Adaptive State Feedback Controller Research Articles

Fuzzy adaptive tracking control for switched nonlinear systems with full time-varying state constraints

In this paper, a novel fuzzy adaptive tracking control scheme is presented for a class of nonstrict-feedback uncertain switched nonlinear systems by taking into account constraint. The considered switched nonlinear system contains unknown nonlinearities. In the design process, firstly, the problem of state constraints is coped with by utilizing the asymmetric time-varying barrier Lyapunov functions (TABLFs), and the problem of “explosion of complexity” is solved by dynamic surface control (DSC) technology. Secondly, fuzzy logic systems (FLSs) are utilized to approximate the unknown nonlinear dynamics. Under the framework of adaptive control design, the switched adaptive state feedback controller is designed, which can guarantee all states cannot violate their constrained sets. Then, based on the Lyapunov function and average dwell time (ADT) approach, the theoretical analysis is provided for the closed-loop systems within constraint performance bounded. Finally, a numerical example is proposed to further elaborate the effectiveness of the presented control scheme.

Path following algorithm for skid-steering mobile robot based on adaptive discontinuous posture control

ABSTRACTThe kinematic model of a skid-steering mobile robot (SSMR) is manipulated using signed polar transformation which represents a discontinuous state transformation. The influence of relative position between the instantaneous center of rotation (ICR) and SSMR center of mass is considered. Then, adaptive state feedback controller is designed and stability regions are studied. Subsequently, a point-to-point tracking algorithm is introduced to track a trajectory that is defined by a set of way-points, which is the more realistic case of dangerous exploration or landmine detection purposes. The closed-loop system is simulated using MATLAB environment and experimentally validated using a modified TURTLEBOT3 Burger. Results show that the proposed controller reaches almost zero steady state error with smooth paths for point stabilization, moreover, good tracking capabilities are demonstrated. The proposed control system integrates both posture and tracking algorithm, thus achieve trajectory tacking which is defined by a set of way-points.

Fixed-time cluster synchronization in directed community networks with diverse coupling and different-order nodes

In this paper, fixed-time cluster synchronization of directed community networks (DCNs) with diverse coupling and different-order nodes is explored. For the DCN model, the inherent dynamics and state dimensions of the nodes in different communities can be nonidentical, and moreover, the interactive nodes can differ in their types of connections in different communities and the connections between any pair of different communities can be nonidentical as well. Two types of control strategies, state feedback control and adaptive feedback control, are adopted to force such DCNs to realize cluster synchronization in fixed-time. By utilizing reduction to absurdity, some sufficient conditions ensuring the fixed-time cluster synchronization are derived for the proposed two control schemes. Moreover, it is revealed theoretically that our estimated settling time is more precise and less conservative than that presented in the previous researches. Finally, the validity of the obtained fixed-time cluster synchronization criteria is verified via numerical simulations.

Further Results on Adaptive Stabilization of High-Order Stochastic Nonlinear Systems Subject to Uncertainties.

This paper concerns the adaptive state-feedback control for a class of high-order stochastic nonlinear systems with uncertainties including time-varying delay, unknown control gain, and parameter perturbation. The commonly used growth assumptions on system nonlinearities are removed, and the adaptive control technique is combined with the sign function to deal with the unknown control gain. Then, with the help of the radial basis function neural network approximation approach and Lyapunov-Krasovskii functional, an adaptive state-feedback controller is obtained through the backstepping design procedure. It is verified that the constructed controller can render the closed-loop system semiglobally uniformly ultimately bounded. Finally, both the practical and numerical examples are presented to validate the effectiveness of the proposed scheme.

Decentralized adaptive tracking control for high-order interconnected stochastic nonlinear time-varying delay systems with stochastic input-to-state stable inverse dynamics by neural networks

The paper solves the problem of a decentralized adaptive state-feedback neural tracking control for a class of stochastic nonlinear high-order interconnected systems. Under the assumptions that the inverse dynamics of the subsystems are stochastic input-to-state stable (SISS) and for the controller design, Radial basis function (RBF) neural networks (NN) are used to cope with the packaged unknown system dynamics and stochastic uncertainties. Besides, the appropriate Lyapunov-Krosovskii functions and parameters are constructed for a class of large-scale high-order stochastic nonlinear strong interconnected systems with inverse dynamics. It has been proved that the actual controller can be designed so as to guarantee that all the signals in the closed-loop systems remain semi-globally uniformly ultimately bounded, and the tracking errors eventually converge in the small neighborhood of origin. Simulation example has been proposed to show the effectiveness of our results.

Exponential Synchronization for Neutral-Type Neural Network with Stochastic Perturbation and Markovian Jumping Parameters

The problem of exponential synchronization for neutral-type neural network with stochastic perturbation and Markovian switching parameters is considered in this article. Based on Lyapunov functional method and the theory of stochastic process, the exponential synchronism of the neural network is analyzed. By designing an adaptive state feedback controller, the exponential synchronization criterion of the neural network is obtained which can be represented as linear matrix inequality. Furthermore, the update rule for the adaptive controller is obtained. Finally, a simulation example is proposed to explain the availability of the results and method obtained in this article.

Finite-time synchronization of memristive neural networks with discontinuous activation functions and mixed time-varying delays

This paper is concerned with the issue of the finite-time adaptive synchronization and finite-time synchronization of memristive neural networks with discontinuous activation functions and mixed time-varying delays. For synchronizing the drive-response memristive neural networks in finite time, an adaptive state-feedback controller and a state-feedback controller are proposed, respectively. Then by using the theories of differential inclusions and set-valued map, the synchronization issue of drive-response memristive neural networks with discontinuous activation functions and mixed time-varying delays is transformed into the stabilization issue of the error system. Moreover, based on the stability theory, Forti Lemma and Hardy inequality, some novel algebraic synchronization criteria are deduced to ensure the finite-time adaptive synchronization and finite-time synchronization of memristive neural networks with discontinuous activation functions and mixed time-varying delays under the adaptive state-feedback controller and the state-feedback controller. And the settling times for finite-time adaptive synchronization and finite-time synchronization are given. Furthermore, it is hard to estimate the initial conditions for a large system, so the settling times in this paper are not dependent on initial conditions of system. Finally, an example is provided to demonstrate the effectiveness of the obtained results.

Globally adaptive control for stochastic nonlinear time-delay systems with perturbations and its application

This paper addresses the globally adaptive state-feedback control problem for a more general class of stochastic nonlinear systems with an unknown time-varying delay and perturbations. Without imposing any assumptions on the time-varying delay, an adaptive state-feedback controller is skillfully designed by using adaptive backstepping control technique. Then, based on Lyapunov–Razumikhin lemma and stochastic stability theory, it is proven that the constructed controller can guarantee the closed-loop system to be globally asymptotically stable in probability. Finally, a practical example of stochastic chemical reactor system with time delay and perturbations is presented to demonstrate the effectiveness of the proposed control scheme.

Adaptive stabilisation for a class of uncertain coupled parabolic equations

ABSTRACT Adaptive stabilisation is investigated for a class of uncertain coupled parabolic equations in this paper. The presence of unknown coefficients can reduce the rigorousness of system modelling and enlarge the scope of the systems, whereas it could give rise to essential difficulties to control problems. Mainly due to the latter, certain new initiative, such as uncertainty compensation, should be considered to solve the stabilisation problem. For this, by infinite-dimensional backstepping method combining with adaptive compensation technique, an adaptive control scheme is proposed. Then, an adaptive state-feedback controller is constructed which guarantees that all the closed-loop system states are bounded while the original system states converge to zero. A numerical example is provided to validate the effectiveness of the theoretical results.

Sliding Mode Robust Adaptive Control of Maglev Vehicle’s Nonlinear Suspension System Based on Flexible Track: Design and Experiment

The suspension system of Maglev vehicle needs strong robustness and anti-jamming ability in the process of operation and fluctuation control. In order to solve the open-loop instability and strong nonlinearity of the mechanical equation of the suspension system of the Maglev vehicle, the non-linear dynamic equation is established. At present, the research based on the single electromagnet and the rigid track is the most common. However, based on this method, it is impossible to study the coupled vibration caused by track factors. Therefore, based on the dynamic equation of a single span simply supported beam of flexible track and the non-linear equation of the suspended electromagnet itself, an overall control model is needed to discuss the control strategy. Based on this dynamic model, the singularities of the system are solved according to Hurwitz criterion, and the characteristic equation corresponding to the Jacobian matrix is obtained. The stability analysis shows that the system is unstable. At the same time, the necessity of using a feedback control method to control the air gap has been proved. On this basis, a sliding mode adaptive state feedback controller for the maglev system is designed based on the RBF network approximation principle. The corresponding simulation and experimental results are given. The simulation and experimental results show that the controller can ensure the vehicle's stable suspension and effectively suppress external interference. Compared with the traditional PID and fuzzy controllers, the controller can guarantee a faster dynamic response, stronger robustness, and smaller overshoot while considering the flexible track and external disturbances.

Fuzzy adaptive state-feedback control for a revolute-prismatic-revolute robot manipulator

In this work, a fuzzy adaptive state-feedback control is designed for the stabilization of a three-degree of freedom revolute-prismatic-revolute (RPR) robot manipulator. At first, the forward kinem...

Prescribed performance-barrier Lyapunov function for the adaptive control of unknown pure-feedback systems with full-state constraints

In this paper, an adaptive state-feedback control technique is proposed for a class of unknown pure-feedback systems. A remarkable feature is that not only the problem of full-state constraints and prescribed performance tracking is solved together, but also the design is an approximation-free control scheme for pure-feedback systems with completely unknown nonlinearities. These properties will lead to a difficult task for designing a stable controller. To this end, a novel prescribed performance-barrier Lyapunov function is developed to guarantee that all the state constraints are not violated and the tracking error is preserved within a specified prescribed performance bound at all times, simultaneously. Then, by utilizing the mean value theorem, Nussbaum gain technique, a low-pass filter and a novel bounded estimation approach at each step of back-stepping procedure, a novel adaptive dynamics surface control scheme is developed to remove the difficulties of pure-feedback characteristic, unknown nonlinearities, unknown control direction and “explosion of complexity”, which can guarantee that the proposed design is universal and low-complexity. Moreover, it is proved that all the signals in the closed-loop system are global uniformly bounded. Two simulation studies are worked out to illustrate the performance of the proposed approach.

Global adaptive stabilization and practical tracking for nonlinear systems with unknown powers

This paper is devoted to the global stabilization and practical tracking for a class of uncertain nonlinear systems. The presence of unknown powers and serious parameter unknowns makes the systems in question essentially different from those in the related works. By skillfully combining adaptive technique and adding a power integrator, two novel adaptive state-feedback controllers are successfully designed to achieve global stabilization and practical tracking, respectively. Remarkably, the typical feature of the two controllers lies in the introduction of the adaptive dynamic and the terms of lower and higher powers (with respect to the unknown system powers), which makes the controller powerful enough to compensate the serious parameter unknowns and the unknown powers of the system. Finally, simulation examples are provided to illustrate the effectiveness of the designed controllers.

Distributed model reference adaptive containment control of heterogeneous uncertain multi-agent systems

In this paper, a distributed model reference adaptive control (MRAC) design framework is proposed for containment control of heterogeneous uncertain multi-agent systems (MAS). Both groups of leaders and followers are considered to have general linear dynamics with the leaders subject to bounded external inputs and the followers subject to uncertain system dynamics. Two distributed adaptive control protocols are developed under this framework. The first protocol assumes measurable leaders’ input signals for a subset of the followers, and employs distributed observers with state-feedback adaptive controllers to achieve exact containment control performance. The second protocol incorporates robust adaptive control with nonlinear compensator techniques to handle a more challenging scenario of unmeasurable bounded leaders’ inputs. Convergence of the containment control errors to an arbitrarily adjustable neighborhood of the origin is guaranteed with the second protocol. The proposed MRAC framework provides a promising alternative solution over the prevailing cooperative output regulation framework for heterogeneous linear MAS containment control. It enables us to handle more general system settings under more stringent control environments with limited accessibility of leaders’ information and uncertain follower dynamics. Effectiveness and usefulness of the proposed approaches are demonstrated through extensive simulation studies, including an application to containment control of multiple nonholonomic mobile robots.

Adaptive fuzzy control for uncertain nonlinear systems

ABSTRACTIn this paper, a survey of adaptive fuzzy for uncertain nonlinear systems is presented. The first part introduces adaptive fuzzy control emergence and some typical control methods for uncertain nonlinear systems with matching conditions (single-input single-output systems, multi-input multi-output systems). The last part presents the adaptive fuzzy state feedback and output-feedback control methods for uncertain nonlinear systems with non-matching conditions based on the backstepping technique, including strict-feedback systems, pure-feedback systems and non-strict-feedback systems.

Passivity and synchronisation of complex dynamical networks with multiple derivative couplings

Two network models with multiple derivative couplings and different dimensions of output and input vectors are investigated in this paper. The problem of passivity for the proposed network models is analysed by utilising some inequality techniques and Lyapunov functional method, and several synchronisation conditions for complex dynamical networks with multiple derivative couplings (CDNMDC) are given. Moreover, by employing adaptive state feedback control strategy, some sufficient conditions for guaranteeing passivity and synchronisation of CDNMDC are obtained. In the end, we give two examples to verify the effectiveness of the results.

Cooperative Robust Output Regulation for Second-Order Nonlinear Multiagent Systems With an Unknown Exosystem

The cooperative robust output regulation problem for a class of second-order nonlinear multiagent systems with an exactly known exosystem has been studied recently. This paper further studies the same problem for the same class of systems subject to an unknown exosystem. We first show that the problem can be converted into the adaptive stabilization problem for an augmented system composed of the given multiagent system and the distributed internal model. Due to the unknown parameters in the exosystem, the augmented system is a nonlinear multi-input system with both linearly parameterized uncertainties and norm-bounded nonlinear uncertainty. By combining the adaptive control technique and the robust control technique, we will solve our problem by a distributed adaptive robust state feedback controller.

Adaptive finite-time control of uncertain nonlinear systems with the powers of odd rational numbers

ABSTRACTThis paper studies adaptive finite-time control problem of a class of nonlinear systems with dynamic and parametric uncertainties. The power of systems in this paper is any positive odd rational number but not necessary equal to or greater than one. To solve this problem, finite-time input-to-state stability (FTISS) is used to characterise the unmeasured dynamic uncertainty. By skillfully combining Lyapunov function, sign function, adding a power integrator, adaptive control and FTISS methods, an adaptive state feedback controller is designed to drive the states to the origin in finite time while maintaining all the closed-loop signals bounded.

Adaptive asymptotic tracking using barrier functions

This paper studies the global output tracking problem for a class of unknown time-varying nonlinear systems in strict-feedback form. By utilizing the barrier functions, a universal adaptive state-feedback control strategy is proposed that achieves asymptotic tracking performance. Unlike the existing results in the literature, the proposed control scheme utilizes the barrier functions to ensure the unknown system nonlinearities to be the bounded “disturbance-like” terms, which are adaptively compensated at each step, this enables any approximation structures are not needed. Furthermore, the “explosion of complexity” issue in backstepping-like approaches is avoided without using additional filtering. Simulation results are presented to demonstrate the effectiveness of the proposed methodology.

A New Approach to Adaptive Stabilization of Stochastic High-Order Nonholonomic Systems

This paper studies the problem of adaptive stabilization for a class of stochastic high-order nonholonomic systems. Under the weaker assumptions, by constructing the appropriate Lyapunov function and combining sign function technique, an adaptive state feedback controller is designed to guarantee global asymptotic stability in probability of the closed-loop system. The effectiveness of the controller is demonstrated by a mechanical system.