Nonlinear Output Feedback Research Articles

Passivity control with practically finite-time convergence for large space structures

A nonlinear output feedback control law based on passivity is proposed to reduce the vibration of large space structures. The considered system is assumed to be equipped with collocated actuators and sensors. The concept of practically finite-time stability is first developed to describe the finite-time convergence of a passive system. Then, an output feedback is introduced to drive the trajectories of a passive system into a small set around the origin in finite time. Finally, the proposed control strategy is applied to the vibration suppression of large space structures with distributed thrusters and velocity sensors or torque outputting devices and angular rate sensors. Numerical simulations are conducted to validate the effectiveness of the proposed controller.

Output regulation of output feedback systems with unknown exosystem and unknown high-frequency gain sign

This paper discusses the global robust output regulation problem for a class of nonlinear output feedback systems. It is assumed that the exosystem and the high-frequency gain sign are unknown and that the unknown parameters can be arbitrarily large. To solve this problem, two major challenges are to be overcome. First, the concurrence of the unknown exosystem and the unknown high-frequency gain sign cannot be handled merely by designing estimators for the two unknown parameters respectively. Second, the conventional extended matching design approach cannot be directly implemented, owing to the arbitrarily large unknown parameters. To cope with these difficulties, a new estimator is developed, and the extended matching design approach is modified to obtain a suitable update law for the estimator. The effectiveness of the proposed adaptive controller is illustrated by an example.

Distributed adaptive consensus control of nonlinear output-feedback systems on directed graphs

This paper deals with consensus control in leader–follower format of a class of network-connected uncertain nonlinear systems by output feedback. Each subsystem is in the nonlinear output feedback form with unknown parameters, and the connection graph among the subsystems is directed. Distributed adaptive control inputs are designed to achieve the consensus control in the sense that the subsystem states asymptotically follow the subsystem at node 0 with no input, which is also known as the leader. The proposed adaptive control only uses relative output measurements and the local information of the connection to each subsystem, and hence the proposed adaptive control is fully distributed. The proposed scheme is different from the consensus output regulation schemes literature, and the leader plays a similar role as a reference model in the classic model reference adaptive control.

Dynamic anti-windup design for a class of nonlinear systems

ABSTRACTThis work addresses the dynamic anti-windup design problem for a class of nonlinear systems subject to actuator saturation. The considered class regards the systems that can be cast in a differential algebraic representation (DAR), such as rational and polynomial systems. Considering that a nonlinear dynamic output feedback controller, which can also be written as a DAR, has been designed to stabilise the nonlinear system disregarding the saturation effects, LMI-based conditions are proposed to compute a stabilising dynamic anti-windup compensator. Two problems are considered: the first one regards the regional internal stabilisation; and the second one, assuming that an energy-bounded disturbance acts on the system, concerns the input-to-state stability. The derived conditions can therefore be incorporated in convex optimisation problems that allow to compute the anti-windup compensator in order to maximise the region of guaranteed asymptotic stability, to maximise a bound on the admissible -norm of the disturbance or even to minimise a bound on the -gain between the disturbance and the output. Numerical examples illustrate the proposed methods.

Nonlinear -control under unilateral constraints

ABSTRACTThe primary concern of the work is robust control of hybrid mechanical systems under unilateral constraints of co-dimension one. Sufficient conditions for a local solution of the underlying control problem to exist are given in terms of the appropriate solvability of Hamilton–Jacobi–Isaacs partial differential inequalities, coupled to an extra condition on the plant reset in the closed loop. Nonlinear output feedback synthesis is thus developed in the hybrid setting, covering collision phenomena. Robustness issues of the proposed synthesis are numerically investigated in a benchmark application where the regulation and orbital stabilisation of a simple pendulum, impacting a barrier, illustrate the capability of the proposed approach via position feedback design. Good performance is achieved despite imperfect measurements and the presence of both external disturbances, affecting the collision-free motion phase, and uncertainties that occur in the collision phase.

Smooth dynamic output feedback control for multiple time-delay systems with nonlinear uncertainties

The dynamic output feedback control problem is considered for a class of systems with multiple time delays and nonlinear uncertainties. Based on the control input matrix and output matrix, we decompose the system into two subsystems. The dynamic compensator is designed for the first subsystem, and then the output feedback controller is constructed based on the compensator and the second subsystem. By using the introduced new Lyapunov–Krasovskii functional, we show that the solution of the resultant closed-loop system converges exponentially to an adjustable bounded region. Compared with the previous works, the developed controller in this paper is memoryless and smooth, which only uses the system output. The control design conditions are relaxed because of the developed dynamic compensator. The result is further extended to the general nonlinear case. The corresponding dynamic nonlinear output feedback control method is proposed. Finally, simulations are performed to show the potential of the proposed methods.

Output regulation of nonlinear output feedback systems with exponential parameter convergence

This paper revisits the global robust output regulation (GROR) problem of nonlinear output feedback systems with uncertain exosystems by error output feedback control. The problem was conventionally tackled by employing a linear canonical internal model and as a result, suitable adaptive stabilization has to be done for the augmented system to achieve output regulation. Distinguished from that, a novel nonlinear internal model approach is developed in the present study that successfully converts the GROR problem into a robust non-adaptive stabilization problem for the augmented system. The feature of the new approach is two-fold. On one hand, stabilization of augmented system is disentangled from any extra adaptive control law and thus the procedure is simplified. On the other hand, it leads to explicit strict Lyapunov characterization for the closed-loop system and consequently assures exponential parameter convergence.

Nonlinear output feedback and periodic disturbance attenuation for setpoint tracking of a combustion engine test bench

The quality of control actions depends strongly on the availability and the quality of signals to construct the controller. While most control design tools assume all states, hence signals, are measurable, this is often unrealistic. An observer is often necessary to provide signals to use in controller realization. This paper proposes the construction of a reduced order observer and an output feedback controller to solve a set point tracking problem of a combustion engine test bench modeled as an extended Hammerstein system. The asymptotic convergence of the observer is shown and separation principle is also proved. Because in real practice the measured signals are often affected by periodic disturbance due to the combustion oscillations, the controller is extended with an internal model based filter, to remove the effect of the periodic disturbance. Some simulation results are presented, comparing the performance of the proposed output feedback with the state feedback controller.

A Nonlinear Gain-Scheduling Compensation Approach Using Parameter-Dependent Lyapunov Functions

This paper addresses the gain-scheduling control design for nonlinear systems to achieve output regulation. For gain-scheduling control, the linear parameter-varying (LPV) model is obtained by linearizing the plant about zero-error trajectories upon which an LPV controller is based. A key in this process is to find a nonlinear output feedback compensator such that its linearization matches with the designed LPV controller. Then, the stability and performance properties of LPV control about the zero-error trajectories can be inherited when the nonlinear compensator is implemented. By incorporating the exosystem, nominal input, and measured output information into the LPV model, the LPV control synthesis problem is formulated as linear matrix inequalities (LMIs) using parameter-dependent Lyapunov functions (PDLFs). Moreover, explicit formulae for the construction of the nonlinear gain-scheduled compensator have been derived to meet the linearization requirement. Finally, the validity of the proposed nonlinear gain-scheduling control approach is demonstrated through a ball and beam example.

A comparative study of semi-active control strategies for base isolated buildings

A comparative analytical study of several control strategies for semi-active (SA) devices installed in baseisolated buildings aiming to reduce earthquake induced vibrations is presented. Three force tracking schemes comprising a linear controller plus a “clipped” algorithm and a nonlinear output feedback controller (NOFC) are considered to tackle this problem. Linear controllers include the integral controller (I), the linear quadratic regulator (LQR) and the model predictive controller (MPC). A single degree-of-freedom system subjected to input accelerograms representative of the Portuguese seismic actions are first used to validate and evaluate the feasibility of these strategies. The obtained results show that structural systems using SA devices can in general outperform those equipped with passive devices for lower fundamental frequency structural systems, namely base-isolated buildings. The effectiveness of the proposed strategies is also evaluated on a 10 storey base-isolated dual frame-wall building. The force tracking scheme with an integral controller outperforms the other three as well as the original structure and the structure equipped with passive devices.

Nonlinear Adaptive Output-Feedback Controller Design for Guidance of Flexible Needles

In this paper, a control methodology is proposed for guiding and stabilizing flexible bevel-tip needles to an arbitrary planar slice. The proposed controller is an adaptive version of the previously proposed nonlinear output feedback controller, which was built upon the well-known nonholonomic kinematic model of needle steering. On the grounds that such a model is subject to parametric uncertainty, an adaptive controller is necessary for adjusting the model parameters. In addition, a nonlinear observer is required due to the existence of some unmeasurable state variables. Although the original form of the studied system is linearly parameterized, its canonical form is not, preventing the application of conventional adaptive control schemes. In this paper, a nonlinear adaptive control methodology is proposed and applied to the guidance problem of steerable needles. Through simulation results, it is illustrated that the proposed methodology greatly outperforms the existing feedback linearization-based approach.

Output feedback dynamic surface controller design for airbreathing hypersonic flight vehicle

This paper addresses issues related to nonlinear robust output feedback controller design for a nonlinear model of airbreathing hypersonic vehicle. The control objective is to realize robust tracking of velocity and altitude in the presence of immeasurable states, uncertainties and varying flight conditions. A novel reduced order fuzzy observer is proposed to estimate the immeasurable states. Based on the information of observer and the measured states, a new robust output feedback controller combining dynamic surface theory and fuzzy logic system is proposed for airbreathing hypersonic vehicle. The closedloop system is proved to be semi-globally uniformly ultimately bounded (SUUB), and the tracking error can be made small enough by choosing proper gains of the controller, filter and observer. Simulation results from the full nonlinear vehicle model illustrate the effectiveness and good performance of the proposed control scheme.

Using Inverse Nonlinearities in Robust Output Feedback Guaranteed Cost Control of Nonlinear Systems

This paper extends the result of an earlier paper on constructive robust nonlinear output feedback controller design, which is based on the use of IQCs and minimax LQG control. In this paper, in addition to copies of the nonlinearities, we include copies of the inverses of the nonlinearities in the controller. Consequently more IQCs are exploited in the design procedure, which gives a smaller bound on the closed-loop cost function than the earlier result.

Nonlinear output feedback H∞-control of mechanical systems under unilateral constraints

The work focuses on the output feedback synthesis of hybrid mechanical systems under unilateral constraints. The problem of robust control of mechanical systems is addressed under unilateral constraints by designing a nonlinear state feedback H8-controller developed in the hybrid setting, covering impact phenomena. Performance issues of the developed nonlinear H8-tracking controller are illustrated with numerical tests on a mass-spring-damper system impacting against a barrier.

Nonlinear robust output feedback tracking control of a quadrotor UAV using quaternion representation

In this paper, a new quaternion-based nonlinear robust output feedback tracking controller is developed to address the attitude and altitude tracking problem of a quadrotor unmanned aerial vehicle which is subject to structural uncertainties and unknown external disturbances. By using the unit quaternion representation, the singularity associated with orientation representations can be avoided. A set of non-model-based filters are introduced to provide estimations for the unmeasurable angular velocities and translational velocity in the altitude direction of the quadrotor in the case that velocity feedback is unavailable. Approximation components based on neural network (NN) are introduced to estimate the modeling uncertainties, and robust feedback components are designed to compensate for external disturbances and NN reconstruction errors. The Lyapunov-based stability analysis is employed to prove that a semiglobally asymptotic tracking result is achieved and all the closed-loop states remain bounded. Numerical simulation results are provided to illustrate the good tracking performance of the proposed control methodologies.

Pattern Synchronization of Nonlinear Heterogeneous Multiagent Networks With Jointly Connected Topologies

In this paper, a decentralized control algorithm is proposed for a group of heterogeneous agents with nonlinear dynamics such that it achieves synchronization in diverse collective motion patterns. With the aid of a group of deliberately designed linear homogeneous reference models, the synchronization problem is converted into a class of regulation problem. The regulation problem is hence solved using the nonlinear output feedback control technique. The conversion and, hence, the decentralized synchronization algorithm are valid when the multiagent system is jointly connected in terms of its time-varying network topologies. The effectiveness of the algorithm is verified through theoretical analysis.

A New Robust Output Feedback Variable Structure Controller for Uncertain More Affine Nonlinear Systems with Mismatched Uncertainties and Matched Disturbance

In this note, a new robust nonlinear output feedback variable structure controller is first systematically and generally designed for the output control of more affine uncertain nonlinear systems with mismatched uncertainties and matched disturbance. A transformed integral output feedback sliding surface with a most simple form is applied in order to remove the reaching phase problems. The closed loop exponential stability and the existence condition of the sliding mode on the integral output feedback sliding surface is investigated with a corresponding output feedback control input in Theorem 1. For practical application the continuous implementation of the control input is made by the modified saturation function. The effectiveness of the proposed controller is verified through a design example and simulation study.

Nonlinear Adaptive Output Feedback Control of Flexible-Joint Space Manipulators with Joint Stiffness Uncertainties

Growing research interest in space robotic systems capable of accurately performing autonomous manipulation tasks within an acceptable execution time has led to an increased demand for lightweight materials and mechanisms. As a result, joint flexibility effects become important and represent the main limitation to achieving satisfactory trajectory-tracking performance. This paper addresses the nonlinear adaptive output feedback control problem for flexible-joint space manipulators. Composite control schemes in which decentralized simple adaptive control-based adaptation mechanisms to control the quasi-steady-state robot model are added to a linear correction term to stabilize the boundary-layer model are proposed. An almost strictly passivity-based approach is adopted to guarantee closed-loop stability of the quasi-steady-state model. Simulation results are included to highlight the performance and robustness of the proposed adaptive composite control methodologies to parametric and dynamics modeling uncertainties.

Partial Network Synchronization Using Diffusive Dynamic Couplings

Partial network synchronization is studied for a class of nonlinear oscillators interconnected through diffusive dynamic couplings. We construct diffusive dynamic couplings combining nonlinear observers and output feedback controllers. Sufficient conditions on the systems to be interconnected, on the network topology, on the observer dynamics, and on the coupling strength that guarantee (global) partial synchronization are derived. The results are illustrated by computer simulations of coupled Hindmarsh-Rose oscillators.

Distributed Wireless NetworkedH∞Control for a Class of Lurie-Type Nonlinear Systems

A new approach to solving the distributed control problem for a class of discrete-time nonlinear systems via a wireless neural control network (WNCN) is presented in this paper. A unified Lurie-type model termed delayed standard neural network model (DSNNM) is used to describe these nonlinear systems. We assume that all neuron nodes in WNCN which have limited energy, storage space, and computing ability can be regarded as a subcontroller, then the whole WNCN is characterized by a mesh-like structure with partially connected neurons distributed over a wide geographical area, which can be considered as a fully distributed nonlinear output feedback dynamic controller. The unreliable wireless communication links within WNCN are modeled by fading channels. Based on the Lyapunov functional and the S-procedure, the WNCN is solved and configured for the DSNNM to absolutely stabilize the whole closed-loop system in the sense of mean square with aH∞disturbance attenuation index using LMI approach. A numerical example shows the effectiveness of the proposed design approaches.