Nonlinear Output Feedback Control Research Articles

Finite-time semistability, Filippov systems, and consensus protocols for nonlinear dynamical networks with switching topologies

This paper focuses on semistability and finite-time semistability for discontinuous dynamical systems. Semistability is the property whereby the solutions of a dynamical system converge to Lyapunov stable equilibrium points determined by the system initial conditions. In this paper, we extend the theory of semistability to discontinuous autonomous dynamical systems. In particular, Lyapunov-based tests for strong and weak semistability as well as finite-time semistability for autonomous differential inclusions are established. Using these results we then develop a framework for designing semistable and finite-time semistable protocols for dynamical networks with switching topologies. Specifically, we present distributed nonlinear static and dynamic output feedback controller architectures for multiagent network consensus and rendezvous with dynamically changing communication topologies.

Observer-based output feedback linearizing control applied to a denitrification reactor

In this work a late lumping approach is used in order to design a state feedback linearizing controller for influent disturbance attenuation and regulating the nitrogen concentration at the output of a denitrification biofilter. This controller is associated to a distributed parameter observer to estimate all the states needed to compute the controlled input. It results in an output feedback nonlinear controller with stable closed-loop dynamics.

Tracking control for a velocity-sensorless VTOL aircraft with delayed outputs

This paper presents a nonlinear output-feedback control method to force an underactuated vertical take-off and landing (VTOL) aircraft with delayed measurement outputs to asymptotically track a given reference trajectory. The control development is based on a delayed-output observer. The proposed observer consists of two-step observation algorithms reconstructing the system state with multi-delayed time instants. Conditions are given ensuring global exponential convergence to zero of the observation error for the given the delays in the measurements. Moreover, two low-dimensional controllers are designed separately to stabilize the two decomposed flight dynamics, and make the overall closed-loop system stable. The merits of method include its simple implementation and interesting application. Numerical simulations illustrate the effectiveness of the proposed control method.

Robust non-linear output-feedback control of a magnetic levitation system by K-filter approach

A robust non-linear output-feedback controller by the K-filter approach is proposed for position-tracking problem of a magnetic levitation system, where only the position measurement is available for control. Instead of the popular adaptive control techniques, a disturbance observer (DOB) is merged into the K-filter-based output-feedback controller to compensate the external disturbance and model mismatch, so that a much simpler controller is constructed. Rigorous stability of the non-linear control system is established. Experimental results are included to show the excellent performance of the designed controller.

Non-linear filter-based adaptive output feedback control for spacecraft formation flying

This paper presents a non-linear filter-based adaptive output control for spacecraft formation flying missions. The study is motivated by the fact that only accurate position measurements are available for some systems, and velocities have to be estimated from those measurements. The proposed adaptive output controller guarantees asymptotic stability of the position and velocity tracking motion, even in the presence of uncertainties and external perturbations. The effectiveness of the proposed controller is verified by numerical simulations.

Nonlinear adaptive depth tracking and attitude control of an underwater towed vehicle

This paper addresses the problem of simultaneous depth tracking and precise attitude control of an underwater towed vehicle integrated in a two-stage towing arrangement. A nonlinear Lyapunov-based output feedback controller is designed to operate in the presence of plant parameter uncertainty and proven to regulate pitch, yaw, and depth tracking errors to zero. When subjected to bounded external disturbances, the tracking errors converge to a neighborhood of the origin that can be made arbitrarily small. In the implementation proposed, a nonlinear observer is used to estimate the linear velocities used by the controller. The results obtained with computer simulations including sea wave driven disturbances and sensor noise, show that the controlled system exhibits good performance about different operating conditions and holds considerable potential for oceanographic missions that require simultaneous depth and attitude control.

Output feedback control design for station keeping of AUVs under shallow water wave disturbances

AbstractIn this paper, we consider the problem of autonomous underwater vehicle (AUV) station keeping (SK) in shallow water area. During SK, an AUV is required to maintain position and orientation with respect to a fixed reference point at the sea floor. When AUV operates in shallow water, high‐frequency disturbances due to waves will significantly affect the motion of the AUV. In order to derive wave disturbance information for control purposes, a nonlinear observer is first designed to estimate the shallow water wave velocities and AUV relative velocities by using position and attitude measurement. Using the observer estimates, a nonlinear output feedback controller is subsequently synthesized by applying observer backstepping technique. Global exponential stability (GES) of the proposed nonlinear observer–controller design is proved through Lyapunov stability theory. Simulation studies on a model based on an actual AUV were performed to verify the performance of the proposed nonlinear observer and output feedback controller. Copyright © 2008 John Wiley & Sons, Ltd.

Non-linear output feedback tracking control for AUVs in shallow wave disturbance condition

This article presents a non-linear output feedback tracking controller deisgn for autonomous underwater vehicles (AUVs) operating in shallow water area. In a shallow water environment, significant disturbances due to shallow water waves affect the motion of marine vehicles greatly. Since it is not energy efficient to counteract the oscillatory disturbances due to waves, it is critical to obtain the wave information or wave induced disturbance information and design an energy efficient controller to reduce the action of actuators to counteract wave disturbances to avoid wear and tear on actuators. In this article, a non-linear observer is first designed to estimate the low frequency (LF) motion of AUVs and to filter out wave-frequency (WF) motion of AUVs due to shallow water wave by using position and attitude measurements. Based on the designed observer, a non-linear output feedback controller is subsequently derived by using the observer backstepping technique. By using this approach, the AUV achieves global exponential tracking without excessive energy consumption to counteract the wave disturbance and also avoids excessive wear and tear on thrusters. Global exponential stability (GES) of overall observer-controller system is proved through Lyapunov stability theory. A set of simulations is carried out by using the KAMBARA (Silpa-Anan 2001) AUV model to demonstrate the performance of the proposed observer and output feedback controller.

An adaptive nonlinear output feedback controller using dynamic bounding with an aircraft control application

AbstractAn adaptive output feedback control scheme is developed for a class of nonlinear systems with uncertain nonlinearities, which are bounded by both static and dynamic functions of the system output, and with actuator failures whose failure time instants, patterns and values are unknown, as motivated from an aircraft flight control application. An adaptive backstepping control law using dynamic bounding is constructed to deal with unknown actuator failures as well as system parameter and dynamics uncertainties to guarantee desired system performance. Complete stability and performance analysis and illustrative simulation results of an application to aircraft flight control are presented. Copyright © 2008 John Wiley & Sons, Ltd.

Dynamic output feedback covariance control of stochastic dissipative partial differential equations

In this work, we develop a method for dynamic output feedback covariance control of the state covariance of linear dissipative stochastic partial differential equations (PDEs) using spatially distributed control actuation and sensing with noise. Such stochastic PDEs arise naturally in the modeling of surface height profile evolution in thin film growth and sputtering processes. We begin with the formulation of the stochastic PDE into a system of infinite stochastic ordinary differential equations (ODEs) by using modal decomposition. A finite-dimensional approximation is then obtained to capture the dominant mode contribution to the surface roughness profile (i.e., the covariance of the surface height profile). Subsequently, a state feedback controller and a Kalman–Bucy filter are designed on the basis of the finite-dimensional approximation. The dynamic output feedback covariance controller is subsequently obtained by combining the state feedback controller and the state estimator. The steady-state expected surface covariance under the dynamic output feedback controller is then estimated on the basis of the closed-loop finite-dimensional system. An analysis is performed to obtain a theoretical estimate of the expected surface covariance of the closed-loop infinite-dimensional system. Applications of the linear dynamic output feedback controller to both the linearized and the nonlinear stochastic Kuramoto–Sivashinsky equations (KSEs) are presented. Finally, nonlinear state feedback controller and nonlinear output feedback controller designs are also presented and applied to the nonlinear stochastic KSE.

Nonlinear Output Feedback Control for Linear Systems with Input Saturation

In this paper, nonlinear output feedback control design for linear systems subject to input saturation is addressed. Main issues of this paper are 1. stability analysis of the feedback system for both of state and output feedback and 2. design of stabilizing nonlinear feedback law. Sufficient global stability conditions for both of state and output feedback are derived. Furthermore, a design approach based on analytical solution of partial differential equations is proposed. It is shown that a class of feedback laws can be explicitly obtained, which is parameterized by nonlinear functions.

Robust nonlinear output feedback control for brake by wire control systems

This work proposes a nonlinear output feedback control law for active braking control systems. The control law guarantees bounded control action and can cope also with input constraints. Moreover, the closed-loop system properties are such that the control algorithm allows to detect—without the need of a friction estimator—if the closed-loop system is operating in the unstable region of the friction curve, thereby allowing to enhance both braking performance and safety. The design is performed via Lyapunov-based methods and its effectiveness is assessed via simulations on a multibody vehicle simulator.

Unified stabilizing controller synthesis approach for discrete-time intelligent systems with time delays by dynamic output feedback

A novel model, termed the standard neural network model (SNNM), is advanced to describe some delayed (or non-delayed) discrete-time intelligent systems composed of neural networks and Takagi and Sugeno (T-S) fuzzy models. The SNNM is composed of a discrete-time linear dynamic system and a bounded static nonlinear operator. Based on the global asymptotic stability analysis of the SNNMs, linear and nonlinear dynamic output feedback controllers are designed for the SNNMs to stabilize the closed-loop systems, respectively. The control design equations are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms to determine the control signals. Most neural-network-based (or fuzzy) discrete-time intelligent systems with time delays or without time delays can be transformed into the SNNMs for controller synthesis in a unified way. Three application examples show that the SNNMs not only make controller synthesis of neural-network-based (or fuzzy) discrete-time intelligent systems much easier, but also provide a new approach to the synthesis of the controllers for the other type of nonlinear systems.

Handling sensor malfunctions in control of particulate processes

This work focuses on feedback control of particulate processes in the presence of sensor data losses. Two typical particulate process examples, a continuous crystallizer and a batch protein crystallizer, modeled by population balance models (PBMs), are considered. In the case of the continuous crystallizer, a Lyapunov-based nonlinear output feedback controller is first designed on the basis of an approximate moment model and is shown to stabilize an open-loop unstable steady-state of the PBM in the presence of input constraints. Then, the problem of modeling sensor data losses is investigated and the robustness of the nonlinear controller with respect to data losses is extensively investigated through simulations. In the case of the batch crystallizer, a predictive controller is first designed to obtain a desired crystal size distribution at the end of the batch while satisfying state and input constraints. Subsequently, we point out how the constraints in the predictive controller can be modified as a means of achieving constraint satisfaction in the closed-loop system in the presence of sensor data losses.

Output Feedback Stabilization of Linear Systems With Actuator Saturation

The note presents a method for designing an output feedback law that stabilizes a linear system subject to actuator saturation with a large domain of attraction. This method applies to general linear systems including strictly unstable ones. A nonlinear output feedback controller is first expressed in the form of a quasi-LPV system. Conditions under which the closed-loop system is locally asymptotically stable are then established in terms of the coefficient matrices of the controller. The design of the controller (coefficient matrices) that maximizes an estimate of the domain of attraction is then formulated and solved as an optimization problem with LMI constraints

Evaluation study of an efficient output feedback nonlinear model predictive control for temperature tracking in an industrial batch reactor

The paper illustrates the benefits of nonlinear model predictive control (NMPC) for the setpoint tracking control of an industrial batch polymerization reactor. Real-time feasibility of the on-line optimization problem from the NMPC is achieved using an efficient multiple shooting algorithm. A real-time formulation of the NMPC that takes computational delay into account is described. The control relevant model for the NMPC is derived from the complex-first principles model and is fitted to the experimental data using maximum likelihood estimation. A parameter adaptive extended Kalman filter (PAEKF) is used for state estimation and on-line model adaptation. The performance of the NMPC implementation is assessed via simulation and experimental results.

Congestion control in compartmental network systems

In many practical applications of control engineering, the dynamical system under consideration is described by a compartmental network system. This means that the system is governed by a law of mass conservation and that the state variables are constrained to remain non-negative along the system trajectories. In such systems, network congestion arises when the inflow demand exceeds the throughput capacity of the network. When congestion occurs, some links of the network are saturated with the undesirable consequence that there is an overflow of some compartments. Our contribution in this paper is to show that congestion can be automatically prevented by using a nonlinear output feedback controller having an appropriate compartmental structure.

Two-degree-of-freedom output feedback controllers for nonlinear processes

In this work, a nonlinear output feedback control algorithm is proposed, in the spirit of model-state feedback control. The structure provides state estimates using a process model, the measured output, and the residual between the model output and the measured output. These estimates will track the process states at a rate determined by a set of tunable parameters. An algebraic transformation of the state estimates is incorporated in the control structure to ensure that the input/output gain of the observer matches the model upon which the static state feedback control law is based. The transformed states are then used in the control law. This leads to a controller of minimal order possessing integral action. The control structure is shown to have the same properties as the standard model-state feedback structure. The resulting algorithm is a two-degree of freedom control law, in the sense that the control action is not a function of the error only, but the output and the set point are processed in different ways. Finally, a simulation example using an exothermic CSTR operating at an open-loop unstable steady state is used to demonstrate the closed-loop performance of the proposed method.

NONLINEAR OUTPUT FEEDBACK CONTROL OF A 5DOF AMB SYSTEM

A nonlinear dynamic output feedback control method for a 5-degree-of-freedom AMB is presented in this paper. This method is based on the system structure of AMB and a quadratic-like Lyapunov function. It is shown that backstepping and completing square techniques enable the construction of the voltage input by using measured output only. The control law guarantees the asymptotic stability of the closed loop system.

Computing Output Feedback Controllers to Enlarge the Domain of Attraction in Polynomial Systems

The problem of computing controllers to enlarge the domain of attraction (DA) of equilibrium points of polynomial systems is considered. In order to deal with such a problem, a technique for computing static nonlinear output feedback controllers, which maximize the largest estimate of the DA (LEDA) induced by a given polynomial Lyapunov function, is proposed. The main contribution of the note is to show that a lower bound of the maximum achievable LEDA and a corresponding controller can be obtained through linear matrix inequality optimizations. Moreover, a necessary condition for tightness of this lower bound is presented, which is also a sufficient condition to establish the tightness of the lower bound of the LEDA for a given controller.