Decentralized adaptive controller design of large-scale uncertain robotic systems

In this paper, we develop a decentralized neural network control design for robotic systems. Using this design, it is not necessary to derive the robotic dynamical system (robotic model) for the control of each of the robotic components, as in traditional robot control. The advantage of the proposed neural network controller is that, under a mild assumption, unknown nonlinear dynamics such as inertia matrix and Coriolis/centripetal matrix and friction, as well as interconnections with arbitrary nonlinear bounds can be accommodated with on-line learning.     

Robust adaptive tracking control of robotic systems with uncertainties

To deal with the uncertainty factors of robotic systems, a robust adaptive tracking controller is proposed. The knowledge of the uncertainty factors is assumed to be unidentified; the proposed controller can guarantee robustness to parametric and dynamics uncertainties and can also reject any bounded, immeasurable disturbances entering the system. The stability of the proposed controller is proven by the Lyapunov method. The proposed controller can easily be implemented and the stability of the closed system can be ensured; the tracking error and adaptation parameter error are uniformly ultimately bounded （UUB）. Finally, some simulation examples are utilized to illustrate the control performance.     

A new method for adaptive model-based control of non-linear dynamic plants using a neuro-fuzzy-fractal approach

 We describe in this paper a new method for adaptive model-based control of non-linear dynamic plants using Neural Networks, Fuzzy Logic and Fractal Theory. The new neuro-fuzzy-fractal method combines Soft Computing (SC) techniques with the concept of the fractal dimension for the domain of Non-Linear Dynamic Plant Control. The new method for adaptive model-based control has been implemented as a computer program to show that our neuro-fuzzy-fractal approach is a good alternative for controlling non-linear dynamic plants. We illustrate in this paper our new methodology with the case of controlling biochemical reactors in the food industry. For this case, we use mathematical models for the simulation of bacteria growth for several types of food. The goal of constructing these models is to capture the dynamics of bacteria population in food, so as to have a way of controlling this dynamics for industrial purposes.     

An observer-based adaptive neural network tracking control of robotic systems

Robotic systems have inherently nonlinear phenomena as joints undergo sliding and/or rotating. This in turn requires that the system running states be predicted correctly. This paper makes a full analysis of the robot states by applying observer-based adaptive wavelet neural network (OBAWNN) tracking control scheme to tackle these phenomena such as system uncertainties, multiple time-delayed state uncertainties, and external disturbances such that the closed loop system signals must obey uniform ultimate boundedness and achieve H^∞ tracking performance. The recurrent adaptive wavelet neural network model is used to approximate the dynamics of the robotic system, while an observer-based adaptive control scheme is to stabilize the system. The advantage of employing adaptive wavelet neural dynamics is that we can utilize the neuron information by activation functions to on-line tune the hidden-to-output weights, and the adaptation parameters to estimate the robot parameters and the bounds of the gains of delay states directly using linear analytical results. It is shown that the stability of the closed-loop system is guaranteed by some sufficient conditions derived from Lyapunov criterion and Riccati-inequality. Finally, a numerical example of a three-links rolling cart is given to illustrate the effectiveness of the proposed control scheme.     

A global adaptive learning control for robotic manipulators

This paper addresses the problem of designing a global adaptive learning control for robotic manipulators with revolute joints and uncertain dynamics. The reference signals to be tracked are assumed to be smooth and periodic with known period. By developing in Fourier series expansion the input reference signals of every joint, an adaptive learning PD control is designed which ‘learns’ the input reference signals by identifying their Fourier coefficients: global asymptotic and local exponential stability of the tracking error dynamics are obtained when the Fourier series expansion of each input reference signal is finite, while arbitrary small tracking errors are achieved otherwise. The resulting control is not model based and depends only on the period of the reference signals and on some constant bounds on the robot dynamics.     

Neural model-based adaptive control for systems with unknown Preisach-type hysteresis

An adaptive control scheme is presented for systems with unknown hysteresis. In order to handle the case where the hysteresis output is unmeasurale, a novel model is firstly developed to describe the characteristic of hysteresis. This model is motivated by Preisach model but implemented by using neural networks (NN). The main advantage is that it is easily used for controller design. Then, the adaptive controller based on the proposed model is presented for a class of SISO nonlinear systems preceded by unknown hysteresis, which is estimated by the proposed model. The hws for model updating and the control hws for the neural adaptive controller are derived from Lyaptmov stability theorem, therefore the semi - global stability of the closed-loop system is guaranteed. At last, the simulation results are illuswated.     

Direct adaptive control of robotic systems

This paper presents a new approach to adaptive motion control of an important class of robotic systems. The control schemes developed using this approach are very simple and computationally efficient since they do not require knowledge of either the mathematical model or the parameter values of the robotic system dynamics. It is shown that the control strategies are globally stable in the presence of bounded disturbances, and that the size of the tracking errors can be made arbitrarily small. The proposed controllers are very general and are implementable with a wide variety of robotic systems, including both open- and closed-kinematic-chain manipulators. Computer simulation results are given for a seven degree-of-freedom (DOF) Robotics Research Corporation Model K-1607 arm. These results demonstrate that accurate and robust trajectory tracking can be achieved by using the proposed schemes.     

Direct adaptive fuzzy control for a class of MIMO nonlinear systems

This article presents a direct adaptive fuzzy control scheme for a class of uncertain continuous-time multi-input multi-output nonlinear (MIMO) dynamic systems. Within this scheme, fuzzy systems are employed to approximate an unknown ideal controller that can achieve control objectives. The adjustable parameters of the used fuzzy systems are updated using a gradient descent algorithm that is designed to minimize the error between the unknown ideal controller and the fuzzy controller. The stability analysis of the closed-loop system is performed using a Lyapunov approach. In particular, it is shown that the tracking errors are bounded and converge to a neighborhood of the origin. Simulations performed on a two-link robot manipulator illustrate the approach and exhibit its performance.     

Adaptive learning tracking control of robotic manipulators with uncertainties

An adaptive learning tracking control scheme is developed for robotic manipulators by a synthesis of adaptive control and learning control approaches. The proposed controller possesses both adaptive and learning properties and thereby is able to handle robotic systems with both time-varying periodic uncertainties and time invariant parameters. Theoretical proofs are established to show that proposed controllers ensure asymptotical tracking performance. The effectiveness of the proposed approaches is validated through extensive numerical simulation results.     

An adaptive control algorithm for robotic deburring

This paper presents the topic of adaptive control for robotic deburring by presenting some nonreal-time and some real-time schemes found in literature. Thereafter, a real-time adaptive control algorithm for robotic deburring is presented. Experiments are presented in which an IBM RS/1 robot is used to simulate the operation of the algorithm.     

Robust adaptive control of nonlinear non-minimum phase systems with uncertainties

This paper, presents a robust adaptive control method for a class of nonlinear non-minimum phase systems with uncertainties. The development of the control method comprises two steps. First, stabilization of the system is considered based on the availability of the output and internal dynamics of the system. The reference signal is designed to stabilize the internal dynamics with respect to the output tracking error. Moreover, a combined neuro-adaptive controller is proposed to guarantee asymptotic stability of the tracking error. Then, the overall stability is achieved using the small gain theorem. Next, the availability of internal dynamics is relaxed by using a linear error observer. The unmatched uncertainty is compensated using a suitable reference signal. The ultimate boundedness of the reconstruction error signals is analytically shown using an extension of the Lyapunov theory. The theoretical results are applied to a translational oscillator/rotational actuator model to illustrate the effectiveness of the proposed scheme.     

Nonlinear adaptive control of robotic manipulators - hyperstability approach

A nonlinear model reference adaptive controller based on hyperstability approach, is presented for the control of robot manipulators. Use of hyperstability approach simplifies the stability proof of the adaptive system. The unknown parameters of the system, as well as its variable payload, are estimated on line and are adaptive to their actual values; tending to reduce the system error. In addition, any sudden change in the system parameters or payload is detected by the proposed intelligent controller. Robot path tracking, with unknown parameter values and variable payload, is simulated to show the effectiveness of the proposed adaptive control algorithm. Both system output error and parameter estimation error vanish under the proposed parameter adaptation algorithm.     

Further result on a dynamic recurrent neural-network-based adaptive observer for a class of nonlinear systems

In Kim et al. [(1997) A dynamic recurrent neural-network-based adaptive observer for a class of nonlinear systems. Automatica 33(8), 1539–1543], authors present an excellent neural network (NN) observer for a class of nonlinear systems. However, the output error equation in their paper is strictly positive real (SPR) which is restrictive assumption for nonlinear systems. In this note, by introducing a vector b₀ and Lyapunov equation, the observer design is obtained without requiring the SPR condition. Thus, our observer can be applied to a wider class of systems.     

Neural adaptive control for a class of nonlinear systems with unknown deadzone

This paper focuses on the adaptive control of a class of nonlinear systems with unknown deadzone using neural networks. By constructing a deadzone pre-compensator, a neural adaptive control scheme is developed using backstepping design techniques. Transient performance is guaranteed and semi-globally uniformly ultimately bounded stability is obtained. Another feature of this scheme is that the neural networks reconstruction error bound is assumed to be unknown and can be estimated online. Simulation results are given to demonstrate the effectiveness of the proposed controller.     

Dissipative-based adaptive neural control for nonlinear systems

A dissipative-based adaptive neural control scheme was developed for a class of nonlinear uncertain systems with unknown nonlinearities that might not be linearly parameterized. The major advantage of the present work was to relax the requirement of matching condition, i.e., the unknown nonlinearities appear on the same equation as the control input in a state-space representation, which was required in most of the available neural network controllers. By synthesizing a state-feedback neural controller to make the closed-loop system dissipative with respect to a quadratic supply rate, the developed control scheme guarantees that the L2-gain of controlled system was less than or equal to a prescribed level. And then, it is shown that the output tracking error is uniformly ultimate bounded. The design scheme is illustrated using a numerical simulation.     

Finite-horizon neuro-optimal tracking control for a class of discrete-time nonlinear systems using adaptive dynamic programming approach

In this paper, a finite-horizon neuro-optimal tracking control strategy for a class of discrete-time nonlinear systems is proposed. Through system transformation, the optimal tracking problem is converted into designing a finite-horizon optimal regulator for the tracking error dynamics. Then, with convergence analysis in terms of cost function and control law, the iterative adaptive dynamic programming (ADP) algorithm via heuristic dynamic programming (HDP) technique is introduced to obtain the finite-horizon optimal tracking controller which makes the cost function close to its optimal value within an ?-error bound. Three neural networks are used as parametric structures to implement the algorithm, which aims at approximating the cost function, the control law, and the error dynamics, respectively. Two simulation examples are included to complement the theoretical discussions.     

Hierarchical hybrid fuzzy-neural networks for approximation with mixed input variables

Real-world systems usually involve both continuous and discrete input variables. However, in existing learning algorithms of both neural networks and fuzzy systems, these mixed variables are usually treated as continuous without taking into account the special features of discrete variables. It is inefficient to represent each discrete input variable having only a few fixed values by one input neuron with full connection to the hidden layer. This paper proposes a novel hierarchical hybrid fuzzy neural network to represent systems with mixed input variables. The proposed model consists of two levels: the lower level are fuzzy sub-systems each of which aggregates several discrete input variables into an intermediate variable as its output; the higher level is a neural network whose input variables consist of continuous input variables and intermediate variables. For systems or function approximations with mixed variables, it is shown that the proposed hierarchical hybrid fuzzy neural networks outperform standard neural networks in accuracy with fewer parameters, and both provide greater transparency and preserve the universal approximation property (i.e., they can approximate any function with mixed input variables to any degree of accuracy).     

MIMO adaptive fuzzy terminal sliding-mode controller for robotic manipulators

A new design approach of a multiple-input-multiple-output (MIMO) adaptive fuzzy terminal sliding-mode controller (AFTSMC) for robotic manipulators is described in this article. A terminal sliding-mode controller (TSMC) can drive system tracking error to converge to zero in finite time. The AFTSMC, incorporating the fuzzy logic controller (FLC), the TSMC, and an adaptive scheme, is designed to retain the advantages of the TSMC while reducing the chattering. The adaptive law is designed on the basis of the Lyapunov stability criterion. The self-tuning parameters are adapted online to improve the performance of the fuzzy terminal sliding-mode controller (FTSMC). Thus, it does not require detailed system parameters for the presented AFTSMC. The simulation results demonstrate that the MIMO AFTSMC can provide a reasonable tracking performance.     

New stable adaptive fuzzy approach to control uncertain nonlinear SISO systems

This paper deals with the synthesis of a new robust adaptive fuzzy control for a class of nonlinear and disturbed single-input single-output (SISO) systems. To attenuate the effect of both of the approximation errors and the external disturbances to a prescribed level, two signals are added to the indirect adaptive fuzzy control law: the first deduced from a fuzzy system allows approximation errors and external disturbances to eliminated; the second signal deduced from the Riccati equation attenuates the effect of the residual errors to a prescribed level. To illustrate the efficiency of the proposed approach, a simulation example is presented.     

On the model-based approach to nonlinear networked control systems

The problem of model-based stabilization of a nonlinear system based on its approximate discrete-time model is addressed, under the assumption that both the feedforward and the feedback paths are subject to network-induced constraints. These constraints include irregularity of the transfer intervals, time-varying communication delays, and the possibility of packet losses. A communication protocol that copes with these constraints is proposed. A “Stability+performance recovery” result for the nonlinear model-based networked control system (NCS) is formulated and proven.Simulation results presented confirm that the proposed method improves the maximum allowable transfer interval.