Uncertain Nonlinear Dynamics Research Articles

Cooperative deterministic learning control for a group of homogeneous nonlinear uncertain robot manipulators

This paper addresses the learning control problem for a group of robotmanipulators with homogeneous nonlinear uncertaindynamics, where all the robots have an identical system structure but the reference signals to be tracked differ. The control objective is twofold: to track on reference trajectories andto learn/identify uncertain dynamics. For this purpose, deterministic learning theoryis combined with consensus theory to find a common neural network(NN) approximation of the nonlinear uncertain dynamics for a multi-robotsystem. Specifically, we first present a control scheme called cooperativedeterministic learning using adaptive NNs to enable the robotic agentsto track their respective reference trajectories on one hand andto exchange their estimated NN weights online through networked communicationon the other. As a result, a consensus about one common NN approximationfor the nonlinear uncertain dynamics is achieved for all the agents.Thus, the trained distributed NNs have a better generalization capabilitythan those obtained by existing techniques. By virtue of the convergenceof partial NN weights to their ideal values under the proposed scheme,the cooperatively learned knowledge can be stored/represented by NNswith constant/converged weights, so that it can be used to improvethe tracking control performance without re-adaptation. Numericalsimulations of a team of two-degree-of-freedom robot manipulatorswere conducted to demonstrate the effectiveness of the proposedapproach.

Cooperative global robust group output regulation for multi-agent systems with heterogeneous uncertain second-order nonlinear dynamics

In this paper, we study the global robust group output regulation problem for multi-agent systems with heterogeneous uncertain second-order nonlinear dynamics. The intelligence factor is introduced to construct a designed graph matrix which overcomes the communication influence between multiple coupled subnetworks with different exosystems. In terms of internal model principle, the global robust group output regulation problem is converted into the global robust dynamic stability problem of the so-called augmented multi-agent system. Further, the augmented multi-agent system is globally stabilized via a distributed state feedback control law. A special case of the main result of this paper leads to the solution of the global robust multi-tracking control problem for nonlinear multi-agent networks. A simulation is performed to illustrate the effectiveness of the theoretical results.

Fault Diagnosis of Uncertain Hybrid Systems

This paper presents an online monitoring and fault diagnosis architecture for hybrid systems with nonlinear uncertain discrete-time dynamics. The architecture features a modular observer based on a modified hybrid automaton framework, that models each subsystem individually and the whole system as a composition of these models. The fault detection scheme can detect both discrete and parametric faults using a mode dependent time-varying threshold that guarantees no false-positives alarms due to modeling uncertainty. The fault isolation scheme can anticipate which fault events may have occurred and dynamically employs only the necessary number of isolation estimators that try to isolate the fault by calculating residual thresholds and approximating the unknown parameter values. Simulation results of a two-tank hybrid system example illustrate the effectiveness of the proposed approach.

Centralized Fault Detection of Complex Uncertain Hybrid Systems

This paper presents a centralized fault detection scheme for hybrid systems with nonlinear uncertain continuous dynamics and measurement noise. The scheme features a modular observer based on a modified hybrid automaton framework, that models each subsystem individually and the whole system as a composition of these models. The fault detection scheme employs a filtering approach, that attenuates the effect of measurement noise and allows tighter detection thresholds, and also an algorithm that handles autonomous mode transitions. As a result, the proposed approach can detect both discrete and parametric faults and guarantees no false alarms under all circumstances. Simulation results from a two-tank hybrid system example illustrate the effectiveness of the proposed scheme.

Command filter based globally stable adaptive neural control for cooperative path following of multiple underactuated autonomous underwater vehicles with partial knowledge of the reference speed

Abstract This paper investigates the problem of cooperative path following for a fleet of underactuated autonomous underwater vehicles (AUVs) with uncertain nonlinear dynamics. Path following controllers for individual AUVs are developed to ensure that each AUV converges to the desired position. The coordination mission is completed by reaching synchronization on a suitably defined path variable, even in the presence of partial knowledge of the reference speed. The key features of the proposed cooperative path following design scheme can be summarized as follows. First, the command filter design technique based cooperative path following control strategy is derived by introducing compensating error signals to remove the requirement of the higher derivative of reference signal, and a simplified cooperative path following controller is proposed. Second, a smoothly switching function is designed to yield neural network (NN) based energy-efficient controller. Third, by designing the distributed speed estimator, the global knowledge of the reference speed is relaxed. Finally, all the signals in the closed-loop system are guaranteed to be globally uniformly ultimately bounded (GUUB) under the proposed algorithm, and the path following error is proven to converge to a small neighborhood of the origin. Simulation example is provided to validate the performance of the control strategy.

Formation Learning Control of Multiple Autonomous Underwater Vehicles With Heterogeneous Nonlinear Uncertain Dynamics.

In this paper, a new concept of formation learning control is introduced to the field of formation control of multiple autonomous underwater vehicles (AUVs), which specifies a joint objective of distributed formation tracking control and learning/identification of nonlinear uncertain AUV dynamics. A novel two-layer distributed formation learning control scheme is proposed, which consists of an upper-layer distributed adaptive observer and a lower-layer decentralized deterministic learning controller. This new formation learning control scheme advances existing techniques in three important ways: 1) the multi-AUV system under consideration has heterogeneous nonlinear uncertain dynamics; 2) the formation learning control protocol can be designed and implemented by each local AUV agent in a fully distributed fashion without using any global information; and 3) in addition to the formation control performance, the distributed control protocol is also capable of accurately identifying the AUVs' heterogeneous nonlinear uncertain dynamics and utilizing experiences to improve formation control performance. Extensive simulations have been conducted to demonstrate the effectiveness of the proposed results.

Power maximization of variable-speed variable-pitch wind turbines using passive adaptive neural fault tolerant control

Power maximization has always been a practical consideration in wind turbines. The question of how to address optimal power capture, especially when the system dynamics are nonlinear and the actuators are subject to unknown faults, is significant. This paper studies the control methodology for variable-speed variable-pitch wind turbines including the effects of uncertain nonlinear dynamics, system fault uncertainties, and unknown external disturbances. The nonlinear model of the wind turbine is presented, and the problem of maximizing extracted energy is formulated by designing the optimal desired states. With the known system, a model-based nonlinear controller is designed; then, to handle uncertainties, the unknown nonlinearities of the wind turbine are estimated by utilizing radial basis function neural networks. The adaptive neural fault tolerant control is designed passively to be robust on model uncertainties, disturbances including wind speed and model noises, and completely unknown actuator faults including generator torque and pitch actuator torque. The Lyapunov direct method is employed to prove that the closed-loop system is uniformly bounded. Simulation studies are performed to verify the effectiveness of the proposed method.

Model-Based Reinforcement Learning in Differential Graphical Games

This paper seeks to combine differential game theory with the actor-critic-identifier architecture to determine forward-in-time, approximate optimal controllers for formation tracking in multi-agent systems, where the agents have uncertain heterogeneous nonlinear dynamics. A continuous control strategy is proposed, using communication feedback from extended neighbors on a communication topology that has a spanning tree. A model-based reinforcement learning technique is developed to cooperatively control a group of agents to track a trajectory in a desired formation. Simulation results are presented to demonstrate the performance of the developed technique.

Single-parameter-learning-based fuzzy fault-tolerant output feedback dynamic surface control of constrained-input nonlinear systems

This paper addresses the problem of adaptive fuzzy fault-tolerant dynamic surface control for a class of constrained-input nonlinear systems. To resolve this problem, the design of an observer-based single-parameter-learning (SPL) control method using output feedback is proposed. The Takagi-Sugeno (T-S) fuzzy system is used to identify and approximate online the uncertain nonlinear dynamics, requiring no knowledge. The barriers that restrict the applications of the traditional backstepping and approximation-based approach, including the explosion of complexity and the dimension curse problems, are circumvented via dynamic surface control and SPL techniques. The merit of the proposed method lies in that only one parameter in the entire control scheme requires online adjustment, regardless of the number of parameters in the T-S fuzzy system that characterizes the fuzzy rules; the calculation burden, in this sense, is reduced to the extent of the minimum value. The truncated adaptation method is used to avoid the chattering and instability caused by constrained input. It is shown with rigorous proof using the Lyapunov and invariant set theorems that all the closed-loop signals are guaranteed semi-globally uniformly ultimately bounded. The output tracking error is adjustable by means of design parameters in an explicit form, and can be adjusted to an arbitrarily small value around zero by appropriately chosen control parameters, even under faulty and constrained actuators. Simulation and comparative results are provided to demonstrate the effectiveness of the proposed control approach.

Distributed Adaptive Finite-Time Approach for Formation-Containment Control of Networked Nonlinear Systems Under Directed Topology.

This paper presents a distributed adaptive finite-time control solution to the formation-containment problem for multiple networked systems with uncertain nonlinear dynamics and directed communication constraints. By integrating the special topology feature of the new constructed symmetrical matrix, the technical difficulty in finite-time formation-containment control arising from the asymmetrical Laplacian matrix under single-way directed communication is circumvented. Based upon fractional power feedback of the local error, an adaptive distributed control scheme is established to drive the leaders into the prespecified formation configuration in finite time. Meanwhile, a distributed adaptive control scheme, independent of the unavailable inputs of the leaders, is designed to keep the followers within a bounded distance from the moving leaders and then to make the followers enter the convex hull shaped by the formation of the leaders in finite time. The effectiveness of the proposed control scheme is confirmed by the simulation.

Adaptive quantised observer‐based output feedback control for non‐linear systems with input and output quantisation

This study investigates the case of simultaneous input and output quantisation for a class of non-linear output feedback systems subject to uncertain non-linear dynamics and non-zero initial states. An adaptive quantised observer-based output feedback controller is designed to guarantee bounded stability and H∞ performance despite input and output quantisation. In comparison with the existing work, the main contributions of this study are that: (i) an important lemma is proposed to remove the matrix equality constraint used in many existing results, and three new design methods in strict terms of linear matrix inequality techniques are proposed; (ii) this study focuses on eliminating the impact of both input and output quantisation errors. Since the impact of input and output quantisation errors cannot be fully eliminated, the estimation error is proved to be ultimately bounded and to converge to a residual set; and (iii) an adaptive compensation term is constructed to compensate for the time-variant effects caused by non-linear dynamics and uncertain parameter vectors. Finally, two numerical examples are given to show the efficacy and advantages of the proposed methods.

Leader-following consensus for a class of high-order nonlinear multi-agent systems

The finite-time leader-following consensus problem is addressed for a class of high-order multi-agent systems with uncertain nonlinear dynamics. Each follower node is modeled by lower-triangular system. By using recursive method, we develop the finite-time consensus control design scheme. Based on finite-time Lyapunov stability theorem and matrix theory, we prove that the finite-time consensus of high-order uncertain nonlinear multi-agent systems is guaranteed by non-lipschitz continuous control laws. Simulation results are given to illustrate the effectiveness of the theoretical results.

Adaptive finite time coordinated consensus for high-order multi-agent systems: Adjustable fraction power feedback approach

Finite-time consensus for multi-agent systems (MAS) with high-order nonlinear uncertain dynamics under directed communication topology is still an open problem due to the involvement of high-order nonlinear uncertain dynamics; one-way directed communication constraints; and unknown time-varying control effectiveness gain. In this paper, based upon the locally defined consensus error and fractionally composed virtual error, a number of useful intermediate results are derived, with which, a finite time consensus solution is established for networked MAS with high-order uncertain dynamics under single-way directed communication topology. By including fraction power integration as part of the Lyapunov function candidate and by using inductive analysis, it is shown that the proposed distributed solution is able to achieve consensus in finite time with sufficient accuracy. The benefits and effectiveness of the developed algorithm are also confirmed by numerical simulations.

Adaptive consensus of nonlinear multi-agent systems with unknown backlash-like hysteresis

In this brief, we consider the consensus problem of high-order nonlinear multi-agent systems with unknown backlash-like hysteresis and unknown control direction. By using backstepping technique, a distributed adaptive control scheme, with the adoption of Nussbaum-type function, is developed to solve this consensus problem. Radial basis function neural network is employed to neutralize the uncertain nonlinear dynamics. The approximation error of the neural networks, together with external disturbance and a bounded term from the hysteresis model, is adaptively estimated and counteracted by a robust term. Under undirected connected communication topology, it is proved that the consensus can be achieved asymptotically with the proposed control protocol. Finally, a numerical example is presented to illustrate the performance of the proposed protocol.

Global output‐feedback control of systems with dynamic nonlinear input uncertainties through singular perturbation‐based dynamic scaling

SummaryA general class of uncertain nonlinear systems with dynamic input nonlinearities is considered. The system structure includes a core nominal subsystem of triangular structure with additive uncertain nonlinear functions, coupled uncertain nonlinear appended dynamics, and uncertain nonlinear input unmodeled dynamics. The control design is based on dual controller/observer dynamic high‐gain scaling with an additional dynamic scaling based on a singular perturbation‐like redesign to address the non‐affine and uncertain nature of the input appearance in the system dynamics. The proposed approach yields a constructive global robust adaptive output‐feedback control design that is robust to the dynamic input uncertainties and to uncertain nonlinear functions allowed throughout the system structure. Copyright © 2015 John Wiley & Sons, Ltd.

Cyclic-small-gain method for distributed nonlinear control

Distributed control has attracted considerable attention from control and other scientific communities. Complex nonlinear uncertain dynamics is ubiquitous in control systems, and the distributed control for this kind of systems has not been fully studied. One fundamental problem is caused by the coexistence of constraints on information exchange and complex nonlinear dynamics in distributed control systems. The cyclic-small-gain methods have recently shown to be a powerful tool for the design of distributed nonlinear controllers. This paper reviews the main results on the cyclic-small-gain methods for distributed control, and pinpoints several directions for future research.

Robust consensus controller design for heterogeneous multi-UAV systems

In this paper, distributed consensus tracking control for heterogeneous multi-uav systems with nonlinearities and uncertainty is considered. It is assumed that the leaders output is time-varying and unmanned aerial vehicles have different nonlinear uncertain dynamics. A distributed robust consensus protocol is designed to restrain the effect of nonlinear uncertainties on the multi-UAV systems and guarantee the consensus tracking between the followers and the leader. The designed robust consensus protocol includes a nominal virtual controller and a robust virtual compensator. The nominal virtual controller is first designed to get desired consensus tracking property for the nominal disturbance-free subsystem, and then the robust virtual compensator is designed to restrain the effect of the uncertainties. From the Lyapunov stability theorem, it is shown that the consensus tracking errors can be made as small as desired with expect converge rate. Finally, an example is presented to illustrate the theoretical results.

Further Results on Predictor-Based Control of Neuromuscular Electrical Stimulation.

Electromechanical delay (EMD) and uncertain nonlinear muscle dynamics can cause destabilizing effects and performance loss during closed-loop control of neuromuscular electrical stimulation (NMES). Linear control methods for NMES often perform poorly due to these technical challenges. A new predictor-based closed-loop controller called proportional integral derivative controller with delay compensation (PID-DC) is presented in this paper. The PID-DC controller was designed to compensate for EMDs during NMES. Further, the robust controller can be implemented despite uncertainties or in the absence of model knowledge of the nonlinear musculoskeletal dynamics. Lyapunov stability analysis was used to synthesize the new controller. The effectiveness of the new controller was validated and compared with two recently developed nonlinear NMES controllers, through a series of closed-loop control experiments on four able-bodied human subjects. Experimental results depict statistically significant improved performance with PID-DC. The new controller is shown to be robust to variations in an estimated EMD value.

Passivity and Stability of Human–Robot Interaction Control for Upper-Limb Rehabilitation Robots

Each year, stroke and traumatic brain injury leave millions of survivors with motion control loss, which results in great demand for recovery training. The great labor intensity in traditional human-based therapies has recently boosted the research on rehabilitation robotics. Existing controllers for rehabilitative robotics cannot solve the closed-loop system stability with uncertain nonlinear dynamics and conflicting human–robot interactions. This paper presents a theoretical framework that establishes the passivity of the closed-loop upper-limb rehabilitative robotic systems and allows rigorous stability analysis of human–robot interaction. Position-dependent stiffness and position-dependent desired trajectory are employed to resolve the possible conflicts in motions between patient and robot. The proposed method also realizes the “assist-as-needed” strategy. In addition, it handles human–robot interactions in such a way that correct movements are encouraged and incorrect ones are suppressed to make the training process more effective. While guaranteeing these properties, the proposed controller allows parameter adjustment to provide flexibility for therapists to adjust and fine tune depending on the conditions of the patients and the progress of their recovery. Simulation and experiment results are presented to illustrate the performance of the method.

Neural network-based adaptive consensus tracking control for multi-agent systems under actuator faults

In this paper, a distributed output feedback consensus tracking control scheme is proposed for second-order multi-agent systems in the presence of uncertain nonlinear dynamics, external disturbances, input constraints, and partial loss of control effectiveness. The proposed controllers incorporate reduced-order filters to account for the unmeasured states, and the neural networks technique is implemented to approximate the uncertain nonlinear dynamics in the synthesis of control algorithms. In order to compensate the partial loss of actuator effectiveness faults, fault-tolerant parts are included in controllers. Using the Lyapunov approach and graph theory, it is proved that the controllers guarantee a group of agents that simultaneously track a common time-varying state of leader, even when the state of leader is available only to a subset of the members of a group. Simulation results are provided to demonstrate the effectiveness of the proposed consensus tracking method.