Robust Adaptive Control Design Research Articles

A robust adaptive control design for active tuned mass damper systems of multistory buildings

In this study, a robust adaptive controller is designed to be used in an active tuned mass damper system that can be used to damp undesired vibrations that occurred on the multistory buildings during the earthquake. To realize the controller design, all of the system parameters are assumed to be unknown, and the adaptive structure of the designed controller is obtained by designing adaptive compensation rules for system parameters. A backstepping control design approach is utilized for the control design by considering the appropriateness of the system’s structure of multistory buildings having an active tuned mass damper system at the top of the structure. The proposed control design is supported with a Lyapunov-based stability analysis where it is proven that the designed controller is able to protect the overall system’s stability while reaching the main control purpose. In addition to these, in the simulation studies realized for a nine-story building under the effect of a major earthquake, it is shown that the designed controller can be used to reach the main control purpose efficiently.

Optimum Design of Robust Adaptive Controller with Actuator Constraints

In this paper, a direct optimal adaptive nonlinear tracking control method for a class of uncertain Multi-Input Multi-Output (MIMO) nonlinear systems with actuator amplitude constraints in presence of unknown disturbance is developed. In order to handle parametric model uncertainties and external disturbance, an adaptive controller is presented. Particle Swarm Optimization (PSO) algorithm is employed to prevent constraints violation through determining the optimal adaptive controller parameters. The performance of this control approach is studied using a new index function in time-domain, and the stability analysis is conducted by Lyapunov theory. In addition, indicative robot examples are provided to illustrate how investigated method effectively stabilizes system and confines tracking error to prescribed bounds without control input saturation, particularly with large parametric uncertainties.

Novel algebraic meal disturbance estimation based adaptive robust control design for blood glucose regulation in type 1 diabetes patients.

This study designs a robust closed-loop control algorithm for elevated blood glucose level stabilisation in type 1 diabetic patients. The control algorithm is based on a novel control action resulting from integrating algebraic meal disturbance estimator with back-stepping integral sliding mode control (BISMC) technique. The estimator shows finite time convergence leading to accurate and fast estimation of meal disturbance. Moreover, compensation of the estimated disturbance in controller provides significant reduction in chattering phenomenon, which is inherent drawback of sliding mode control (SMC). The controller is applied to one of the most reliable models of type 1 diabetic patients, named Bergman's minimal model. The effectiveness and superiority of the designed controller is shown by comparing it to classical SMC and super-twisting sliding mode control. The designed controller is subject to three different cases for detailed analysis of the controller's robustness against meal disturbance. The three cases considered are hyperglycaemia, hyperglycaemia combined with meal disturbance and three meal disturbance. The simulation results confirm superior performance of algebraic disturbance estimator based BISMC controller for all the cases mentioned above.

Novel Optimal Adaptive Robust Control for Fuzzy Underactuated Mechanical Systems: A Nash Game Approach

This article addresses the problems of the adaptive robust control design and the parameters optimization for a class of underactuated mechanical systems. We describe the uncertainty by using the fuzzy set theory to form the fuzzy dynamical systems. A novel adaptive robust control with two tunable gain parameters is designed based on the formed system, and the nonholonomic servo constraints are also considered in the control design. By employing the principle of the Nash game theory, we establish an optimization method for the two gain parameters, and the Nash equilibrium orients the optimal values of the two gain parameters. Finally, the effectiveness of the designed optimal control is shown by a numerical simulation.

LMI-based robust adaptive neural network control for Euler–Bernoulli beam with uncertain parameters and disturbances

This paper is concerned with the stabilisation problem of an Euler–Bernoulli beam with uncertain parameters and disturbances. To correctly represent the beam's behaviour, the partial differential equations model is utilised for the control design of the beam without missing any high-order mode information. Then the linear matrix inequalities (LMIs) method is applied to the robust adaptive neural network control design to cope with systematic uncertainties and stabilise the beam system with disturbance compensation. Through resolving LMIs, feasible sets of designed control parameters can be effectively obtained without model linearisation. Finally, numerical simulations are done to validate the effectiveness of the proposed control.

Adaptive Robust Control and Optimal Design for Fuzzy Unmanned Helicopter Tail Reduction

This paper develops an adaptive robust control scheme combined with optimal design for the unmanned helicopter tail reduction (UHTR) system. The dynamical model of the UHTR system with uncertainties is established. The uncertainties are assumed to be bounded and expressed by fuzzy set theory. With this prerequisite, an adaptive robust controller is proposed to drive the system to meet the trajectory requirements approximately. The adaptive law with leakage and dead zone is performance based and flexibly adjustable. By means of Lyapunov stability theorem, the UHTR system is both uniform bounded and uniform ultimate bounded with the proposed controller. The control scheme is deterministic rather than fuzzy if-then rules-based control. Moreover, the fuzzy performance index which contains the steady-state system performance and control cost is presented. In this way, the optimal design problem can be replaced by minimizing the performance index. Overall, the resulting control scheme can guarantee deterministic performance of the UHTR system and minimize the fuzzy performance index simultaneously.

Optimal Design of Adaptive Robust Control for the Delta Robot with Uncertainty: Fuzzy Set-Based Approach

An optimal control design for the uncertain Delta robot is proposed in the paper. The uncertain factors of the Delta robot include the unknown dynamic parameters, the residual vibration disturbances and the nonlinear joints friction, which are (possibly fast) time-varying and bounded. A fuzzy set theoretic approach is creatively used to describe the system uncertainty. With the fuzzily depicted uncertainty, an adaptive robust control, based on the fuzzy dynamic model, is established. It designs an adaptation mechanism, consisting of the leakage term and the dead-zone, to estimate the uncertainty information. An optimal design is constructed for the Delta robot and solved by minimizing a fuzzy set-based performance index. Unlike the traditional fuzzy control methods (if-then rules-based), the proposed control scheme is deterministic and fuzzily optimized. It is proven that the global solution in the closed form for this optimal design always exists and is unique. This research provides the Delta parallel robot a novel optimal control to guarantee the system performance regardless of the uncertainty. The effectiveness of the proposed control is illustrated by a series of simulation experiments. The results reveal that the further applications in other robots are feasible.

A New Design Scheme for Intelligent Upper Limb Rehabilitation Training Robot.

In view of the urgent need for intelligent rehabilitation equipment for some disabled people, an intelligent, upper limb rehabilitation training robot is designed by applying the theories of artificial intelligence, information, control, human-machine engineering, and more. A new robot structure is proposed that combines the use of a flexible rope with an exoskeleton. By introducing environmentally intelligent ergonomics, combined with virtual reality, multi-channel information fusion interaction technology and big-data analysis, a collaborative, efficient, and intelligent remote rehabilitation system based on a human’s natural response and other related big-data information is constructed. For the multi-degree of the freedom robot system, optimal adaptive robust control design is introduced based on Udwdia-Kalaba theory and fuzzy set theory. The new equipment will help doctors and medical institutions to optimize both rehabilitation programs and their management, so that patients are more comfortable, safer, and more active in their rehabilitation training in order to obtain better rehabilitation results.

Robust Fuzzy Adaptive Finite-Time Control for High-Order Nonlinear Systems With Unmodeled Dynamics

This article studies the problem of the robust fuzzy adaptive finite-time control design for a class of single-input single-output high-order nonlinear systems. The considered plants contain unknown nonlinear functions, unmodeled dynamics, and dynamical disturbances. In this control design, fuzzy logic systems are utilized to approximate unknown nonlinear functions, and dynamical signal functions are introduced to solve unmodeled dynamics and dynamical disturbances. Under the framework of an adaptive backstepping control and adding a power integrator control design technique, a robust fuzzy adaptive finite-time control scheme is developed, which can not only guarantee the controlled system to be semiglobal practical finite-time stable, but also have the robustness to unmodeled dynamics and dynamical disturbances. Both numerical and practical simulation examples are provided to check the effectiveness of the proposed control method.

Robust adaptive control of nonlinearly parametrized multivariable systems with unmatched disturbances

SummaryA new robust adaptive control scheme is developed for nonlinearly parametrized multivariable systems in the presence of parameter uncertainties and unmatched disturbances. The developed control scheme employs a new integrated framework of a functional bounding technique for handling nonlinearly parametrized system dynamics, an adaptive parameter estimation algorithm for dealing with parameter uncertainties, a nonlinear feedback controller structure for stabilization of interconnected system states, and a robust adaptive control design for accommodating unmatched disturbances. It is proved that such a new robust adaptive control scheme is capable of ensuring the global boundedness and mean convergence of all closed‐loop system signals. A complete simulation study on an air vehicle system with nonlinear parametrization in the presence of an unmatched wind disturbance is conducted, and its results verify the effectiveness of the proposed robust adaptive control scheme.

An optimal fuzzy-theoretic setting of adaptive robust control design for a lower limb exoskeleton robot system

Aim to recover the motor function of impaired lower limbs of stroke patients, in this paper, we propose a novel adaptive robust control with a fuzzy optimal gain design approach for an effective rehabilitation training equipment, i.e. the 2DOF lower limb exoskeleton robot system (LLERs). Our proposed control method includes two parts, the first part is a novel adaptive robust control, as a bottom line, it will guarantee the uniform boundedness and uniform ultimate boundedness regardless of uncertainties and disturbances. The second part is a novel optimization method for control gain parameter, since the uncertainties and disturbances will arise in the practical 2DOF LLERs inevitably, we adopt the fuzzy set theory to describe these uncertainties and disturbances, and the bounds of these uncertainties and disturbances are characterized by membership functions. Based on such descriptions and several subsequent fuzzy operations, a fuzzy performance index which contains average fuzzy system performances and control costs will be constructed to seek an optimal control gain for the adaptive robust control put forward, in addition, the existence of optimal control gain has been also verified theoretically. Eventually, the simulation results presented have demonstrated the effectiveness of our proposed algorithm on rehabilitation training of lower limbs.

Design of Adaptive Robust Controller for Second-Order Non-affine Systems with Input Saturation

In this paper, two techniques are introduced to transform an uncertain second-order non-affine system under input saturation to an equivalent affine model. First, this affine model is obtained using the linearization technique with respect to the system inputs. In the case of the system being non-differentiable or its derivative with respect to the input being zero, this technique cannot be used. Then, to cope with this problem, an average dynamical model is suggested using the Filippov’s model and the pulse width modulation. Afterward, an adaptive sliding mode controller is designed to overcome the approximation errors appeared in this transformation and inherent system uncertainties. Stability analysis is also derived using the Lyapunov theory. Ultimately, the capability of the proposed method is shown through MATLAB simulations.

Optimal Design of Adaptive Robust Control for Bounded Constraint-Following Error in Fuzzy Mechanical Systems

This paper proposes an optimal indirect approach for asymmetric bounds in constraint-following in mechanical systems with (possibly fast) time-varying fuzzy uncertainty. The uncertainty is described with fuzzy set theory. We aim at optimal controller to drive the constraint-following error of the concerned fuzzy system to lie within a desired (possibly asymmetric) bound all the time and get to be sufficiently small eventually. For deterministic performance, we transform the fuzzy original system into a constructed fuzzy system, for which a deterministic (not the usual if-then rules-based) adaptive robust control is designed for uniform boundedness and uniform ultimate boundedness. For optimal performance, a performance index is proposed based on the fuzzy information, by minimizing which an optimal control gain design problem is formulated and solved. When the constructed fuzzy system is uniform boundedness and uniform ultimate boundedness, the constraint-following error of the original fuzzy system is proved to be bounded. As a result, the control design can render out deterministic performance and minimum performance index.

RBF-Neural-Network-Based Adaptive Robust Control for Nonlinear Bilateral Teleoperation Manipulators With Uncertainty and Time Delay

The bilateral teleoperation system has raised expansive concern as its excellent behaviors in executing the tasks in the remote, unstructured, and dangerous areas via the cooperative operation systems. In this article, an radial basis function (RBF) neural network based adaptive robust control design is proposed for nonlinear bilateral teleoperation manipulators to cope with the main issues including the communication time delay, various nonlinearities, and uncertainties. Specifically, the slave environmental dynamics is modeled by a general RBF neural network, and its parameters are estimated and then transmitted for the environmental torque reconstruction in the master side. Since the parameters of the neural network (which are nonpower signals) are transmitted instead of the traditional environmental torque in the communication channel, the previous existing passivity problem under time delay is avoided. In both of master and slave sides, the trajectory creators are applied to generate the desired trajectories, and the RBF-neural-network-based adaptive robust controllers are designed subsequently to handle the nonlinearities and uncertainties. Theoretically, the proposed control algorithm can guarantee the global stability of bilateral teleoperation manipulators under time delay, and the good transparency performance with both position tracking and force feedback is also achieved simultaneously. The real platform comparative experiments are carried out, and the results show the good position tracking to execute precise operation and the good force feedback to detect the sudden disturbance in the environment dynamics.

Adaptive Robust Nonlinear Control Design for Course Tracking of Ships Subject to External Disturbances and Input Saturation

An adaptive robust control law is proposed for the course tracking problem of ships in this paper incorporating a Nussbaum function and an auxiliary dynamic system into the adaptive dynamic surface control (DSC) technique. The ship steering dynamics is described by the Norrbin nonlinear model with completely unknown control coefficient, parameter uncertainties, and unknown external disturbances and input saturation caused by the rudder constraint. The Nussbaum function is adopted to deal with completely unknown control coefficient and avoid the controller singularity problem. An auxiliary dynamic system is introduced to handle the effect of input saturation. The DSC technique makes the control law be simple to compute and easy to implement in engineering practice. It is proved that the proposed course tracking control law of ships makes the course tracking error be arbitrarily small by an appropriate choice of the design parameters and guarantees the uniform ultimate boundedness of all signals in the closed-loop ship course control system. Finally, simulation results on two ships and simulation comparison with an existing adaptive neural control scheme demonstrate the effectiveness and the superiority of the proposed control scheme.

Dynamic-free robust adaptive intelligent fault-tolerant controller design with prescribed performance for stable motion of quadruped robots

In this article, a robust adaptive intelligent fault-tolerant controller with prescribed performance is proposed for an uncertain quadruped robot with actuator fault. The control system comprised of three terms: (1) a full-state feedback controller which includes the prescribed performance function, (2) an adaptive intelligent wavelet-based Takagi-Sugeno fuzzy network (TSFN), and (3) a robust control term. The proposed controller does not utilize the robot dynamic model. A wavelet-based TSFN is utilized to approximate adaptively the lumped nonlinear terms, parameter uncertainties, and defective torque signal. The wavelet block acts as a feature extractor, reduces the number of fuzzy rules, and also acts as a normalization function. The parameters of TSFN are tuned online by an adaptive law based on Lyapunov stability theory. The proposed controller guarantees the desired specification such as minimum speed of convergence, maximum steady-state error, overshoot concerning the position tracking error, and also bounded closed-loop signals. Numerical simulations on MATLAB/SimMechanics environment demonstrate the stable walking of the quadruped robot in the presence of the actuator faults and parameter uncertainties.

A Novel Delay-Independent Robust Adaptive Controller Design for Uncertain Nonlinear Systems With Time-Varying State Delay

Abstract In this paper, two novel adaptive control strategies are presented based on the linear matrix inequality for nonlinear Lipschitz systems. The proposed approaches are developed by creatively using Krasovskii stability theory to compensate parametric uncertainty, unknown time-varying internal delay, and bounded matched or mismatched disturbance effects in closed-loop system of nonlinear systems. The online adaptive tuning controllers are designed such that reference input tracking and asymptotic stability of the closed-loop system are guaranteed. A novel structural algorithm is developed based on linear matrix inequality (LMI) and boundaries of the system delay or uncertainty. The capabilities of the proposed tracking and regulation methods are verified by simulation of three physical uncertain nonlinear system with real practical parameters subject to internal or state time delay and disturbance.

Event‐triggered robust adaptive control for discrete time uncertain systems with unmodelled dynamics and disturbances

In practice, modelling errors caused by high-order unmodelled dynamics and external disturbances are unavoidable. How to ensure the robustness of an adaptive controller with respect to such modelling errors is always a critical concern. In this study, the authors consider the design of event-triggered robust adaptive control for a class of discrete-time uncertain systems which involve such modelling errors and also are allowed to be non-minimum phase. Unlike some existing event-triggered control schemes, the developed controllers do not require that the measurement errors meet the corresponding input-to-state stable condition. Global stability of the closed-loop system which means that all the signals are bounded is established in the presence of unmodelled dynamics and disturbances. Besides, in contrast to existing robust adaptive schemes, the designed adaptive controller does not involve parameters related to unmodelled dynamics and disturbances which are difficult to be chosen for ensuring such stability. An example is given to verify the effectiveness of the proposed control strategy.

A New Multi-objective Artificial Bee Colony Algorithm for Optimal Adaptive Robust Controller Design

Artificial bee colony algorithm as a recent meta-heuristic algorithm, inspired from the foraging behavior of honey bees, can be considered as a proper technique to handle optimization problems. In this paper, a multi-objective artificial bee colony algorithm is introduced in which an archive is defined to store non-dominated solutions. Furthermore, to reduce computations and to have evenly distributed solutions, the archive is pruned using a technique based on neighborhood radius concepts. A group of bees that is responsible for improvement of the solutions chooses and exploits one solution of the archive. Because of the definition of neighborhood radius and retaining adjacent solutions, the remaining solutions have an equal chance to be selected by onlooker bees. In order to examine the proposed algorithm, some benchmark functions are used and the results are compared with true Pareto fronts. Moreover, the algorithm is utilized to optimize the coefficients of a new combined controller applied to a ball-beam system. In fact, the proposed controller is a combination of robust decoupled sliding mode and adaption laws based on the gradient decent method. The objective functions are considered as the integral time of absolute of errors of the ball position and the beam angle that should be minimized with a constraint on the control effort. To evaluate and validate the suggested approach, the obtained time responses of the ball-beam system are compared with those of other recently reported controllers.

Robust Adaptive Saturated Fault-tolerant Control of Autonomous Rendezvous with Mismatched Disturbances

This paper investigates the robust adaptive relative pose control design for spacecraft rendezvous and docking missions in the presence of parametric uncertainty, matched and mismatched disturbances, actuator saturation and faults. An adaptive saturated fault-tolerant controller is developed by incorporating the anti-windup compensator to adaptive backstepping technique. In contrast to traditional saturated fault-tolerant controllers for the spacecraft systems, the advantage of the proposed control approach can deal with the mismatched disturbances in the model. Also this approach does not require exact knowledge of the actuator faults and is implemented with uncertain value of fault information. Lyapunov analysis is employed to prove the ultimately uniformly bounded stability of the closed-loop system, where relative pose and velocities converge to adjustable small neighborhoods of zero. Numerical simulation results demonstrate the effectiveness of the proposed control approach.