Continuous Adaptive Controller Research Articles

On fixed-time interlayer synchronization of two-layer multiweighted complex dynamic networks: An economic and practical non-chattering adaptive control approach

This paper investigates the adaptive fixed-time (FxT) interlayer synchronization issue of two-layer complex dynamic networks (CDNs), where both multiple weights and interlayer links are considered. Above all, a new FxT stability lemma is given, which offers a more flexible condition and some more precise estimates of stabilized convergence time compared with the existing results. Subsequently, an economic and practical non-chattering continuous adaptive controller is designed, which is superior to the currently available ones by excluding the signum function and linear part and removing the parity restriction on the exponents in control law. Furthermore, by means of the Lyapunov method and the newly-established FxT stability theory, some novel FxT interlayer synchronization criteria are derived for the addressed two-layer multiweighted CDNs with the designed non-chattering continuous adaptive controller, and the synchronized settling time (SST) is also reckoned. It is found that the interlayer links weights can contribute to the interlayer synchronization, and the SST becomes smaller with the increase of interlayer link weight. Finally, the proposed results are validated by numerical examples.

Fixed-time control for free-floating space manipulators with prescribed constraints and input saturation

Abstract This paper investigates the issue of tracking control for a free-floating space manipulator with prescribed performance constraints, considering the inertia uncertainties, internal disturbances and input saturation. An inherently continuous adaptive controller is proposed by incorporating non-singular fixed-time sliding mode control, prescribed performance control (PPC), and auxiliary compensation. First, a modified non-singular fast fixed-time terminal sliding surface is constructed, which has a shorten convergence time than the conventional fixed-time sliding surface. Unlike the existing complicated PPCs, a simple structure controller is developed to satisfy prescribed performance constraints through a unique tangent-type PPC technique. The input saturation is then compensated adaptively by an auxiliary mechanism. The Lyapunov theory thoroughly validates the stability and fixed-time convergence of the closed-loop tracking system. With the suggested control scheme, the system states can converge quickly to a small neighbourhood around the origin within a preassigned time, while the position tracking error can be confined within a prescribed performance bounds even in the presence of input saturation. Compared to the existing tracking methods, the suggested control approach has the advantages of faster transient convergence, higher steady-state tracking precision, and stronger robustness. Simulation comparisons demonstrate the effectiveness and superiority of the proposed controller.

Adaptive stabilisation of output-constrained high-order nonlinear systems with high-order and low-order nonlinearities

This paper investigates the adaptive stabilisation of output-constrained high-order nonlinear systems with more general high-order and low-order nonlinearities. By skilfully introducing nonlinear mappings, a key coordinate transformation, integral Lyapunov functions and the sign function into the adding a power integrator technique, and combining a novel analysis method, a continuous adaptive state-feedback controller is constructed. When the initial value of system states lies in the constrained set, it is rigorously proved that all the closed-loop signals are uniformly bounded, the asymmetric output constraint isn't transgressed, and the equilibrium point of the closed-loop system is uniformly asymptotically stable. A simulation example shows the effectiveness of this control scheme.

Disturbance observer-based adaptive sliding mode synchronization control for uncertain chaotic systems

<abstract><p>The synchronization control problem of a class of chaotic systems with unknown uncertainties and outside perturbation is addressed in this article by employing an innovative adaptive sliding mode controller (SM, SMC) constructed using a disturbance observer (DO). For the synchronous error system, the external disturbances estimated by the disturbance observer cannot be measured directly. If the appropriate gain matrix is chosen, the DO can approximate the unknown external disturbances well. Then a continuous adaptive SM controller based on the DO's output is designed by using adaptive techniques and the system dimensional expansion method. The Duffing-Holmes chaotic system is finally selected to numerically test the efficiency of the suggested strategy.</p></abstract>

Adaptive Control of Time-Varying Parameter Systems With Asymptotic Tracking

A continuous adaptive controller is developed for nonlinear dynamical systems with linearly parameterizable uncertainty involving time-varying uncertain parameters. Through a unique stability analysis strategy, a new adaptive feedforward term is developed along with specialized feedback terms, to yield an asymptotic tracking error convergence result by compensating for the time-varying nature of the uncertain parameters. A Lyapunov-based stability analysis is shown for Euler–Lagrange systems, which ensures asymptotic tracking error convergence and boundedness of the closed-loop signals. Additionally, the time-varying uncertain function approximation error is shown to converge to zero. A simulation example of a two-link manipulator is provided to demonstrate the asymptotic tracking result.

Distributed Adaptive Output Feedback Consensus of Parabolic PDE Agents on Undirected Networks.

In this article, we investigate the distributed adaptive consensus problem of parabolic partial differential equation (PDE) agents by output feedback on undirected communication networks, in which two cases of no leader and leader-follower with a leader are taken into account. For the leaderless case, a novel distributed adaptive protocol, namely, the vertex-based protocol, is designed to achieve consensus by taking advantage of the relative output information of itself and its neighbors for any given undirected connected communication graph. For the case of leader-follower, a distributed continuous adaptive controller is put forward to converge the tracking error to a bounded domain by using the Lyapunov function, graph theory, and PDE theory. Furthermore, a corollary that the tracking error tends to zero by replacing the continuous controller with the discontinuous controller is given. Finally, the relevant simulation results are further demonstrated to demonstrate the theoretical results obtained.

Adaptive Disturbance-Observer-Based Continuous Sliding Mode Control for Small Autonomous Underwater Vehicles in the Trans-Atlantic Geotraverse Hydrothermal Field with Trajectory Modeling Based on the Path

Considering intense hydrothermal activities and rugged topography in a near-bottom environment of the trans-Atlantic geotraverse (TAG) hydrothermal mound, a small autonomous underwater vehicle (S-AUV) will suffer from time-varying disturbances, model uncertainties, actuator faults, and input saturations. To handle these issues, a fault-tolerant adaptive robust sliding mode control method is presented in this paper. Firstly, unknown disturbances, model uncertainties, and actuator faults of the S-AUV are synthesized into a lumped uncertain vector. Without requiring the upper bound and gradient of the uncertainties, a continuous adaptive finite-time extended state observer is designed to estimate the lumped uncertain vector. Then, an auxiliary dynamic system composed of continuous functions is introduced to deal with input saturations, thereby contributing to achieving fixed-time trajectory tracking control of S-AUVs. Based on a designed continuous fixed-time nonsingular fast sliding mode surface, the proposed continuous adaptive controller is chattering free. Simulated topography is built according to topographic data of the TAG mound, and a smooth trajectory model is constructed by cubic spline interpolation. Comprehensive simulations performed on an actual S-AUV model are given to validate the effectiveness and superiority of the presented algorithm.

A Fully Distributed Protocol for Flocking of Time-Varying Linear Systems With Dynamic Leader and External Disturbance

This article studies the flocking problem of multiagent systems (MASs) with a dynamic virtual leader (VL) for the linear systems subject to time-varying uncertainties and external disturbance problems. We assume that the agents follow a leader with a bounded acceleration, which information is sensed only by the informed agents. We assign an adaptive estimator to each uninformed agent to estimate the velocity of the leader. By deriving a lemma and using a standard adaptive law, we design a continuous adaptive controller for solving the problem under the mentioned challenges, which is also fully distributed. The designed flocking control ensures that the velocity of followers asymptotically is converged to that of the VL. Also, the agents’ network remains connected, and no collision occurs among agents. Finally, we present a simulation that illustrates the validity of the results.

Fast finite-time adaptive stabilization of high-order uncertain nonlinear system with an asymmetric output constraint

This paper is concerned with two essential problems in adaptive control. The first is to improve the stability criteria in the presence of the constraint and unknown parameters, and the second is to establish a fast finite-time control scheme for high-order uncertain nonlinear systems with inherent nonlinearities and an asymmetric output constraint. A continuous adaptive controller is constructed by utilizing a new barrier function and a serial of nonnegative integral functions equipped with sign functions, which guarantees that the output is restricted in a prescribed region and the state converges to zero in a faster speed compared to some traditional finite-time stabilizers. Unlike some existing control schemes developed for systems with the output constraint, the proposed method unifies finite-time control design in dealing with both constrained and unconstrained systems for the first time by taking the structure of the high-order system into consideration. Finally, a simulation example confirms the effectiveness of theoretical results.

PWM-Based Adaptive Trajectory Tracking of Switched Buck Power Converters

Based on pulse width modulation (PWM) technique, adaptive trajectory tracking of switched Buck power converters with parameter uncertainty is investigated in this article. By the aid of the backstepping technique, an equivalent continuous adaptive tracking controller is designed to guarantee the asymptotic stability of the closed-loop error continuous system. For the switched Buck converter with unknown parameters, PWM-based adaptive tracking with the equivalent adaptive continuous control input is proposed such that the closed-loop error digital system is practically asymptotically stable, and the tracking error converges to an arbitrarily small neighborhood of the origin. Simulation results are shown to illustrate the effectiveness of the proposed new control schemes.

Continuous Stabilizing Control for a Class Of Non-holonomic systems: Brockett System Example

A continuous adaptive controller is designed for a famous example of Brockett system which is an example of a class of non-holonomic systems. The controllability Lie Algebra of the Brockett’s system contains Lie brackets of depth one. It is shown that the closed loop system is globally uniformly asymptotically stable. The advantage of this method is that it does not require the conversion of the system model into a “chained form,” and thus does not rely on any special transformation techniques. The practical effectiveness of the controller is illustrated by numerical simulations.

Robust Finite-time Attitude Tracking Control of Rigid Spacecraft Under Actuator Saturation

This paper investigates the robust finite-time attitude tracking control problem for rigid spacecraft considering the modeling uncertainty, external disturbance and actuator saturation. An auxiliary system is proposed to directly compensate for the saturated control input. First, the basic controller is formulated based on the fast nonsingular terminal sliding mode surface (FNTSMS), the fast-TSM-type reaching law and the auxiliary system in the presence of upper bounded external disturbance. Then, when facing system uncertainty which consists of both modeling uncertainty and external disturbance and has upper bounded first derivative, the extended state observer (ESO) is associated with the first controller to improve the robustness of control system. Furthermore, to handle more general system uncertainty which is upper bounded by a polynomial function of the closed-loop system states, a continuous adaptive controller is designed to compensate for the total system uncertainty on line. The proposed controllers are able to deal with system uncertainty, input singularity and actuator saturation, while simultaneously providing fast finite-time convergence speed for the control system. And the problems of complex parameters selection process and repeated differentiations of nonlinear functions can be avoided. Rigorous stability analyses are given via the Lyapunov stability theory and digital simulations are conducted to illustrate the effectiveness of the proposed controllers.

Forgetting Factor Nonlinear Functional Analysis for Iterative Learning System with Time-Varying Disturbances and Unknown Uncertain

This paper focuses on the iterative learning tracking control problem for a class of nonlinear system with time-varying disturbances. First, because of the mismatches in time-varying disturbances functions, a high-order feed-forward iterative learning control (ILC) is employed to change the original system into an iterative system. Secondly, a variable forgetting factor is developed to stabilize the system. Based on the feed-forward iterative learning controller, a memory controller is constructed for the nonlinear system. By choosing a new variable forgetting factor, we show that the designed continuous adaptive controller makes the solutions of the closed-loop system convergent to a ball exponentially. Finally, a numerical example is given to show the feasibility and effectiveness of the proposed method.

Artificial Intelligence Based First Order Adaptive Sliding Mode Controller for Position Control of a DC Motor Actuator

This paper presents an Artificial Intelligence (AI) based approach uniquely applied to Permanent Magnet DC motor actuator for position control. The AI method employed in this work is Fuzzy logic. A first order lag Sliding mode controller is tuned and combined with an Adaptive Fuzzy- PI controller architecture which operates in parallel. The controller architecture proposed in this study is aimed at improving the disturbance rejection capability, steady state as well as transient performance of the conventional Adaptive Fuzzy-PI controller and sliding mode controller. Hence, the robust control law of the proposed controller (SM+FZ-PI) consists of a discontinuous Sliding mode output added to a continuous Adaptive Fuzzy-PI controller output. The sliding mode controller switches on only when disturbance in the system is detected. The performance of the proposed controller architecture has been compared with a conventional PID and Adaptive Fuzzy-PI controllers for performance evaluation with respect to several operating conditions such as load torque disturbance injection, noise injection in feedback loop, motor non-linearity exhibited by parameters variation, and a step change in reference input demand. The proposed controller (SM+FZ-PI), had the best disturbance rejection and steady state error elimination.

Global Adaptive Finite-Time Control for Stochastic Nonlinear Systems via State Feedback

This paper discusses the problem of global adaptive finite-time control for a class of stochastic nonlinear systems with parametric uncertainty. Under the assumption that the drift and diffusion terms satisfy lower-triangular growth conditions, a continuous adaptive controller is designed based on the adding one power integrator technique and parameter separation principle. By constructing an adaptive law to counteract the effects of uncertain parameters, it is proved that system states can be regulated to the origin almost surely in a finite time. Two simulation examples are given to demonstrate the effectiveness of the proposed control procedure.

Exact tracking control of uncertain non‐linear systems with additive disturbance

This study deals with adaptive control of non-linear systems in the strict-feedback form with parametric uncertainties and additive disturbance. The disturbance in the systems is assumed to be bounded. No knowledge of the uncertain parameters, an upper bound of the uncertain parameter vector, a bound of unknown disturbance and the differentiability of the external disturbance is required. Under the weakened assumptions, two continuous robust adaptive control schemes are proposed. In the first control scheme, a modified adaptive backstepping design procedure is proposed to remove overparameterisation. A novel damping term with the estimate of unknown disturbance bound and a positive time-varying integral function are introduced in the control law to counteract the destabilising effects of the external disturbance. In the second scheme, an alternative continuous adaptive controller is designed. Instead of the estimate of the disturbance bound, an adaptive parameter is incorporated into the control design. In both of the two control schemes, the design parameters are freely chosen to improve the control performance. It is proved that the proposed two adaptive control schemes can guarantee that the closed-loop signals are bounded and the output tracking error converges to zero asymptotically in spite of the disturbance. Finally, a numerical example is included to show the effectiveness of the presented control methods.

Fully distributed adaptive sliding-mode controller design for containment control of multiple Lagrangian systems

In this paper, we study the containment control problem for multiple Lagrangian systems with multiple dynamic leaders in the presence of parametric uncertainties and external disturbances with fully distributed controllers under an undirected graph. We first propose a fully distributed adaptive sliding-mode control algorithm combined with distributed sliding-mode estimators, without requiring the upper bounds of the derivatives of the leaders’ states and any other global information to be known by each follower. To reduce the effect on the varying gain during the adaption mainly caused by the initial error, fully distributed adaptive time-varying sliding-mode control is presented for controller design. To tackle the chattering effect caused by the discontinuous controller, we further propose a fully distributed continuous adaptive controller, under which both the containment errors and the adaptive gains are ultimately bounded. Simulation results are given to illustrate the theoretical results.

Distributed adaptive attitude tracking of multiple spacecraft with a leader of nonzero input

This paper considers the distributed attitude tracking problem of multiple spacecraft with a leader whose control input is possibly nonzero, bounded, and not available to any follower. Based on the relative attitudes and angular velocities of neighboring spacecraft, we design a distributed discontinuous adaptive controller to each follower to guarantee that the attitude errors between the followers and the leader converge to zero for any communication graph containing a directed spanning tree with the leader as the root. To tackle the chattering effect caused by the discontinuous controller, we further propose a distributed continuous adaptive controller, under which both the attitude tracking errors and the adaptive gains are ultimately bounded.

Novel Nonlinear Control Design for a Two-Dimensional Airfoil Under Unsteady Flow

In this paper, a particular class of trailing-edge flap-controlled two-dimensional aeroelastic systems with structural nonlinearities in plunging and pitching, and operating in an unsteady aerodynamic incompressible flowfield, is considered. By using the flap hinge torque of the trailing edge flap surface as the control input, a partial state feedback continuous adaptive controller is proposed in order to suppress the aeroelastic vibrations of the wing section model. It is shown that the control design with respect to an appropriately chosen output variable yields an asymptotic stability result for all three of the pitching, plunging, and flapping degrees of freedom. Numerical simulation results clearly demonstrate the effectiveness of the control strategy toward suppressing aeroelastic vibration at both pre- and post-flutter flight speed regimes.

Decentralized MRAC for large-scale interconnected systems with time-varying delays and applications to chemical reactor systems

The model reference adaptive control problem is investigated for a class of large-scale systems with time-varying delays. The considered systems have mismatched delay functions and matched interconnections. Firstly, a state coordinate transformation is employed to convert the original error system into a cascade system. Secondly, a delay-dependent virtual linear state feedback controller is developed to stabilize the first subsystem. Based on the virtual controller, a memoryless state feedback controller is constructed for the second subsystem. By choosing new Lyapunov Krasovskii functional, we show that the designed decentralized continuous adaptive controller renders that the solutions of the closed-loop system converge exponentially to a bounded region. Finally, the theoretic achievements are applied to the control design of a chemical reactor system with two subsystems. The control results show the effectiveness of the proposed method.