts many researchers’ close attention. This paper focuses on the method to get a strong robustness and high-performance controller for HPSV. In general, the full-state feedback condition of nonlinear cascade control (NC) cannot be easily satisfied in the industrial application. Therefore, the reduced-order extended state observer (RESO) is proposed to estimate the unmeasured state variables and the lumped uncertainties (mainly the unmodeled uncertainty and disturbance). Then, this paper presents an NC-based RESO for HPSV. To obtain an excellent control performance of NC, the desired compensation is adopted to reduce the interference of measurement noise, especially when the tracking error is reduced to the same order as the measurement noise. The system stability and error boundedness of the desired compensation NC based on RESO (DCNCRESO) are proved theoretically in this paper. To validate the effectiveness of DCNCRESO, several different types of experiments are carried out under different working conditions. Even when the supply pressure has great fluctuation, the DCNCRESO still behaves well, which manifests its strong robustness.

New Polynomial Lyapunov Functional Approach to Observer-Based Control for Polynomial Fuzzy Systems with Time Delay

This paper presents a new Line-integral polynomial Lyapunov functional approach for observer-based control for a class of polynomial fuzzy systems with time delay and unmeasured state variables. To guarantee the global asymptotic stability and estimation error convergence, a design method is proposed. In this work we consider a Line-integral polynomial Lyapunov function in which the Lyapunov matrices are polynomial matrices depending not only of the estimated states but also of the estimated delayed states and we use the dual system to reduce the computational efforts. The design conditions are established in terms of Sum Of Squares (SOS) which can be numerically and symbolically solved via the recent developed SOSTOOLS and a Semi-Definite Program solver. Finally, numerical examples are proposed to show the validity and applicability of the proposed results .

Dynamical compensation and structural identifiability of biological models: Analysis, implications, and reconciliation.

The concept of dynamical compensation has been recently introduced to describe the ability of a biological system to keep its output dynamics unchanged in the face of varying parameters. However, the original definition of dynamical compensation amounts to lack of structural identifiability. This is relevant if model parameters need to be estimated, as is often the case in biological modelling. Care should we taken when using an unidentifiable model to extract biological insight: the estimated values of structurally unidentifiable parameters are meaningless, and model predictions about unmeasured state variables can be wrong. Taking this into account, we explore alternative definitions of dynamical compensation that do not necessarily imply structural unidentifiability. Accordingly, we show different ways in which a model can be made identifiable while exhibiting dynamical compensation. Our analyses enable the use of the new concept of dynamical compensation in the context of parameter identification, and reconcile it with the desirable property of structural identifiability.

Adaptive observer based backstepping controller design for dynamic ship positioning

Modified adaptive observer based backstepping control system for dynamic positioning of ship is proposed. As an improvement, the adaptive observer takes the first-order wave frequency model and the bias term which represent the slowly varying environmental disturbances and the unmodeled dynamics. Thus, the wave-frequency motions are filtered out, and only the reconstructed low-frequency motions are sent as inputs of the controller. Furthermore, as the ship dynamics parameters are unknown, the adaptive estimation law is designed for both the unknown ship dynamics and the unmeasured state variables. Based on the estimated states and parameters, backstepping controller considering the integral action is designed. Global exponential stability (GES) for the total system is proved using Lyapunov direct method. Simulation results show a good performance of the observer and control system.

A Moving Horizon Estimation Algorithm Based on Carleman Approximation: Design and Stability Analysis

The moving horizon estimation (MHE) method is an optimization-based technique to estimate the unmeasurable state variables of a nonlinear dynamic system with noise in transition and measurement. One of the advantages of MHE over extended Kalman filter, the alternative approach in this area, is that it considers the physical constraints in its formulation. However, to offer this feature, MHE needs to solve a constrained nonlinear dynamic optimization problem which slows down the estimation process. In this paper, we introduce and employ the Carleman approximation method in the MHE design to accelerate the solution of the optimization problem. The Carleman method approximates the nonlinear system with a polynomial system at a desired accuracy level and recasts it in a bilinear form. By making this approximation, the Karush–Kuhn–Tucker (KKT) matrix required to solve the optimization problem becomes analytically available. Additionally, we perform a stability analysis for the proposed MHE design. As a result ...

An Interval Estimator for Chlorine Monitoring in Drinking Water Distribution Systems Under Uncertain System Dynamics, Inputs and Chlorine Concentration Measurement Errors

Abstract The design of an interval observer for estimation of unmeasured state variables with application to drinking water distribution systems is described. In particular, the design process of such an observer is considered for estimation of the water quality described by the concentration of free chlorine. The interval observer is derived to produce the robust interval bounds on the estimated water quality state variables. The stability and robustness of the interval observer are investigated under uncertainty in system dynamics, inputs, initial conditions and measurement errors. The bounds on the estimated variables are generated by solving two systems of first-order ordinary differential equations. For that reason, despite a large scale of the systems, the numerical efficiency is sufficient for the on-line monitoring of the water quality. Finally, in order to validate the performance of the observer, it is applied to the model of a real water distribution network.

Low-complexity differentiator-based decentralized fault-tolerant control of uncertain large-scale nonlinear systems with unknown dead zone

This paper investigates a low-complexity robust decentralized fault-tolerant prescribed performance control scheme for uncertain larger-scale nonlinear systems with consideration of the unknown nonlinearity, actuator failures, dead-zone input, and external disturbance. Firstly, a new simple finite-time-convergent differentiator is developed to obtain the unmeasurable state variables with arbitrary accuracy. Then, a time-varying sliding manifold involving the output tracking error and its high-order derivatives is constructed to tackle the high-order dynamics of subsystems. Sequentially, a robust decentralized fault-tolerant control scheme is proposed for each sliding manifold with prescribed convergence rate. The prominent advantage of the proposed fault-tolerant control scheme is that any specialized approximation technique, disturbance observer, and recursive procedure of backstepping technique are avoided, which dramatically alleviates the complexity of controller design. Finally, two groups of illustrative examples are employed to demonstrate the effectiveness of the low-complexity decentralized fault-tolerant control scheme under the developed finite-time-convergent differentiator.