Uncertain Nonlinear Dynamics Research Articles

Neural network based adaptive backstepping dynamic surface control of drug dosage regimens in cancer treatment

This manuscript aims at investigating the neural adaptive control of drug dosage regimens in cancer treatment. The goal of the treatment is to get an appropriate scheme for the drug dosage in order to reduce the tumor cells. To obtain a controller presenting good performances, the cancer immunotherapy system is first described by Caputo fractional differential equations. Second, Nussbaum functions and neural networks are introduced to deal with the unknown control directions and the uncertain nonlinear dynamics, respectively. Then, the backstepping dynamic surface control method is deployed to regulate the updating laws and the control signals, simultaneously. Through rigorous analysis based on the Lyapunov stability theory, it is shown that by means of the proposed adaptive controller, the boundedness of all variables in the closed-loop system and the semi-global asymptotic tracking are well ensured for any bounded initial conditions. It is also demonstrated that the performances of the drug treatment based on our proposed adaptive neural control scheme are better than a number of existing schemes. Finally, simulation results are given to demonstrate the feasibility of the proposed control scheme in the diminution of the number of tumor cells in the cancer model.

Single-Agent Indirect Herding of Multiple Targets With Uncertain Dynamics

In this paper, an indirect herding problem is considered for a single herder that is outnumbered by multiple target agents. Indirect herding is a problem that involves a network of one or more controllable herding agents and indirectly controlled target agents (i.e., the target agents can only be controlled through the herder by exploiting herder–target interactions), where the goal is to achieve a network-wide objective. This paper investigates the unique problem where a single herder is required to regulate all the target agents to some desired formation. The problem is further complicated by the fact that the target agents have uncertain nonlinear dynamics, including uncertainties in the herder–target interaction. Neural network function approximation methods are used along with switched systems methods to ensure uniformly ultimately bounded convergence of the agent trajectories provided the developed sufficient dwell-time conditions are satisfied. Simulation and experimental results that involve one herding agent and multiple target agents demonstrate the validity of the designed controller and function approximation scheme for multiple herding objectives.

Non-singular Terminal Sliding Mode Control of Robot Manipulators with $$H_\infty $$ Trajectory Tracking Performance

This paper develops a novel non-singular terminal sliding mode control scheme for trajectory tracking of robot manipulators in the presence of external disturbances and uncertainties. Firstly, with the introduction of two nonlinear terms, a newly terminal sliding surface is designed. Then utilizing this sliding surface, a novel non-singular terminal sliding mode controller is proposed to eliminate the reaching interval, singularity issue and subsequently with this controller, the finite time error convergence is also assured. In the proposed controller, radial basis function neural network is employed to approximate highly uncertain nonlinear dynamics of robot manipulators using update laws derived with Lyapunov approach. Meanwhile, the effects of approximation errors are attenuated with $$H_\infty $$ performance criterion by introducing a robust term into the controller. As a result of proposed approach, asymptotic convergence of tracking errors is achieved within finite time and the approximation errors are attenuated to desired levels. The numerical simulation result shows the effectiveness of proposed controller for the case of microbot type robot manipulator.

Small fault detection from discrete-time closed-loop control using fault dynamics residuals

This paper addresses the problem of small fault detection from closed-loop control for discrete-time nonlinear uncertain systems. The problem is challenging due to (i) the considered system is subject to unstructured nonlinear uncertain dynamics; (ii) the faults are considered to be “small” in the sense that system states and control inputs in faulty mode remain close to those in normal mode; and (iii) fault detection needs to be accomplished during closed-loop control which might counteract the fault effects and thus diminish fault information for detection use. To overcome these challenges, a novel adaptive dynamics learning based fault detection scheme is proposed. Specifically, a new concept of fault dynamics residual is first developed to extract and represent enhanced fault information from closed-loop control. Then, an ideal estimator is constructed by using absolute measures of the proposed fault dynamics residuals. To make the ideal estimator implementable for systems with nonlinear uncertain dynamics, an adaptive dynamics learning approach is subsequently proposed to achieve the locally-accurate approximation of the uncertain fault dynamics. Finally, an adaptive threshold is developed based on the actual estimation system for real-time decision making, i.e., the fault is claimed to be detected when the associated residual signal becomes larger than the adaptive threshold. Rigorous analysis is performed to deduce the small fault detectability condition, which is shown to be significantly relaxed compared to those of existing fault detection methods. Extensive simulations have also been conducted to demonstrate the effectiveness and advantages of the proposed approach.

Fuzzy finite-frequency output feedback control for nonlinear active suspension systems with time delay and output constraints

• The T-S fuzzy method is used to approximate the nonlinear uncertain dynamics. • A finite frequency control criterion is formulated based on the Lyapunov theory. • A parallel-distributed compensation strategy is used in the fuzzy SOF controller. This paper investigates the problem of fuzzy finite-frequency output feedback control for nonlinear active suspension systems with time delay and output constraints. Firstly, as the physical suspension systems always exist the phenomenon of sprung and un-sprung mass variation and time delay, the Takagi-Sugeno (T-S) fuzzy model is adopted to represent the nonlinear uncertain active suspension system with uncertainties and time delay. Secondly, since the human body is much more sensitive to vertical vibrations between 4 and 8 Hz, a finite-frequency control criterion is formulated for the controller deign with consideration of time delay and output constraints. Other mechanical constraints such as suspension travel, tire dynamic deflection and actuator saturation are also considered. Thirdly, on a practical point of view, not all the states are online measurable. Hence, a novel fuzzy static output feedback (SOF) controller is proposed by applying the parallel-distributed compensation (PDC) scheme. The sufficient conditions for deriving the fuzzy SOF controller are obtained in terms of linear matrix inequalities (LMIs). Finally, numerical simulations on a quarter-car suspension model are conducted to validate the effectiveness and applicability of the proposed fuzzy SOF controller.

Composite cooperative synchronization and decentralized learning of multi-robot manipulators with heterogeneous nonlinear uncertain dynamics

This paper studies the problem of composite synchronization and learning of multiple coordinated robot manipulators subject to heterogeneous nonlinear uncertain dynamics under the leader-follower framework. A new two-layer distributed adaptive learning control scheme is proposed, which consists of the first-layer distributed cooperative estimator and the second-layer decentralized deterministic learning controller. The first layer aims to enable each robotic agent to estimate the leader’s information. The second layer is responsible for not only controlling each individual robotic agent to track over desired reference trajectory, but also accurately identifying/learning each robot’s nonlinear uncertain dynamics. Design and implementation of this two-layer distributed controller can be carried out in a fully-distributed manner, which do not require any global information including global connectivity of the communication network. The Lyapunov method is applied to rigorously analyze stability and parameter convergence of the resulting closed-loop system. Numerical simulations on a team of two-degree-of-freedom robot manipulators have been conducted to demonstrate the effectiveness of the proposed results.

Motion/force control scheme for electrically driven cooperative multiple mobile manipulators

This paper presents the motion and force control problem of rigid-link electrically driven cooperative mobile manipulators handling a rigid object. Although, the motion/force control problem of cooperative mobile manipulators has been enthusiastically studied. But there is little research on the motion/force control of electrically driven cooperative mobile manipulators. Due to the inclusion of the actuator dynamics with the manipulator’s dynamics, the controller exhibits some important characteristics. For the electromechanical system, we have designed a novel controller at the dynamic level as well as at the actuator level. In the proposed control scheme, at the dynamic level, uncertain non-linear mechanical dynamics is approximated with a hybrid controller containing model-based control scheme combined with model-free neural network based control scheme together with an adaptive bound. The adaptive bound is used to suppress the effects of external disturbances, friction terms, and reconstruction error of the neural network. At the actuator level, for the approximation of the unknown electrical dynamics, the model-free neural network is utilized. The developed control scheme provides that the position tracking errors, as well as the internal force, converge to the desired levels. Additionally, direct current motors are also controlled in such a way that the desired currents and torques can be attained. In order to make the overall system to be asymptotically stable, online learning of the weights and the parameter adaptation of the parameters is utilized in the Lyapunov function. The superiority of the developed control method is carried out with the numerical simulation results and its superior robustness is shown in a comparative manner.

Adaptive Neural Feedback Linearizing Control of Type (m,s) Mobile Manipulators with a Guaranteed Prescribed Performance

SummaryIn this paper, a neural network (NN)-based tracking controller is proposed for a general class of type (m,s) wheeled mobile manipulators (WMMs) subjected to model uncertainties with prescribed transient and steady-state performance specifications. First, an input–output model of WMMs is derived by introducing proper output equations. Then, the prescribed performance technique is employed to propose a proportional integral derivative trajectory tracking controller for WMMs to ensure that the tracking errors converge to a smaller, arbitrary ultimate bound with a predefined maximum overshoot/undershoot and convergence speed. The learning capabilities of multilayer NNs are incorporated into the controller to approximate the uncertain nonlinear dynamics of the robot. An adaptive saturation-type controller is utilized to compensate NN estimation errors and external disturbances. A Lyapunov-based stability analysis is used to demonstrate that the tracking errors are uniformly ultimately bounded and converge to a small neighborhood of zero with a guaranteed prescribed performance. Numerical computer simulations are presented to show the effectiveness of the proposed controller.

Neuro-adaptive tracking control of non-integer order systems with input nonlinearities and time-varying output constraints

This paper studies the design of neuro-adaptive tracking control schemes for non-integer order non-square systems subject to time-varying output constraints and input nonlinearities. It should first be stated that by employing the mean-value theorem, the original non-affine non-square system with actuator nonlinearities is converted into an equivalent affine square form. Neural networks, Barrier Lyapunov Functions and Nussbaum functions are then incorporated to overcome the difficulties raised by the uncertain nonlinear dynamics, output constraints and unknown control directions, respectively. In a further step, in order to systematically derive the control signals and updating laws, the Backstepping technique is applied. It is shown that by using the proposed adaptive controller, the semi-global asymptotic tracking and the boundedness of all variables in the closed-loop system are guaranteed without transgression of the constraints. The foremost contributions of this paper include: (1) by means of new lemmas and corollaries based on Caputo fractional derivative definitions, techniques and approaches related to the stability analysis and controllability of integer-order plants are extended to fractional-order non-square ones, and (2) the ‘explosion of complexity’ issue is fixed. Finally, simulation results are provided to reveal the effectiveness of the proposed control scheme.

Entropy Analysis and Neural Network-Based Adaptive Control of a Non-Equilibrium Four-Dimensional Chaotic System with Hidden Attractors.

Today, four-dimensional chaotic systems are attracting considerable attention because of their special characteristics. This paper presents a non-equilibrium four-dimensional chaotic system with hidden attractors and investigates its dynamical behavior using a bifurcation diagram, as well as three well-known entropy measures, such as approximate entropy, sample entropy, and Fuzzy entropy. In order to stabilize the proposed chaotic system, an adaptive radial-basis function neural network (RBF-NN)–based control method is proposed to represent the model of the uncertain nonlinear dynamics of the system. The Lyapunov direct method-based stability analysis of the proposed approach guarantees that all of the closed-loop signals are semi-globally uniformly ultimately bounded. Also, adaptive learning laws are proposed to tune the weight coefficients of the RBF-NN. The proposed adaptive control approach requires neither the prior information about the uncertain dynamics nor the parameters value of the considered system. Results of simulation validate the performance of the proposed control method.

Cooperative Deterministic Learning-Based Formation Control for a Group of Nonlinear Uncertain Mechanical Systems

This paper addresses the formation control problem for a group of mechanical systems with nonlinear uncertain dynamics under the virtual leader-following framework. New cooperative deterministic learning-based adaptive formation control algorithms are proposed. Specifically, the virtual leader dynamics is constructed as a linear system subject to unknown bounded inputs, so as to produce more diverse reference signals for formation tracking control. A cooperative discontinuous nonlinear estimation protocol is first proposed to estimate the leader's state information. Based on this, a cooperative deterministic learning formation control protocol is developed using artificial neural networks, such that formation tracking control and locally-accurate nonlinear identification with learning knowledge consensus can be achieved simultaneously. Finally, by utilizing the learned knowledge represented by constant neural networks, an experience-based distributed control protocol is further proposed to enable position-swappable formation control. Numerical simulations using a group of autonomous underwater vehicles have been conducted to demonstrate the effectiveness and usefulness of the proposed results.

Leader–Follower Formation Control of USVs With Prescribed Performance and Collision Avoidance

This paper addresses a decentralized leader–follower formation control problem for a group of fully actuated unmanned surface vehicles with prescribed performance and collision avoidance. The vehicles are subject to time-varying external disturbances, and the vehicle dynamics include both parametric uncertainties and uncertain nonlinear functions. The control objective is to make each vehicle follow its reference trajectory and avoid collision between each vehicle and its leader. We consider prescribed performance constraints, including transient and steady-state performance constraints, on formation tracking errors. In the kinematic design, we introduce the dynamic surface control technique to avoid the use of vehicle's acceleration. To compensate for the uncertainties and disturbances, we apply an adaptive control technique to estimate the uncertain parameters including the upper bounds of the disturbances and present neural network approximators to estimate uncertain nonlinear dynamics. Consequently, we design a decentralized adaptive formation controller that ensures uniformly ultimate boundedness of the closed-loop system with prescribed performance and avoids collision between each vehicle and its leader. Simulation results illustrate the effectiveness of the decentralized formation controller.

Analytical design of active disturbance rejection control for nonlinear uncertain systems with delay

For first-order nonlinear uncertain systems with delay, the analytical design of active disturbance rejection control (ADRC) with matched time delay is rigorously studied. The conditions of stabilizing the closed-loop system are studied in the form of parameters’ explicit sets such that the tuning laws of ADRC can be directly obtained and intuitively demonstrated in engineering practice. The necessary and sufficient condition of the asymptotical stability for the closed-loop system in the case of linear time-invariant is explicitly given. The condition of stabilizing the closed-loop system with nonlinear uncertain dynamics is quantitatively presented. Moreover, the water tank experiment illustrates the proposed tuning laws.

Distributed Adaptive Dynamic Surface Control for Synchronization of Uncertain Nonlinear Multi-agent Systems

In this paper a distributed adaptive dynamic surface controller is proposed for multi-agent systems under fixed directed graph topologies. The agents have uncertain nonlinear dynamics and are influenced by bounded unknown disturbances. The controller should synchronize the states of all agents with the corresponding states of the nonautonomous leader. It is proved that, with the proposed controller, the synchronization error remains bounded; and the bounds can be arbitrarily decreased by increasing the controller gains. The control rules are designed such that each agent only requires the state information of its neighbors, rendering a distributed control. The effectiveness of the proposed method is demonstrated through two simulation examples.

Finite-time boundedness of Markovain jump nonlinear systems with incomplete information

ABSTRACT This paper deals with the finite-time H ∞ bounded control problem of a class of uncertain Markovian jump nonlinear systems with partially unknown transition probabilities and norm-bounded disturbances. The purpose of the paper is to derive a stochastic finite-time controller such that the resulting nominal or uncertain stochastic nonlinear model is stochastically finite-time H ∞ bounded by applying stochastic analysis techniques and free connection weighting matrix approach. We also provide stochastic finite-time stability and stochastic finite-time boundedness criteria of the class of nominal or uncertain stochastic nonlinear dynamics. Moreover, the derived criteria can be simplified into linear matrix inequalities (LMIs), which could be solved by employing Matlab LMI toolbox. Finally, the effectiveness of proposed approaches is demonstrated by a practical example.

On disturbance rejection in magnetic levitation

Magnetic levitation systems belong to an important and challenging class of control engineering problems with nonlinear uncertain dynamics, multiple disturbances and large sensor noise. To obtain a simple and practical solution that does not depends on the exact model information, a time-varying active disturbance rejection solution is proposed and validated in both numerical and experimental results. The proposed method is confirmed with rigorous analysis of transient performance and noise attenuation. Moreover, the proposed solution is tested in a magnetic levitation ball system with disturbances and measurement noise. The results show that the proposed solution is effective and practical.

Dynamic learning from adaptive neural control for flexible joint robot with tracking error constraints using high-gain observer

ABSTRACTThis paper presents dynamic learning from adaptive neural control with prescribed tracking error performance for flexible joint robot (FJR) included unknown dynamics. Firstly, a system transformation method is introduced to convert the original FJR system into a normal system. As a result, only one neural network (NN) approximator is used to identify the uncertain system nonlinear dynamics and the verification on the convergence of neural weights is simplified extremely. To further solve the predefined performance issue, a performance function is introduced to describe a tracking error constraint and a error transformation technique is used to convert the constrained tracking control problem into the unconstrained stabilization of error system. By combining a high-gain observer and the backsteppig method, the adaptive neural controller is presented to stabilize the unconstrained error system. Under the satisfaction of the partial persistent excitation condition, the adaptive neural controller is shown to be capable of achieving unknown dynamics acquisition, expression and storage. Furthermore, a neural learning control with using the stored NN weights is proposed for the same or similar control task so that a time-consuming NN online adjustment process can be avoided and a better control performance can be obtained. Simulation results demonstrate the effectiveness of the proposed control method.

Passive and active rehabilitation control of human upper-limb exoskeleton robot with dynamic uncertainties

SUMMARYThis paper investigates the passive and active control strategies to provide a physical assistance and rehabilitation by a 7-DOF exoskeleton robot with nonlinear uncertain dynamics and unknown bounded external disturbances due to the robot user's physiological characteristics. An Integral backstepping controller incorporated with Time Delay Estimation (BITDE) is used, which permits the exoskeleton robot to achieve the desired performance of working under the mentioned uncertainties constraints. Time Delay Estimation (TDE) is employed to estimate the nonlinear uncertain dynamics of the robot and the unknown disturbances. To overcome the limitation of the time delay error inherent of the TDE approach, a recursive algorithm is used to further reduce its effect. The integral action is employed to decrease the impact of the unmodeled dynamics. Besides, the Damped Least Square method is introduced to estimate the desired movement intention of the subject with the objective to provide active rehabilitation. The controller scheme is to ensure that the robot system performs passive and active rehabilitation exercises with a high level of tracking accuracy and robustness, despite the unknown dynamics of the exoskeleton robot and the presence of unknown bounded disturbances. The design, stability, and convergence analysis are formulated and proven based on the Lyapunov–Krasovskii functional theory. Experimental results with healthy subjects, using a virtual environment, show the feasibility, and ease of implementation of the control scheme. Its robustness and flexibility to deal with parameter variations due to the unknown external disturbances are also shown.

Anti-disturbance dynamic surface control scheme for a class of uncertain nonlinear systems with asymmetric dead-zone nonlinearity

This study proposes anti-disturbance dynamic surface control scheme for nonlinear strict-feedback systems subjected simultaneously to unknown asymmetric dead-zone nonlinearity, unmatched external disturbance and uncertain nonlinear dynamics. Radial basis function-neural network (RBF-NN) is invoked to approximate the uncertain dynamics of the system, and the dead-zone nonlinearity is represented as a time-varying system with a bounded disturbance. The nonlinear disturbance observer (NDO) is proposed to estimate the unmatched external disturbance which further will be used to compensate the effect of the disturbance. Then, by integrating RBF-NN, NDO and dynamic surface control (DSC) approaches, the proposed anti-disturbance control scheme is designed. Stability analysis of the closed-loop system shows that all signals of the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error can be made arbitrarily small by proper selection of the design parameters. In comparison with the existing methods, the proposed scheme deals with the unmatched external disturbance, uncertain dynamics and unknown asymmetric dead-zone nonlinearity, simultaneously; it avoids the "explosion of complexity" problem and develops the simple control law without singularity concern. Furthermore, some imposed assumptions to the dead-zone input and disturbances are relaxed. Simulation and comparison results verify the effectiveness of the proposed approach.

Adaptive neural output-feedback control for nonstrict-feedback time-delay fractional-order systems with output constraints and actuator nonlinearities

This study addresses the issue of the adaptive output tracking control for a category of uncertain nonstrict-feedback delayed incommensurate fractional-order systems in the presence of nonaffine structures, unmeasured pseudo-states, unknown control directions, unknown actuator nonlinearities and output constraints. Firstly, the mean value theorem and the Gaussian error function are introduced to eliminate the difficulties that arise from the nonaffine structures and the unknown actuator nonlinearities, respectively. Secondly, the immeasurable tracking error variables are suitably estimated by constructing a fractional-order linear observer. Thirdly, the neural network, the Razumikhin Lemma, the variable separation approach, and the smooth Nussbaum-type function are used to deal with the uncertain nonlinear dynamics, the unknown time-varying delays, the nonstrict feedback and the unknown control directions, respectively. Fourthly, asymmetric barrier Lyapunov functions are employed to overcome the violation of the output constraints and to tune online the parameters of the adaptive neural controller. Through rigorous analysis, it is proved that the boundedness of all variables in the closed-loop system and the semi global asymptotic tracking are ensured without transgression of the constraints. The principal contributions of this study can be summarized as follows: (1) based on Caputo’s definitions and new lemmas, methods concerning the controllability, observability and stability analysis of integer-order systems are extended to fractional-order ones, (2) the output tracking objective for a relatively large class of uncertain systems is achieved with a simple controller and less tuning parameters. Finally, computer-simulation studies from the robotic field are given to demonstrate the effectiveness of the proposed controller.