Finite-time Observer Research Articles

Multivariable uniform finite-time output feedback reentry attitude control for RLV with mismatched disturbance

A continuous multivariable uniform finite-time output feedback reentry attitude control scheme is developed for Reusable Launch Vehicle (RLV) with both matched and mismatched disturbances. A novel finite-time controller is derived using the bi-limit homogeneous technique, which ensures that the attitude tracking can be achieved in a uniformly bounded convergence time from any initial states. A multivariable uniform finite-time observer is designed based on an arbitrary order robust sliding mode differentiator to estimate the unknown states and the external disturbances, simultaneously. Then, an output feedback control scheme is established through the combination of the developed controller and the observer. A rigorous proof of the uniform finite-time stability of the closed-loop system is presented using Lyapunov and homogeneous techniques. Finally, numerical simulation is provided to demonstrate the efficiency of the proposed scheme.

Attitude stabilization of flapping micro-air vehicles via an observer-based sliding mode control method

This paper introduces an observer-based sliding mode control strategy for stabilizing the attitude of flapping micro-air vehicles in the presence of unknown uncertainties and external disturbances. First, a finite-time observer is designed to estimate the lumped disturbances. Next, a controller is developed to provide attitude stabilization with high robustness where the lumped disturbances could be completely rejected after a finite amount of time. The stability of the closed-loop system is rigorously proven. By employing MATLAB/Simulink software, a numerical simulation example including a comparison between the proposed method and a conventional sliding mode controller is provided to illustrate the effectiveness of the proposed method and to confirm the theoretical results.

Distributed Finite-Time State Estimation of Interconnected Complex Metabolic Networks

A set of distributed robust finite-time state observers was developed and tested to estimate the main biochemical substances in interconnected metabolic networks with complex structure. The finite-time estimator was designed by composing several supertwisting based step-by-step state observers. This segmented structure was proposed accordingly to the partition of metabolic network obtained as a result of applying the observability analysis of the model used to represent metabolic networks. The observer was developed under the assumption that a sufficient and small number of intracellular compounds can be obtained by some feasible analytic techniques. These techniques are enlisted to demonstrate the feasibility of designing the proposed observer. A set of numerical simulations was proposed to test the observer design over the hydrogen producing metabolic behavior of Escherichia coli. The numerical evaluations showed the superior performance of the observer (on recovering immeasurable state values) over classical approaches (high gain). The variations of internal metabolites inserted in the hydrogen productive metabolic networks were collected from databases. This information supplied to the observer served to validate its ability to recover the time evolution of nonmeasurable metabolites.

Finite Time Estimation via Piecewise Constant Measurements

We study a broad class of linear continuous-time time-varying systems that contain piecewise continuous disturbances and piecewise constant outputs. Under an observability assumption, we construct a new type of observer to estimate the state of the system in a predetermined finite time in the presence of the disturbances. In contrast to the well-established finite time observer design techniques which estimate the system state using a continuous output, our proposed observer only requires a piecewise constant output. Our simulations illustrate the efficacy of our observer.

Finite-Time Observer Based Guidance and Control of Underactuated Surface Vehicles With Unknown Sideslip Angles and Disturbances

Suffering from complex sideslip angles, path following control of an under actuated surface vehicle (USV) becomes significantly challenging and remains unresolved. In this paper, a finite-time observer based guidance and control (FOGC) scheme for path following of an USV with time-varying and large sideslip angles and unknown external disturbances is proposed. The salient features of the proposed FOGC scheme are as follows: 1) time-varying large sideslip angle is exactly estimated by a finite-time sideslip observer, and thereby contributing to the sideslip-tangent line-of-sight guidance law which significantly enhances the robustness of the guidance system to unknown sideslip angles which are significantly large and time-varying; 2) a finite-time disturbance observer (FDO) is devised to exactly observe unknown external disturbances, and thereby implementing FDO-based surge and heading robust tracking controllers, which possess remarkable tracking accuracy and precise disturbance rejection, simultaneously; and 3) by virtue of cascade analysis and Lyapunov approach, global asymptotic stability of the integrated guidance-control system is rigorously ensured. Simulation studies and comparisons are conducted to demonstrate the effectiveness and superiority of the proposed FOGC scheme.

Finite-Time Attitude Trajectory Tracking Control of Rigid Spacecraft

In this paper, we investigate the finite-time attitude tracking control problem for a rigid spacecraft on the special orthogonal group ( $SO(3)$ ). The exponential coordinates, derived from the exponential and logarithmic maps of Lie group, are utilized to describe the attitude tracking error on $SO(3)$ almost globally unique except for a zero measure set on which the logarithmic map is double valued. To avoid this issue, a novel nonsingular sliding surface is designed to guarantee that the attitude tracking error will never reach the zero measure set and provide fixed-time stability during the sliding phase. Then, a novel continuous second-order sliding mode control scheme is developed to force the system state to reach the desired sliding surface in finite time. The salient feature of the proposed control scheme is that it significantly suppresses the chattering phenomenon. In addition, to address the lack of angular velocity measurements, a finite-time observer is proposed to recover the unknown angular velocity information in finite time. Then, an observer-based finite-time output feedback control strategy is obtained. Finally, numerical simulations are presented to demonstrate the effectiveness of the proposed control scheme.

Novel disturbance-observer-based control for systems with high-order mismatched disturbances

ABSTRACTA novel disturbance-observer-based control method is investigated to attenuate the high-order mismatched disturbances. First, a finite-time disturbance observer (FTDO) is proposed to estimate the disturbances as well as the derivatives. By incorporating the outputs of FTDO, the original system is then reconstructed, where the mismatched disturbances are transformed to the matched ones that are compensated by feed-forward algorithm. Moreover, a feedback control law is developed to achieve the stability and tracking performance requirements for the systems. Finally, the proposed composite control method is applied to an unmanned helicopter system. The simulation results demonstrate that the proposed control method exhibits excellent control performance in the presence of high-order matched and mismatched disturbances.

Finite-time estimation for linear time-delay systems via homogeneous method

ABSTRACTThis paper presents a finite-time observer for linear time-delay systems with commensurate delay. Unlike the existing observers in the literature which converge asymptotically, the proposed observer provides a finite-time estimation. This is realised by using the well-known homogeneous technique, and the results are also extended to investigate the estimation problem for linear time-delay systems with unknown inputs. Simulation results are presented in order to illustrate the feasibility of the proposed method.

Finite Time Estimation for Switched Nonlinear Systems: Application to Stirred Tank Bioreactor

Abstract This work presents the design of a class of finite time observer applied to a nonlinear switched system. The proposed observer is applied to a stirred batch anaerobic bioreactor, described by classic mass balances, where a sulfate-reducing process took place and kinetic regimen alteration is induced by a change in the carbon source. The proposed observer has a simple structure and under an adequate choosing of the observer´s gain the proposed methodology cancels the upper bounds of the system under the different kinetic regimens inducing the required finite time convergence. The performance of the proposed observer is showed via numerical simulations and for comparison purposes a sliding-mode observer is also implemented, both of them are conducted and experimentally corroborated. The convergence of the observer is done with a simple analysis of the estimation error dynamic equations for all the corresponding subspaces and is showed that the convergence of the estimator is reached under the required conditions.

Finite-time stabilization of port-controlled Hamiltonian systems with nonvanishing disturbances

This paper concerns the problem of finite-time stabilization of nonlinear port-controlled Hamiltonian systems subject to nonvanishing disturbances via a composite control manner. The composite controller is developed by combining the damping injection, the finite-time feedback control and the finite-time disturbance observer techniques. The key idea is that a finite-time disturbance observer is designed to estimate disturbances and the estimation of disturbances is employed to feedforward compensate the disturbances. Finite-time stability analysis for the augmented system is presented. An example of a nonlinear circuit system with simulation results demonstrates the effectiveness of the proposed method.

Leader-following control of high-order multi-agent systems under directed graphs: Pre-specified finite time approach

In this work we address the full state finite-time distributed consensus control problem for high-order multi-agent systems (MAS) under directed communication topology. Existing protocols for finite time consensus of MAS are normally based on the signum function or fractional power state feedback, and the finite convergence time is contingent upon the initial conditions and other design parameters. In this paper, by using regular local state feedback only, we present a distributed and smooth finite time control scheme to achieve leader–follower consensus under the communication topology containing a directed spanning tree. The proposed control consists of a finite time observer and a finite time compensator. The salient feature of the proposed method is that both the finite time intervals for observing leader states and for reaching consensus are independent of initial conditions and any other design parameters, thus can be explicitly pre-specified. Leader-following problem of MAS with both single and multiple leaders are studied.

Finite-time observer based accurate tracking control of a marine vehicle with complex unknowns

In this paper, a finite-time observer based accurate tracking control (FO-ATC) scheme is addressed for trajectory tracking of a marine vehicle (MV) with complex unknowns including unmodeled dynamics and disturbances. Main contributions are as follows: (1) An accurate tracking control (ATC) scheme is first proposed for a nominal MV tracking system with known dynamics, such that global finite-time stability of can be ensured to achieve fast convergence and precise tracking performance; (2) To exactly attenuate external disturbances, a finite-time disturbance observer (DO) is incorporated into the ATC framework, and establishes the DO-based ATC (DO-ATC) scheme which therefore produces strong disturbance rejection in addition to accurate trajectory tracking; (3) Aiming to precisely identify completely unknown dynamics together with external disturbances, simultaneously, a finite-time unknown observer (UO) is further created within the ATC approach, and thereby contributing to the UO-based ATC (UO-ATC) scheme which eventually achieves accurate trajectory tracking of an MV with fully unknown dynamics under harsh marine environment. Simulation studies and comprehensive comparisons are exhaustively provided to demonstrate the effectiveness and superiority of the proposed ATC schemes.

Observer-Based Fault-Tolerant Attitude Control for Rigid Spacecraft

This paper addresses the problem of robust fault-tolerant control of spacecraft attitude stabilization in the presence of model uncertainties, actuator failures, and external disturbances simultaneously. Utilizing the fast nonsingular terminal sliding mode control technique, a novel finite-time extended state observer is first proposed to estimate and compensate for the specified synthetic uncertainties derived from actuator failures and/or model deviations. And also the detailed derivations of the observer are provided, along with a thorough analysis for the associated ultimately bounded stability and estimation error convergence property in the sense of finite-time control. Then, with the reconstructed information achieving from the finite-time observer, an adaptive robust sliding mode based fault-tolerant control approach is developed to ensure that the closed-loop attitude control system reach the real sliding mode surface in finite time. Meanwhile, the chattering problem has been restrained via the modified gain adjusting law. The key feature of the proposed strategies is that the whole closed-loop fault-tolerant control system can be guaranteed theoretically to be finite-time stable by the development of Lyapunov methodology. Finally, numerical simulation results are presented to illustrate and highlight the fine performance benefits obtained using the proposed schemes.

Distributed finite-time trajectory tracking control for multiple nonholonomic mobile robots with uncertainties and external disturbances

ABSTRACTThis paper investigates the distributed finite-time trajectory tracking control for a group of nonholonomic mobile robots with time-varying unknown parameters and external disturbances. At first, the tracking error system is derived for each mobile robot with the aid of a global invertible transformation, which consists of two subsystems, one is a first-order subsystem and another is a second-order subsystem. Then, the two subsystems are studied respectively, and finite-time disturbance observers are proposed for each robot to estimate the external disturbances. Meanwhile, distributed finite-time tracking controllers are developed for each mobile robot such that all states of each robot can reach the desired value in finite time, where the desired reference value is assumed to be the trajectory of a virtual leader whose information is available to only a subset of the followers, and the followers are assumed to have only local interaction. The effectiveness of the theoretical results is finally illustrated by numerical simulations.

Adaptive reaching law based three-dimensional finite-time guidance law against maneuvering targets with input saturation

Considering the problem of a missile intercepting a maneuvering target with impact angles constraints, three-dimensional engagement dynamics are established in this paper. Then two finite-time guidance laws are proposed based on the coupled dynamics. The first finite-time anti-saturation guidance law is designed using the finite-time observer. Besides, this guidance law uses the exponential reaching law, which requires the upper bounds of observation errors. Therefore, to solve the defects existing in the exponential reaching law, a novel reaching law is proposed, which can accelerate the convergence rate of sliding mode surfaces and weaken the chattering phenomenon. Moreover, it can be widely used in the design of sliding mode controllers. Next, based on the novel reaching law, the second finite-time guidance law is given without the knowledge of the upper bounds of observation errors. Numerical simulations are introduced to demonstrate the effectiveness and superiority of the designed composite guidance laws in theory.

Robust control of post-stall pitching maneuver based on finite-time observer

This article presents a robust finite-time maneuver control scheme for the longitudinal attitude dynamic of the aircraft with unsteady aerodynamic disturbances and input saturation. To efficiently eliminate the influence of unsteady aerodynamic disturbances, nonlinear finite-time observers are developed. Despite the existence of the nonlinearity and the coupling between aircraft states and unsteady aerodynamic disturbances, the proposed observers can still precisely estimate the unmeasurable unsteady aerodynamic disturbances in finite time. To attenuate the effect caused by input saturation, a finite-time auxiliary system is constructed. With the error between the desired control input and saturation input as the input of the auxiliary system, the additional signals are generated to compensate for the effect of input saturation. Combined with the finite-time observers and the finite-time auxiliary system, a robust finite-time backstepping attitude control design is developed. The finite-time convergence of all closed-loop system signals is rigorously proved via Lyapunov analysis method under the developed robust attitude control schemes. Finally, simulation results are presented to illustrate the effectiveness of the proposed attitude control approaches.

A Deadbeat Observer for Two and Three-dimensional LTI Systems by a Time/Output-Dependent State Mapping

The problem of deadbeat state reconstruction for non-autonomous linear systems has been solved since several decades, but all the architectures formulated since now require either high-gain output injection, which amplifies measurement noises (e.g., in the case of sliding-mode observers), either state augmentation, which yields a non-minimal realization of the deadbeat observer (e.g., in the case of integral methods and delay-based methods). In this context, the present paper presents, for the first time, a finite-time observer for continuous-time linear systems enjoying minimal linear-time-varying dynamics, that is, the observer has the same order of the observed system. The key idea behind the proposed method is the introduction of an almost-always invertible time/output-dependent state mapping which allows to recast the dynamics of the system in a new observer canonical form whose initial conditions are known.

Tracking consensus for nonlinear heterogeneous multi-agent systems subject to unknown disturbances via sliding mode control**Project supported by the National Natural Science Foundation of China (Grant No. 61203142) and the Natural Science Foundation of Hebei Province, China (Grant Nos. F2014202206 and F2017202009).

We investigate the tracking control for a class of nonlinear heterogeneous leader–follower multi-agent systems (MAS) with unknown external disturbances. Firstly, the neighbor-based distributed finite-time observers are proposed for the followers to estimate the position and velocity of the leader. Then, two novel distributed adaptive control laws are designed by means of linear sliding mode (LSM) as well as nonsingular terminal sliding mode (NTSM), respectively. One can prove that the tracking consensus can be achieved asymptotically under LSM and the tracking error can converge to a quite small neighborhood of the origin in finite time by NTSM in spite of uncertainties and disturbances. Finally, a simulation example is given to verify the effectiveness of the obtained theoretical results.

Fixed-time observer with simple gains for uncertain systems

In this article, we consider the problem of fixed-time observer for nonlinear systems, that is a finite-time observer whose settling time can be bounded independently of the initial condition. We consider a large class of nonlinear systems which includes two main classes: linearizable systems up to input–output injection and uniformly observable systems. Furthermore, the effect of noise and uncertainty is analyzed.

Distributed MPC-Based Secondary Voltage Control Scheme for Autonomous Droop-Controlled Microgrids

In this study, we propose a novel distributed secondary control scheme for both voltage and frequency in autonomous microgrids. By incorporating predictive mechanisms into distributed generations, the secondary voltage control is converted to a tracker consensus problem of distributed model predictive control, with the synchronous convergence procedure for voltage magnitudes to the reference value drastically accelerated at a low communication cost. A sufficient local stability condition with the parameter analysis is established. Thus, a distributed proportional integral method combined with a finite-time observer to estimate the global reference information is presented in the frequency restoration while maintaining accurate active power sharing. Our approach accommodates model uncertainty, plug-and-play capability, and especially robustness against information update intervals, which is essential when the conventional method probably yields toward a poor performance. Meanwhile, the distributed architecture implemented on the local and neighboring information allows for a sparse communication network and eliminates the requirement for a centralized controller. Simulation results are provided to verify the effectiveness of the proposed control methodology.