Adaptive λ-tracking for locomotion systems

This paper deals with the (adaptive) control of mechanical systems, which are inspired by biological ideas. We introduce a certain type of mathematical models of worm-like locomotion systems and present some theoretical control investigations.Only discrete straight worms will be considered in this paper: chains of point masses moving along a straight line. We introduce locomotion systems in the form of a straight chain of $k=3$ interconnected point masses, where we focus on interaction which emerges from a surface texture as asymmetric Coulomb friction. We consider two different types of drives: (i) The point masses are under the action of external forces, which can be regarded as external force control inputs. (ii) We deal with massless linear springs of fixed stiffnesses and controllable original spring lengths, which can be regarded as internal control inputs.The locomotion systems with these two types of drive mechanisms are described by mathematical models, which fall into the category of nonlinearly perturbed, multi-input, multi-output systems (MIMO-systems), where the outputs of the system are, for instance, the positions of the point masses or the displacements of the point masses.The goal is to simply control these systems in order to track given reference trajectories to achieve movement of the system. Because one cannot expect to have complete information about a sophisticated mechanical or biological system, but instead only structural properties are known, we deal with uncertain systems. Therefore, the method of adaptive control is chosen in this paper. Since we deal with nonlinearly perturbed MIMO-systems, we focus on the adaptive $\lambda$-tracking control objective to achieve our goal. This means tracking of a given reference signal for any pre-specified accuracy $\lambda >0$. The objective is not to obtain information about the characteristics of the system or about system parameters, but simply to control the unknown system. This control objective allows us to design simple adaptive controllers, which achieve $\lambda$-tracking.Numerical simulations of tracking different reference signals, for an arbitrary choice of the system parameters, will demonstrate and illustrate, that the introduced, simple adaptive controller works successfully and effectively.     

Robust adaptive fuzzy controller for non‐affine nonlinear systems with dynamic rule activation

This paper describes the design of a robust adaptive fuzzy controller for an uncertain single‐input single‐output nonlinear dynamical systems. While most recent results on fuzzy controllers considers affine systems with fixed rule‐base fuzzy systems, we propose a control scheme for non‐affine nonlinear systems and a dynamic fuzzy rule activation scheme in which an appropriate number of the fuzzy rules are chosen on‐line. By using the proposed scheme, we can reduce the computation time, storage space, and dynamic order of the adaptive fuzzy system without significant performance degradation. The Lyapunov synthesis approach is used to guarantee a uniform ultimate boundedness property for the tracking error, as well as for all other signals in the closed loop. No a priori knowledge of an upper bounds on the uncertainties is required. The theoretical results are illustrated through a simulation example. Copyright © 2002 John Wiley & Sons, Ltd.     

Adaptive Regulation Against Unknown Narrow Band Disturbances Applied to the Flying Height Control in Data Storage Systems

This paper presents an adaptive regulation approach in linear systems against exogenous narrow band inputs such as disturbances or reference signals consisting of a linear combination of biased sinusoids with unknown amplitudes, frequencies, and phases. The design of the regulator is based on considering a Q‐parameterized set of stabilizing controllers for the linear system, where an adaptive FIR filter with fixed IIR filtering is adopted as the Q parameter. The goal of the adaptation is to search within the set of stabilizing controllers for a controller, or equivalently a Q parameter, that yields regulation in the closed loop system. The proposed adaptive regulation algorithm is applied to an active suspension beam system, which is motivated by the flying height control problem in data storage systems. The experimental result of the closed loop system shows the effectiveness of the proposed adaptive regulator in achieving the desired tracking performance under unknown exogenous disturbances.     

Computing actuator bandwidth limits for model reference adaptive control

Although model reference adaptive control theory has been used in numerous applications to achieve system performance without excessive reliance on dynamical system models, the presence of actuator dynamics can seriously limit the stability and the achievable performance of adaptive controllers. In this paper, a linear matrix inequalities-based hedging approach is developed and evaluated for model reference adaptive control of uncertain dynamical systems in the presence of actuator dynamics. The hedging method modifies the ideal reference model dynamics in order to allow correct adaptation that is not affected by the presence of actuator dynamics. Specifically, we first generalise the hedging approach to cover a variety of cases in which actuator output and the control effectiveness matrix of the uncertain dynamical system are known and unknown. We then show the stability of the closed-loop dynamical system using Lyapunov-based stability analysis tools and propose a linear matrix inequality-based framework for the computation of the minimum allowable actuator bandwidth limits such that the closed-loop dynamical system remains stable. Finally, an illustrative numerical example is provided to demonstrate the efficacy of the proposed approach.     

A family of adaptive H �� controllers with full information for dissipative hamiltonian systems

This paper investigates a parameterization method of adaptive H _∞ controllers for dissipative Hamiltonian systems with disturbances and unknown parameters. The family of adaptive H _∞ controllers with full information is obtained by interconnecting an adaptive H _∞ controller with a generalized zero-energy-gradient (ZEG) detectable, free generalized Hamiltonian system. The present parameterization method avoids solving Hamilton-Jacobi-Issacs equations and thus the controllers obtained are easier in operation as compared to some existing ones. Simulations show the effectiveness and feasibility of the adaptive control strategy proposed in this paper.     

A family of robust adaptive excitation controllers for synchronous generators with steam valve via Hamiltonian function method

Using the Hamiltonian function method,this paper proposes a family of robust adaptive excitation controllers for synchronous generators with steam valve control.First,a parameterization method of robus...     

TRACKING CONTROL IN THE PRESENCE OF NONLINEAR DYNAMIC FRICTIONAL EFFECTS: ROBOT EXTENSION

In this paper, we extend the observer/control strategies previously published in [25] to an n-link, serially connected, direct drive, rigid link, revolute robot operating in the presence of nonlinear friction effects modeled by the Lu-Gre model. In addition, we also present a new adaptive control technique for compensating for the nonlinear parameterizable Stribeck effects. Specifically, an adaptive observer/controller scheme is developed which contains a feedforward approximation of the Stribeck effects. This feedforward approximation is used in a composite controller/observer strategy which forces the average square integral of the position tracking error to an arbitrarily small value. Experimental results are included to illustrate the performance of the proposed controllers.     

Adaptive neuro-genetic control of chaos applied to the attitude control problem

Conventional adaptive control techniques have, for the most part, been based on methods for linear or weakly non-linear systems. More recently, neural network and genetic algorithm controllers have started to be applied to complex, non-linear dynamic systems. The control of chaotic dynamic systems poses a series of especially challenging problems. In this paper, an adaptive control architecture using neural networks and genetic algorithms is applied to a complex, highly nonlinear, chaotic dynamic system: the adaptive attitude control problem (for a satellite), in the presence of large, external forces (which left to themselves led the system into a chaotic motion). In contrast to the OGY method, which uses small control adjustments to stabilize a chaotic system in an otherwise unstable but natural periodic orbit of the system, the neuro-genetic controller may use large control adjustments and proves capable of effectively attaining any specified system state, with no a prioriknowledge of the dynamics, even in the presence of significant noise.This work was partly supported by SERC grant 90800355.     

Incremental Q-learning strategy for adaptive PID control of mobile robots

Expert and intelligent systems are being developed to control many technological systems including mobile robots. However, the PID (Proportional-Integral-Derivative) controller is a fast low-level control strategy widely used in many control engineering tasks. Classic control theory has contributed with different tuning methods to obtain the gains of PID controllers for specific operation conditions. Nevertheless, when the system is not fully known and the operative conditions are variable and not previously known, classical techniques are not entirely suitable for the PID tuning. To overcome these drawbacks many adaptive approaches have been arisen, mainly from the field of artificial intelligent. In this work, we propose an incremental Q-learning strategy for adaptive PID control. In order to improve the learning efficiency we define a temporal memory into the learning process. While the memory remains invariant, a non-uniform specialization process is carried out generating new limited subspaces of learning. An implementation on a real mobile robot demonstrates the applicability of the proposed approach for a real-time simultaneous tuning of multiples adaptive PID controllers for a real system operating under variable conditions in a real environment.     

Adaptive robust stabilisation of uncertain nonlinear dynamical systems: an improved backstepping approach

The main purpose of this paper is to propose a design approach by which some simple adaptive robust controllers can be synthesised for a class of uncertain nonlinear dynamical systems which can be transformed into uncertain strict-feedback nonlinear systems. In this paper, an improved backstepping design approach is presented to synthesising a class of continuous adaptive robust state-feedback controllers with a rather simple structure. The improved backstepping design approach can avoid the repeated differentiation problem which appears in using the conventional backstepping algorithm. In particular, it is not required to know the nonlinear upper bound functions of uncertainties. In the light of the presented approach, the state-feedback controllers can be constructed to be linear in the state, with the time-varying control gains which can be self-tuned by the adaptive laws. Similar to the conventional backstepping algorithm, the improved backstepping approach can be extended to a rather large class of uncertain nonlinear systems, and by combining the improved backstepping approach with other control methods, it may be expected to obtain a number of interesting results.     

Adaptive fuzzy control: experiments and comparative analyses

Advances in nonlinear control theory have provided the mathematical foundations necessary to establish conditions for stability of several types of adaptive fuzzy controllers. However, very few, if any, of these techniques have been compared to conventional adaptive or nonadaptive nonlinear controllers or tested beyond simulation; therefore, many of them remain as purely theoretical developments whose practical value is difficult to ascertain. In this paper we develop three case studies where we perform a comparative analysis between the adaptive fuzzy techniques in Spooner and Passino (1995,1996) and some conventional adaptive and nonadaptive nonlinear control techniques. In each case, the analysis is performed both in simulation and in implementation, in order to show practical examples of how the performance of these controllers compares to conventional controllers in real systems     

Immersion and invariance adaptive control of a class of nonlinear systems with unknown control direction

The goal of this article is to extend the adaptive control problem of parametric strict feedback form nonlinear systems, using immersion and invariance to the case of unknown, possibly, time-varying control direction. The idea is to immerse a target system in ? ^n?1, which is stabilised through the design of virtual controllers, into an extended system in ? ^n+p . The designed controller takes advantage of the well-known Nussbaum functions to deal with the unknown sign of input multiplier and is designed through the manifold dynamics belonging to ? ^p+1. The effectiveness of the proposed method is shown through a simulation example and is also compared to the classical adaptive backstepping approach with an unknown control direction.     

Multi-switching adaptive synchronization of two fractional-order chaotic systems with different structure and different order

In this work, we combine the active and adaptive control theories, and propose a novel synchronization scheme for a class of fractional-order chaotic systems with different structure and different order. Based on the new version of fractional-order Lyapunov stability theory, we design the adaptive controllers and updating laws of different switching. We use the fractional-order Lorenz chaotic system and the fractional-order Chen chaotic system as examples to analyze the multi-switching synchronization process for fractional-order chaotic systems with different structures and different orders. Finally, numerical simulations are also given to illustrate the effectiveness and validation of the proposed method, and the model uncertainties and external disturbances are added to the considered systems to verify the robustness of the proposed controllers.     

A multirule-base controller using the robust property of a fuzzycontroller and its design method

This paper suggests a new fuzzy adaptive controller, which is able to solve the problems of classical adaptive controllers and conventional fuzzy adaptive controllers. It explains the architecture of a fuzzy adaptive controller using the robust property of a fuzzy controller. The basic idea of new adaptive control scheme is that an adaptive controller can be constructed with parallel combination of robust controllers. This new adaptive controller uses a multirule-base architecture which has several independent fuzzy controllers in parallel, each with different robust stability area. Out of several independent fuzzy controllers, the most suited one is selected by a system identifier which observes variations in the controlled system parameter. Here, we propose a design procedure which can be carried out mathematically and systematically from the model of a controlled system; related mathematical theorems and their proofs are also given. The performance of the proposed adaptive control algorithm is analyzed through a design example and a DC motor control simulation     

Adaptive tracking of switched nonlinear systems with prescribed performance using a reference-dependent reparametrisation approach

In this paper, adaptive tracking control of switched nonlinear systems in the parametric strict-feedback form is investigated. After defining a reparametrisation lemma in the presence of a non-zero reference signal, we propose a new adaptive backstepping design of the virtual controllers that can handle the extra terms arising from the reparametrisation (and that the state-of-the-art backstepping designs cannot dominate). The proposed adaptive design guarantees, under arbitrarily fast switching, an a priori bound for the steady-state performance of the tracking error and a tunable bound for the transient error. Finally, the proposed method, by overcoming the need for subsystems with common sign of the input vector field, enlarges the class of uncertain switched nonlinear systems for which the adaptive tracking problem can be solved. A numerical example is provided to illustrate the proposed control scheme.     

Adaptive friction compensation of servo mechanisms

In this paper, adaptive friction compensation is investigated using both model-based and neural network (non-model-based) parametrization techniques. After a comprehensive list of commonly used models for friction is presented, model-based and non-modelbased adaptive friction controllers are developed with guaranteed closed-loop stability. Intensive computer simulations are carried out to show the effectiveness of the proposed control techniques, and to illustrate the effects of certain system parameters on the performance of the closed-loop system. It is observed that as the friction models become complex and capture the dominate dynamic behaviours, higher feedback gains for model-based control can be used and the speed of adaptation can also be increased for better control performance. It is also found that neural networks are suitable candidate for friction modelling and adaptive controller design for friction compensation.     

Adaptive backstepping output feedback control of DC motor actuator with friction and load uncertainty compensation

In this paper, we present an output feedback backstepping controller for mechatronic actuators with dynamic adaptive parameters for friction and load compensation. The targeted application is angular position control of automotive mechatronic valves, which possess nonlinear dynamics due to friction. The proposed controller requires only position measurement. The velocity, current, and friction dynamics are obtained by estimation and observation. The adaptive control law compensates the variations in friction behavior and load torque variation, which are common in real life applications. Lyapunov analysis has been used to show the asymptotic convergence of the closed‐loop system to zero. Simulation and laboratory experimental results illustrate the effectiveness and robustness of the controller. Further experiments on an engine test bench demonstrate the applicability of this controller in commercial engines, as well as its effectiveness as compared with conventional PI controllers.Copyright © 2014 John Wiley & Sons, Ltd.     

ROBUST TRACKING FOR NONLINEAR SYSTEMS VIA HYBRID CONTROL

In this paper, the problem of output tracking for single-input/single-output nonlinear systems in the presence of mismatched uncertainty is studied. In our problem, the so-called matching condition in the literature is further relaxed, and a more general condition on the uncertainty is given. To attenuate the effects of uncertainties on the tracking error, a design method which is referred to as the Stable Combined Variable Perturbation Method (SCVPM) is presented. Based on this design method, a new robust tracking controller is derived using hyb rid control strategy. This controller, taken as a root-controller, is then used to generate two other controllers. All these controllers guarantee robustness of the closed-loop system, only with different tracking accuracies. The design method as well as the robust controllers is characterized by a small robust design parameter, ϵ. The tracking error converges to an ϵ-neighbourhood of the origin, and, by letting ϵ go to zero, the accuracy of tracking can be improved to any desired degree. Finally, an example is given and the simulation results confirm the theoretical analyses, thus show the effectiveness of the new design method and controllers.     

Robust H ∞ and adaptive tracking control against actuator faults with a linearised aircraft application

This article studies the problem of designing adaptive fault-tolerant H _∞ tracking controllers for a class of aircraft flight systems against general actuator faults and bounded perturbations. A robust adaptive state-feedback controller is constructed by a stabilising controller gain and an adaptive control gain function. Using mode-dependent Lyapunov functions, linear matrix inequality-based conditions are developed to find the controller gain such that disturbance attenuation performance is optimised. Adaptive control schemes are proposed to estimate the unknown controller parameters on-line for unparametrisable stuck faults and perturbation compensations. Based on Lyapunov stability theory, it is shown that the resulting closed-loop systems can guarantee asymptotic tracking with H _∞ performances in the presence of faults on actuators and perturbations. An application to a decoupled linearised dynamic aircraft system and its simulation results are given.