Manifold In Finite Time Research Articles

Extended state observer-based continuous finite time control for a fixed-wing vertical take-off and landing unmanned aerial vehicle

Dual system Vertical Take-Off and Landing (VTOL) fixed-wing Unmanned Aerial Vehicles (UAVs) combine the advantages of both the rotorcraft and fixed-wing UAV, characterizing horizontal and vertical flight capabilities. However, they face challenges such as aerodynamic coupling between propulsion systems, model uncertainty, and external disturbances, significantly deteriorating the tracking accuracy and robustness. This paper proposes an Extended State Observer based Continuous Finite-Time Control (ESO-CFTC) scheme to solve the attitude and trajectory tracking problem of such a VTOL fixed-wing UAV. Initially, the Nonsingular Fast Terminal Sliding Mode (NFTSM) controller guarantees the tracking errors reach a prescribed manifold in finite time with a continuous reaching law, then converge to the origin in finite time while avoiding singularities. To suppress the inherent chattering problem of the sliding mode control, an ESO technique is incorporated into the ESO-CFTC scheme, which is completely decoupled with the basic NFTSM controller. The supremum of the estimation residual set is derivated theoretically. The scheme forces the tracking errors to converge into the neighborhood of the origin in finite time without requiring prior knowledge of lumped disturbance supremum values. Finally, the numerical simulation results in a Matlab/Simulink environment demonstrate that the presented method outperforms existing benchmark in terms of disturbance estimation, tracking accuracy, convergence rate, and robustness.

Stable Spinning Deployment Control of a Triangle Tethered Formation System.

The tethered formation system has been widely studied due to its extensive use in aerospace engineering, such as Earth observation, orbital location, and deep space exploration. The deployment of such a multitethered system is a problem because of the oscillations and complex formation maintenance caused by the space tether's elasticity and flexibility. In this article, a triangle tethered formation system is modeled, and an exact stable condition for the system's maintaining is carefully analyzed, which is given as the desired trajectories; then, a new control scheme is designed for its spinning deployment and stable maintenance. In the proposed scheme, a novel second-order sliding mode controller is given with a designed nonsingular sliding-variable. Based on the theoretical proof, the addressed sliding variable from the arbitrary initial condition can converge to the manifold in finite time, and then sliding to the equilibrium in finite time as well. The simulation results show that compared with classic second sliding-mode control, the proposed scheme can speed up the convergence of the states and sliding variables.

Event-based distributed sliding mode formation control of multi-agent systems and its applications to robot manipulators

This article deals with the event-based distributed sliding mode formation control issue of leader-following multi-agent systems subject to uncertain perturbations. Firstly, a distributed linear sliding manifold that ensures the asymptotic convergence of the states of multi-agent systems is constructed. Secondly, based on the controller output signal, an event-triggered mechanism is put forward to weaken the demand of continuous monitoring. In spite of external disturbances, the distributed robust sliding mode formation protocol relied on an event-triggered condition can guarantee the closed-loop system to reach the preestablished sliding manifold in finite time and keep a desired formation pattern while eliminating the Zeno behavior. Thirdly, sufficient conditions are derived for the distributed formation control of multi-agent systems. Finally, a numerical example is given and a simulation is performed on the robotic manipulators systems to verify the effectiveness of the proposed strategy.

Complexity and efficiency of minimum entropy production probability paths from quantum dynamical evolutions.

We present an information geometric characterization of quantum driving schemes specified by su(2;C) time-dependent Hamiltonians in terms of both complexity and efficiency concepts. Specifically, starting from pure output quantum states describing the evolution of a spin-1/2 particle in an external time-dependent magnetic field, we consider the probability paths emerging from the parametrized squared probability amplitudes of quantum origin. The information manifold of such paths is equipped with a Riemannian metrization specified by the Fisher information evaluated along the parametrized squared probability amplitudes. By employing a minimum action principle, the optimum path connecting initial and final states on the manifold in finite time is the geodesic path between the two states. In particular, the total entropy production that occurs during the transfer is minimized along these optimum paths. For each optimum path that emerges from the given quantum driving scheme, we evaluate the so-called information geometric complexity (IGC) and our newly proposed measure of entropic efficiency constructed in terms of the constant entropy production rates that specify the entropy minimizing paths being compared. From our analytical estimates of complexity and efficiency, we provide a relative ranking among the driving schemes being investigated. Moreover, we determine that the efficiency and the temporal rate of change of the IGC are monotonic decreasing and increasing functions, respectively, of the constant entropic speed along these optimum paths. Then, after discussing the connection between thermodynamic length and IGC in the physical scenarios being analyzed, we briefly examine the link between IGC and entropy production rate. Finally, we conclude by commenting on the fact that an higher entropic speed in quantum transfer processes seems to necessarily go along with a lower entropic efficiency together with a higher information geometric complexity.

SMC for Semi-Markov Jump Cyber-Physical Systems Subject to Randomly Occurring Deception Attacks

This brief investigates the sliding mode control (SMC) for semi-Markov jump cyber-physical systems (S-MJCPSs) under randomly occurring deception attacks (RODA). It is assumed that the adversaries inject false data into the control signal in probability. First, a mode-dependent sliding surface is designed under the framework of integral form. Second, the criteria to ensure stochastic stability (SS) of the corresponding system are proposed, which establishes the theoretical framework of semi-Markov Lyapunov function. Third, an appropriate SMC law under attacks and uncertainties is constructed to drive the states of S-MJCPSs onto the switching manifold in finite time. Finally, the simulation study on a single-link robot arm model (SLRAM) is provided to demonstrate the obtained results.

A Continuous Multivariable Finite-Time Super-Twisting Attitude and Rate Controller for Improved Rotorcraft Handling

This paper synthesizes a continuous, multivariable, finite-time-convergent, super-twisting attitude and rate controller for rotorcraft with the objective of providing desired handling qualities and robustness characteristics. A sliding manifold is defined in the system state space to represent ideal attitude and rate command response dynamics of relative degree one with respect to the command input. Subsequently, robust command tracking is achieved via the synthesis of a multivariable super-twisting flight controller, which renders the plant states convergent on to the defined sliding manifold in finite-time and in the presence of matched external disturbance input. To validate the efficacy of the controller, simulation results are presented based on a nonlinear, higher-order rotorcraft model operating in turbulence. True system convergence to the sliding manifold from an untrimmed state is shown to lie within the theoretically predicted finite-time convergence bound. Furthermore, simulations with a linear quadratic flight controller are also presented for performance comparison with the proposed super-twisting flight controller.

Dynamic sliding mode control for nonlinear parameter‐varying systems

AbstractThis article deals with the dynamic sliding mode control (SMC) problem for unmatched nonlinear parameter‐varying systems. The unmatched nonlinear model refers to the systems matrices of control input and nonlinearity terms having inconsistent values and structures. A linear sliding surface function is constructed, and the resulting sliding mode dynamics is formulated into a full‐order descriptor nonlinear parameter‐varying system. Then, based on a parameter‐dependent Lyapunov function, the synthesis procedure of the sliding manifold is derived, which guarantees the asymptotic stability of the sliding motion. Furthermore, a dynamic SMC law is proposed to enforce the resultant closed‐loop system towards the sliding manifold in finite time. It is noteworthy that both the sliding surface and control law are depended on both time‐varying and measurable parameters. Finally, simulation studies are provided to unfold the validity of the proposed method.

Minimal and Locally Edge Minimal Fluid Models for Resource-Sharing Networks

We investigate minimal and locally edge minimal fluid models for real-time resource-sharing networks, which are natural counterparts of pathwise minimal and locally edge minimal performance processes for the corresponding real-time stochastic systems. The models under study arise as optimizers of appropriate idleness-based criteria within a suitable family of fluid models for a given resource-sharing network. The class of minimal fluid models is fairly general, corresponding to efficient service protocols in which transmission on each route takes place in the earliest deadline first (EDF) order. For such a model, the distribution of the current lead times of the fluid mass on each route coincides with the fluid arrival measure for this route, truncated below on the current frontier level. Locally edge minimal fluid models may be regarded, in some sense, as fluid counterparts of EDF resource-sharing networks. Under mild assumptions, a locally edge minimal fluid model is uniquely determined by its data. We also show stability of such models in the strictly subcritical case. More generally, each such a subcritical model converges to the invariant manifold in finite time.

Robust Geometric Navigation of a Quadrotor UAV on SE(3)

SUMMARYIn this paper, a robust geometric navigation algorithm, designed on the special Euclidean group SE(3), of a quadrotor is proposed. The equations of motion for the quadrotor are obtained using the Newton–Euler formulation. The geometric navigation considers a guidance frame which is designed to perform autonomous flights with a convergence to the contour of the task with small normal velocity. For this purpose, a super twisting algorithm controls the nonlinear rotational and translational dynamics as a cascade structure in order to establish the fast and yet smooth tracking with the typical robustness of sliding modes. In this sense, the controller provides robustness against parameter uncertainty, disturbances, convergence to the sliding manifold in finite time, and asymptotic convergence of the trajectory tracking. The algorithm validation is presented through experimental results showing the feasibility of the proposed approach and illustrating that the tracking errors converge asymptotically to the origin.

Sliding mode control of the Hodgkin–Huxley mathematical model

In this paper we deal with a feedback control design for the action potential of a neuronal membrane in relation with the non-linear dynamics of the Hodgkin-Huxley mathematical model. More exactly, by using an external current as a control expressed by a relay graph in the equation of the potential, we aim at forcing it to reach a certain manifold in finite time and to slide on it after that. From the mathematical point of view we solve a system involving a parabolic differential inclusion and three nonlinear differential equations via an approximating technique and a fixed point result. The existence of the sliding mode and the determination of the time at which the potential reaches the prescribed manifold is proved by a maximum principle argument. Numerical simulations are presented.

Robust and global attitude stabilization of magnetically actuated spacecraft through sliding mode

The inertial pointing problem of a rigid satellite by solely magnetic torqueing is considered in this paper. To ensure globally uniformly ultimately bounded motion about the reference in inertial space, a sliding mode attitude control law, which consists of equivalent and reaching control terms, based on a novel time-varying sliding manifold is designed. The originality of the sliding manifold relies on the inclusion of two time-integral terms. The usage of the proposed sliding manifold makes the application of the equivalent control method to the considered problem possible, and it is proven that the state trajectories reach the newly designed sliding manifold in finite time even under the effect of four realistically modeled disturbance components and parametric uncertainty of all inertia matrix entries. For the constructed purely magnetic attitude control system, stability and existence of the sliding mode as well as state trajectories' finite time convergence to the sliding manifold are demonstrated via Lyapunov function techniques. The results of a simulation example verify the robust stability of the designed attitude control system. The steady state performance of the attitude control system is evaluated in the altitude range of low-Earth-orbits.

Uncertain Saturated Discrete‐Time Sliding Mode Control for A Wind Turbine Using A Two‐Mass Model

AbstractThe aim of this paper is to propose a new design variable speed wind turbine control by discrete‐time sliding mode approach. The control objective is to obtain a maximum extraction of wind energy, while reducing mechanical loads and rotor speed tracking combined with an electromagnetic torque. For this application, we designed a discrete time sliding mode control using the equivalent discrete time reaching law. Furthermore, a systematic and improved design procedure for uncertainties discrete‐time sliding mode control (SMC) with saturation problem is provided in this paper. The saturation constraint is reported on inputs vector. LMI technique and polytopic models are used in the design of the switching surface. To achieve some performance requirements and good robustness, in the sliding mode, the pole clustering method is investigated. Based on the unit vector control approach, a robust control is developed, then, to direct and maintain the system states onto the sliding manifold in finite time. Finally, a systematic design procedure for DSMC required to achieve a given performance level is provided and its effectiveness is varied by applying it to variable speed wind turbine systems.

Sliding mode control of Schrödinger equation-ODE in the presence of unmatched disturbances

In this paper, we consider boundary stabilization for a cascade of Schrödinger equation-ODE system with both, matched and unmatched disturbances. The backstepping method is first applied to transform the system into an equivalent target system where the target system is input-to-state stable. To reject the matched disturbance, the sliding mode control (SMC) law is designed for the target system. The well-posedness of the closed-loop system is proved, and the reachability of the sliding manifold in finite time is justified by infinite-dimensional system theory. It is shown that the resulting closed-loop system is input-to-state stable. A Numerical example illustrates the efficiency of the sliding mode design that reduces the ultimate bound of the closed-loop system by rejecting the matched disturbance.

Design and Implementation of Clutch Control for Automotive Transmissions Using Terminal-Sliding-Mode Control and Uncertainty Observer

This paper investigates the clutch control problem for automotive transmission systems. This paper focuses on the pressure tracking control for a wet clutch, which has a much shorter stroke and asks for a more precise position and pressure regulation. The system dynamics are highly nonlinear, and the developed model includes unmodeled dynamics and parameter uncertainties. All these factors will influence the closed-loop system performance if not considered carefully during the control design, which makes the control synthesis for clutch systems challenging. Compared with the existing sliding-mode control (SMC) method, an improved method based on nonlinear sliding mode is presented in this paper to further improve the convergence rate and tracking precision of the closed-loop clutch system. This controller ensures that the pressure tracking error not only reaches the sliding manifold in finite time but converges to the equilibrium point in finite time as well. Moreover, considering the chattering phenomenon caused by high switching gains, a composite terminal SMC (TSMC) method based on uncertainty observer is proposed to reduce chattering. Using an extended state observer (ESO) technique, an uncertainty observer is designed for estimating the model uncertainties of pressure dynamics, pressure-reducing-valve flow dynamics, and estimation error of piston displacement. Then, a feedforward compensation term is combined with the terminal-sliding-mode feedback control. Thus, the composite terminal-sliding-mode controller may take smaller control gains for the whole pressure tracking procedure without sacrificing uncertainty compensation performance. Experimental results based on an xPC Target platform of the clutch system are provided to show the superiority of the proposed methods.

Adaptive model‐based event‐triggered sliding mode control

SummaryThis paper addresses the design of a model‐based event‐triggered sliding mode control strategy of adaptive type. The overall proposal can be regarded as a networked control scheme, because one of the design objectives is to reduce the number of transmissions of the plant state over the network used to construct the control loop. The key idea consists in using the actual plant state or the state of a suitably updated nominal model of the plant to generate the control variable, depending on the magnitude of the sliding variable. The proposed adaptive control scheme proves to be capable of steering the sliding variable to a boundary layer of the sliding manifold in finite time, in spite of the presence of bounded uncertainties with unknown bounds. When the sliding variable is confined within the boundary layer, the nominal model state is used to compute the control variable. Then, a continuous control can be analytically determined and applied, which provides a beneficial chattering alleviation effect. The proposed networked control scheme is theoretically analyzed and assessed in simulation with satisfactory results. Copyright © 2016 John Wiley & Sons, Ltd.

Robust sliding mode control approach for systems affected by unmatched uncertainties usingH∞with pole clustering constraints

SUMMARY In this paper, the problem of sliding mode control for a class of systems with unmatched parametric uncertainties and external perturbations is considered. LMI technique and polytopic models are used in the design of the switching surface. To achieve some performance requirements and good robustness, in the sliding mode, the H∞ norm and the pole clustering method are investigated. Based on the unit vector control approach, a robust control is developed, then, to direct and maintain the system states onto the sliding manifold in finite time. Finally, the validity of the proposed design strategy is demonstrated through the simulation of the quarter-car suspension system. Copyright © 2014 John Wiley & Sons, Ltd.

Design and Implementation of Terminal Sliding Mode Control Method for PMSM Speed Regulation System

This paper investigates the speed regulation problem of permanent magnet synchronous motor servo system based on terminal sliding mode control method. By introducing a non-singular terminal sliding mode manifold, a novel terminal sliding mode controller is designed for the speed loop. This controller can make the states not only reach the manifold in finite time, but also converge to the equilibrium point in finite time. Thus, the controller could make the motor speed reach the reference value in finite time, obtaining a faster convergence and a better tracking precision. Meanwhile, considering the large chattering phenomenon caused by high switching gains, a composite terminal sliding mode control method based on disturbance observer is proposed to reduce chattering. Through disturbance estimation for feed-forward compensation, the composite terminal sliding mode controller may take a smaller value for the switching gain without sacrificing disturbance rejection performance. Matlab simulation and TMS320F2808 DSP experimental results are provided to show the superiority of the proposed methods.

Passivity-based fractional-order integral sliding-mode control design for uncertain fractional-order nonlinear systems

This paper concerns with the problem of designing a passivity-based fractional-order (FO) integral sliding mode controller for uncertain FO nonlinear systems. Utilizing the FO calculus, it is showed that the state trajectories of the closed-loop system reach the FO switching manifold in finite time. The control law ensures the asymptotical stability on the sliding surface. A parameter adjustment scheme for FO integral sliding surface is proposed by using the linear matrix inequality (LMI) approach. The proposed controller can be applied to different systems such as chaotic systems. Finally, simulation results are provided to show the effectiveness of the proposed method controlling chaos in FO Chua circuit and FO Van-der-Pol oscillator.

Fractional‐Order Dynamic Output Feedback Sliding Mode Control Design for Robust Stabilization of Uncertain Fractional‐Order Nonlinear Systems

AbstractA robust fractional‐order dynamic output feedback sliding mode control (DOF‐SMC) technique is introduced in this paper for uncertain fractional‐order nonlinear systems. The control law consists of two parts: a linear part and a nonlinear part. The former is generated by the fractional‐order dynamics of the controller and the latter is related to the switching control component. The proposed DOF‐SMC ensures the asymptotical stability of the fractional‐order closed‐loop system whilst it is guaranteed that the system states hit the switching manifold in finite time. Finally, numerical simulation results are presented to illustrate the effectiveness of the proposed method.

Optimal Sliding Mode Control for Linear Singualr System with Input and State Time-Delays

Synthetic problem of variable structure control (VSC) for linear singular system with input and state time-delays is studied. Firstly, the original system with both input and state time-delays is written into a form without time-delay by a linear transformation. Secondly, the system without time-delay is decomposed into two low dimensional subsystems by a restricted system equivalent decomposed method. Thirdly, the quadratic performance index optimal control technique is introduced to design the optimal sliding mode for the restricted equivalent subsystems. By applying reaching law approach, the selected control law ensures that the solution trajectories of the system reach the switching manifold in finite time and have low chattering in the sliding motion. Finally, a simulation example is given to illustrate the feasibility and validity of the proposed method.