Robust moving horizon estimation based output feedback economic model predictive control

In this work, we develop an economic model predictive control scheme for a class of nonlinear systems with bounded process and measurement noise. In order to achieve fast convergence of the state estimates to the actual system state as well as the robustness of the observer to measurement and process noise, a deterministic (high-gain) observer is first applied for a small time period with continuous output measurements to drive the estimation error to a small value; after this initial small time period, a robust moving horizon estimation scheme is used on-line to provide more accurate and smoother state estimates. In the design of the robust moving horizon estimation scheme, the deterministic observer is used to calculate reference estimates and confidence regions that contain the actual system state. Within the confidence regions, the moving horizon estimation scheme is allowed to optimize its estimates. The output feedback economic model predictive controller is designed via Lyapunov techniques based on state estimates provided by the deterministic observer and the moving horizon estimation scheme. The stability of the closed-loop system is analyzed rigorously and conditions that ensure the closed-loop stability are derived. Extensive simulations based on a chemical process example illustrate the effectiveness of the proposed approach.     

Adaptive LFT control of a civil aircraft with online frequency‐domain parameter estimation

This paper describes the application of an indirect linear fractional transformation (LFT)–based state‐space adaptive control scheme to a transport aircraft, within the context of the European project REconfiguration of CONtrol in Flight for Integral Global Upset REcovery. The principle of the scheme is to design and validate off‐line a gain‐scheduled controller, depending on the plant parameters to be estimated, and to combine it online with a model estimator, so as to minimize the onboard computational time and complexity. A modal approach, very classical for the design of a flight control law, is used to directly synthesize the static output feedback LFT controller, depending on the control and stability derivatives, ie, the parameters of the linearized aerodynamic state‐space model to be estimated. Since the gain‐scheduled LFT controller online depends on the parameter estimates instead of the true values, its robustness to transient and asymptotic estimation errors needs to be assessed using μ and integral quadratic constraint analysis techniques. A primary concern being an online implementation, a fully recursive frequency‐domain estimation technique is proposed, with a low online computational burden and the capability to track time‐varying parameters. Full nonlinear simulations along a trajectory validate the good performance properties of the combined estimator and gain‐scheduled flight controller. To some extent, minimal guaranteed stability and performance properties of the adaptive scheme can be ensured by switching to a robust controller when the parameter estimates are not reliable enough, thus bypassing the Certainty Equivalence Principle.     

State Estimation For An Agonistic‐Antagonistic Muscle System

Research on assistive technology, rehabilitation, and prosthetics requires the understanding of human machine interaction, in which human muscular properties play a pivotal role. This paper studies a nonlinear agonistic‐antagonistic muscle system based on the Hill muscle model. To investigate the characteristics of the muscle model, the problem of estimating the state variables and activation signals of the dual muscle system is considered. In this work, parameter uncertainty and unknown inputs are taken into account for the estimation problem. Three observers are presented: a high gain observer, a sliding mode observer, and an adaptive sliding mode observer. Theoretical analysis shows the convergence of the three observers. Numerical simulations reveal that the three observers are comparable and provide reliable estimates.     

Computationally‐Light Non‐Lifted Data‐Driven Norm‐Optimal Iterative Learning Control

Computational complexity and model dependence are two significant limitations on lifted norm optimal iterative learning control (NOILC). To overcome these two issues and retain monotonic convergence in iteration, this paper proposes a computationally‐efficient non‐lifted NOILC strategy for nonlinear discrete‐time systems via a data‐driven approach. First, an iteration‐dependent linear representation of the controlled nonlinear process is introduced by using a dynamical linearization method in the iteration direction. The non‐lifted NOILC is then proposed by utilizing the input and output measurements only, instead of relying on an explicit model of the plant. The computational complexity is reduced by avoiding matrix operation in the learning law. This greatly facilitates its practical application potential. The proposed control law executes in real‐time and utilizes more control information at previous time instants within the same iteration, which can help improve the control performance. The effectiveness of the non‐lifted data‐driven NOILC is demonstrated by rigorous analysis along with a simulation on a batch chemical reaction process.     

A comparison of nonlinear observers for output feedback model-based control of seeded batch crystallization processes

This paper presents a comparative analysis of various nonlinear estimation techniques when applied for output feedback model-based control of batch crystallization processes. Several nonlinear observers, namely an extended Luenberger observer, an extended Kalman filter, an unscented Kalman filter, an ensemble Kalman filer and a moving horizon estimator are used for closed-loop control of a semi-industrial fed-batch crystallizer. The performance of the nonlinear observers is evaluated in terms of their closed-loop behavior as well as their ability to cope with model imperfections and process uncertainties such as measurement errors and uncertain initial conditions. The simulation results suggest that the extended Kalman filter and the unscented Kalman filter provide accurate state estimates that ensure adequate fulfillment of the control objective. The results also confirm that adopting a time-varying process noise covariance matrix further enhances the estimation accuracy of the latter observers at the expense of a slight increase in their computational burden. This tuning method is particularly suited for batch processes as the state variables often vary significantly along the batch run. It is observed that model imperfections and process uncertainties are largely detrimental to the accuracy of state estimates. The degradation in the closed-loop control performance arisen from inadequate state estimation is effectively suppressed by the inclusion of a disturbance model into the observers.     

Efficient moving horizon state and parameter estimation for SMB processes

In this paper, a moving horizon state and parameter estimation scheme for chromatographic simulated moving bed SMB processes is proposed. The simultaneous state and parameter estimation is based on a high-order nonlinear SMB model which incorporates rigorous models of the chromatographic columns and the discrete shiftings of the inlet and outlet ports. The estimation is performed using sparse measurement information: the concentrations of the components are only measured at the two outlet ports (which are periodically switched from one column to the next) and at one fixed location between two columns. The goal is to reconstruct the full state of the system, i.e. the concentration profiles along all columns, and to identify critical model parameters reliably such that the estimated model can be used in the context of online optimizing control. The state estimation scheme is based upon a deterministic model within the prediction horizon, state noise is only present in the state and the parameters prior to and at the beginning of the horizon. By solving the optimization problem with a multiple-shooting method and applying a real-time iteration scheme, the computation times are such that the scheme can be applied online. Numerical simulations of a validated model for a separation problem with nonlinear isotherms of the Langmuir type demonstrate the efficiency of the algorithm.     

Observer‐based controller for constrained uncertain stochastic nonlinear discrete‐time systems

In this paper, an observer‐based control approach is proposed for uncertain stochastic nonlinear discrete‐time systems with input constraints. The widely used extended Kalman filter (EKF) is well known to be inadequate for estimating the states of uncertain nonlinear dynamical systems with strong nonlinearities especially if the time horizon of the estimation process is relatively long. Instead, a modified version of the EKF with improved stability and robustness is proposed for estimating the states of such systems. A constrained observer‐based controller is then developed using the state‐dependent Riccati equation approach. Rigorous analysis of the stability of the developed stochastically controlled system is presented. The developed approach is applied to control the performance of a synchronous generator connected to an infinite bus and chaos in permanent magnet synchronous motor. Simulation results of the synchronous generator show that the estimated states resulting from the proposed estimator are stable, whereas those resulting from the EKF diverge. Moreover, satisfactory performance is achieved by applying the developed observer‐based control strategy on the two practical problems. Copyright © 2015 John Wiley & Sons, Ltd.     

Visual motion and structure estimation using sliding mode observers

The problem of estimating motion and structure from a sequence of images has been a major research theme in machine vision for many years and remains one of the most challenging ones. In this work, we use sliding mode observers to estimate the motion and the structure of a moving body with the aid of a change-coupled device (CCD) camera. We consider a variety of dynamical systems which arise in machine vision applications and develop a novel identification procedure for the estimation of both constant and time-varying parameters. The basic procedure introduced for parameter estimation is to recast image feature dynamics linearly in terms of unknown parameters and construct a sliding mode observer to produce asymptotically correct estimates of the observed image features, and then use the observer input to compute parameters. Much of our analysis has been substantiated by computer simulations and real experiments.     

Constrained state estimation for nonlinear discrete-time systems: stability and moving horizon approximations

State estimator design for a nonlinear discrete-time system is a challenging problem, further complicated when additional physical insight is available in the form of inequality constraints on the state variables and disturbances. One strategy for constrained state estimation is to employ online optimization using a moving horizon approximation. We propose a general theory for constrained moving horizon estimation. Sufficient conditions for asymptotic and bounded stability are established. We apply these results to develop a practical algorithm for constrained linear and nonlinear state estimation. Examples are used to illustrate the benefits of constrained state estimation. Our framework is deterministic.     

Observer‐Based Adaptive Output Feedback Fault Tolerant Control for Nonlinear Hydro‐Turbine Governing System with State Delay

This paper focuses on the problem of adaptive output feedback fault tolerant control for a nonlinear hydro‐turbine governing system. A dynamic mathematical model of the system is established, which aims to investigate the dynamic performance of the model under servomotor delay and actuator faults. Then, a fault estimation adaptive observer is proposed to achieve online real‐time diagnosis of system faults. Based on the online fault estimation information, an observer‐based adaptive output feedback fault tolerant controller is designed. Furthermore, under reasonable assumptions, the results demonstrate that the closed‐loop control system can achieve global asymptotic stability by Lyapunov function. Finally, the numerical simulation results are presented to indicate the satisfaction control effectiveness of the proposed scheme.     

A dual‐observer approach for global output feedback stabilization of planar nonlinear systems with output‐dependent growth rates

In this paper, we investigate the problem of global output feedback stabilization for a class of planar nonlinear systems under a more general growth condition, which encompasses both lower‐order and higher‐order state growths with output‐dependent rates. For more accurate estimation, two new observers with nonlinear gains are constructed to estimate the states on the lower‐order and higher‐order scales, respectively. The estimates produced from the dual‐observer are used delicately in the output feedback control law with both lower‐order and higher‐order modes. The overall stability of the system is guaranteed by rigorously choosing these nonlinear gains in the control law and the dual‐observer.     

Moving horizon numerical observers of nonlinear control systems

In this note, we develop moving horizon numerical observers and analyze the error. In the error estimation, we take into consideration both the integration error and the optimization error. The design facilitates the use of a variety of numerical algorithms to form different observers. As a special case, an Euler-Newton observer is introduced. The numerical observer is independent of any optimization software or toolbox. Furthermore, the observer is formulated in a way that is especially efficient for systems with sampled measurement.     

Event‐triggered cascade high‐gain observer and its application

In this article, we consider the event‐triggered cascade high‐gain observer (ETCHGO) for a class of nonlinear systems. By cascading lower dimensional observers, we design a cascade high‐gain observer together with a Zeno‐free event‐triggered mechanism to estimate the state of the plant. We show that the ETCHGO has the same steady‐state performance as the continuous‐time cascade high‐gain observer, that is, there is a finite time after which the estimation error will not exceed the given threshold, and moreover, the finite time and the threshold can be made sufficiently small by adjusting some design parameters. We also investigate an ETCHGO with saturation, which will reduce the peaking value while maintaining the steady‐state estimation performance. Furthermore, we use the ETCHGO with saturation to solve the output feedback stabilization problem for a class of nonlinear systems. An example is given to illustrate our results.     

A UD factorization‐based nonlinear adaptive set‐membership filter for ellipsoidal estimation

The extended set‐membership filter (ESMF) for nonlinear ellipsoidal estimation suffers from numerical instability, computation complexity as well as the difficulty in filter parameter selection. In this paper, a UD factorization‐based adaptive set‐membership filter is developed and applied to nonlinear joint estimation of both time‐varying states and parameters. As a result of using the proposed UD factorization, combined with a new sequential and selective measurement update strategy, the numerical stability and real‐time applicability of conventional ESMF are substantially improved. Furthermore, an adaptive selection scheme of the filter parameters is derived to reduce the computation complexity and achieve sub‐optimal estimation. Simulation results have shown the efficiency and robustness of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.     

On the Exponential Stability of Moving Horizon Observer for Globally N‐Detectable Nonlinear Systems

A moving horizon observer is analyzed for nonlinear discrete‐time systems. Exponential stability relies on a global detectability assumption that utilizes the concept of incremental input‐to‐state‐stability.     

High‐gain nonlinear observer‐based impedance control for deformable object cooperative teleoperation with nonlinear contact model

Unmeasurable object deformation and local communication time delays between the slave robots influence the manipulation effect for multirobot multioperator teleoperation. In this article, a distributed control method based on high‐gain nonlinear observer, interactive identification, and impedance control is proposed for this problem. First, we use Hunt‐Crossley contact model and deduce the desired synchronizing object state in cooperative teleoperation. Second, an impedance item expressed by the internal position errors is presented to decrease object position tracking errors. For the unmeasurable object deformation, an interactive identification method is proposed for estimating unknown variables. Third, we consider both varying communication time delays and local time delays in the slave side. Two mirror high‐gain nonlinear observers are designed for estimating other slave robots' real‐time state. Finally, we build the system controllers and prove the stability of the closed‐loop system and the boundless of estimating errors using Lyapunov functions. Comparable simulation results executed by the physical system present that the position and internal force tracking errors of the object decrease in the designated cooperative tasks.     

Error‐constrained finite‐horizon tracking control with incomplete measurements and bounded noises

This paper is concerned with the finite‐horizon tracking control problem for discrete nonlinear time‐varying systems with state delays, bounded noises and incomplete measurement output. The exogenous bounded noises are unknown and confined to specified ellipsoidal sets. A deterministic measurement output model is proposed to account for the incomplete data transmission phenomenon caused by possible sensor aging or failures. The aim of the addressed tracking control problem is to develop an observer‐based control over a finite‐horizon such that, for the admissible time delays, nonlinearities and bounded noises, both the quadratic tracking error and the estimation error are not more than certain upper bounds that are minimized at every time step. A recursive linear matrix inequality approach is used to solve the problem addressed. The observer and controller parameters are characterized in terms of the solution to a convex optimization problem that can be easily solved by using the semi‐definite programme method. A simulation example is exploited to illustrate the effectiveness of the proposed design procedures. Copyright © 2011 John Wiley & Sons, Ltd.     

Online solution of nonlinear two‐player zero‐sum games using synchronous policy iteration

The two‐player zero‐sum (ZS) game problem provides the solution to the bounded L₂‐gain problem and so is important for robust control. However, its solution depends on solving a design Hamilton–Jacobi–Isaacs (HJI) equation, which is generally intractable for nonlinear systems. In this paper, we present an online adaptive learning algorithm based on policy iteration to solve the continuous‐time two‐player ZS game with infinite horizon cost for nonlinear systems with known dynamics. That is, the algorithm learns online in real time an approximate local solution to the game HJI equation. This method finds, in real time, suitable approximations of the optimal value and the saddle point feedback control policy and disturbance policy, while also guaranteeing closed‐loop stability. The adaptive algorithm is implemented as an actor/critic/disturbance structure that involves simultaneous continuous‐time adaptation of critic, actor, and disturbance neural networks. We call this online gaming algorithm ‘synchronous’ ZS game policy iteration. A persistence of excitation condition is shown to guarantee convergence of the critic to the actual optimal value function. Novel tuning algorithms are given for critic, actor, and disturbance networks. The convergence to the optimal saddle point solution is proven, and stability of the system is also guaranteed. Simulation examples show the effectiveness of the new algorithm in solving the HJI equation online for a linear system and a complex nonlinear system. Copyright © 2011 John Wiley & Sons, Ltd.     

Integrated fault estimation and fault‐tolerant control for stochastic systems with Brownian motions

This paper presents an integrated robust fault estimation and fault‐tolerant control technique for stochastic systems subjected to Brownian parameter perturbations. The augmented system approach, unknown input observer method, and optimization technique are integrated to achieve robust simultaneous estimates of the system states and the means of faults concerned. Meanwhile, a robust fault‐tolerant control strategy is developed by using actuator and sensor signal compensation techniques. Stochastic linear time‐invariant systems, stochastic systems with Lipschitz nonlinear constraint, and stochastic systems with quadratic inner‐bounded nonlinear constraint are respectively investigated, and the corresponding fault‐tolerant control algorithms are addressed. Finally, the effectiveness of the proposed fault‐tolerant control techniques is demonstrated via the drivetrain system of a 4.8 MW benchmark wind turbine, a 3‐tank system, and a numerical nonlinear model.