Adaptive H2/H∞ tracking control for a class of uncertain robotic systems

This paper addresses the problem of designing mixed H₂/H_∞ tracking control for a large class of uncertain robotic systems. Nonlinear H_∞ control theory, H₂ control theory and intelligent adaptive control algorithm are combined to construct a hybrid adaptive/robust H₂/H_∞ tracking control scheme. One adaptive neural network system is constructed to approximate the behaviour of uncertain robot dynamics, and the other adaptive control algorithm is designed to estimate the behaviour of the modelled disturbance. Moreover, a robust H_∞ control algorithm is designed to attenuate the effects of the unmodelled disturbance. Only a set of algebraic matrix Riccati-like equations is required to implement the proposed mixed H₂/H_∞ tracking controller, and so an explicit and closed-form solution is obtained. Consequently, the mixed H₂/H_∞ adaptive/robust tracking controller developed here can be analytically computed and easily implemented. Finally, simulations are presented to illustrate the effectiveness of the proposed control algorithm.     

WebSail: From On-line Learning to Web Search

In this paper we report our research on building WebSail, an intelligent web search engine that is able to perform real-time adaptive learning. WebSail learns from the user's relevance feedback, so that it is able to speed up its search process and to enhance its search performance. We design an efficient adaptive learning algorithm TW2 to search for web documents. WebSail employs TW2 together with an internal index database and a real-time meta-searcher to perform real-time adaptive learning to find desired documents with as little relevance feedback from the user as possible. The architecture and performance of WebSail are also discussed. Received 3 November 2000 / Revised 13 March 2001 / Accepted in revised form 17 April 2001     

Adaptive mutual exclusion with local spinning

We present an adaptive algorithm for N-process mutual exclusion under read/write atomicity in which all busy waiting is by local spinning. In our algorithm, each process p performs O(k) remote memory references to enter and exit its critical section, where k is the maximum “point contention” experienced by p. The space complexity of our algorithm is Θ(N), which is clearly optimal. Our algorithm is the first mutual exclusion algorithm under read/write atomicity that is adaptive when time complexity is measured by counting remote memory references.A preliminary version of this paper was presented at the 14th International Symposium on Distributed Computing [6].     

Minimal Adaptive Routing on the Mesh with Bounded Queue Size

An adaptive routing algorithm is one in which the path a packet takes from its source to its destination may depend on other packets it encounters. Such algorithms potentially avoid network bottlenecks by routing packets around “hot spots.” Minimal adaptive routing algorithms have the additional advantage that the path each packet takes is a shortest one. For a large class of minimal adaptive routing algorithms, we present an Ω(n²/k²) bound on the worst case time to route a static permutation of packets on ann×nmesh or torus with nodes that can hold up tok≥ 1 packets each. This is the first nontrivial lower bound on adaptive routing algorithms. The argument extends to more general routing problems, such as theh–hrouting problem. It also extends to a large class of dimension order routing algorithms, yielding an Ω(n²/k) time bound. To complement these lower bounds, we present two upper bounds. One is anO(n²/k+n) time dimension order routing algorithm that matches the lower bound. The other is the first instance of a minimal adaptive routing algorithm that achievesO(n) time with constant sized queues per node. We point out why the latter algorithm is outside the model of our lower bounds.     

Adaptive L2 Disturbance Attenuation Of Hamiltonian Systems With Parametric Perturbation And Application To Power Systems

This paper deals with the problem of L₂ disturbance attenuation for Hamiltonian systems. We first show that the L₂ gain from the disturbance to a penalty signal may be reduced to any given level if the penalty signal is defined properly. Then, an adaptive version of the controller will be presented to compensate the parameter perturbation. When the perturbed parameters satisfy a suitable matching condition, it is easy to introduce the adaptive mechanism to the controller. Another contribution of this paper is to apply the proposed method to the excitation control problem for power systems. An adaptive L₂ controller for the power system is designed using the proposed method and a simulation result with the proposed controller is given.     

Long lived adaptive splitter and applications

Summary. Long-lived and adaptive implementations of mutual exclusion and renaming in the read/write shared memory model are presented. An implementation of a task is adaptive if the step complexity of any operation in the implementation is a function of the number of processes that take steps concurrently with the operation. The renaming algorithm assigns a new unique id in the range to any process whose initial unique name is taken from a set of size N, for an arbitrary N and where k is the number of processes that actually take steps or hold a name while the new name is being acquired. The step complexity of acquiring a new name is , while the step complexity of releasing a name is 1. The space complexity of the algorithm is where n is an upper bound on the number of processes that may be active at the same time (acquiring or holding new names), which could be N in the worst case. Both the system response time and the worst case number of operations per process in the presented mutual-exclusion algorithm are adaptive. Both algorithms rely on the basic building block of a long-lived and adaptive splitter. While the adaptive-splitter satisfies a slightly different set of properties than the Moir-Anderson splitter [MA95], it is adaptive and long-lived. In addition, the new splitter properties enable the construction of a non-blocking long-lived (2k-1)-renaming algorithm (which is optimal in the size of the new name space). We believe that the mechanisms introduced in our splitter implementation are interesting on their own, and might be used in other adaptive and long-lived constructions. Received: March 2000 / Accepted July 2001     

A Frequency-Dependent Direct Adaptive Scheme for Robot Manipulators: A Case of Model-Following Motion Control

This paper presents a new frequency-dependent direct adaptive scheme for the optimal and/or suboptimal tracking of the motion of a prescribed model. The idea is based on a closed-loop control scheme in which an _{2 H} optimal/suboptimal controller is applied in parallel with a direct adaptive technique to guide a robot manipulator to follow a certain prescribed trajectory. The H ₂ compensators have to be proper and positively bounded with respect to all dynamic frequencies. Robustness issues are addresses in the paper by lumping all the nonlinear dynamic terms such as the centrifugal and Coriolis effects as well as the mechanical and electrical friction forces of the robot arm, into a general unstructured uncertainty term.     

Robust adaptive fault‐tolerant control of uncertain linear systems via sliding‐mode output feedback

This paper is concerned with the robust adaptive fault‐tolerant compensation control problem via sliding‐mode output feedback for uncertain linear systems with actuator faults and exogenous disturbances. Mismatched disturbance attenuation is performed via H_∞ norm minimization. By incorporating the matrix full‐rank factorization technique with sliding surface design successfully, the total failure of certain actuators can be coped with, under the assumption that redundancy is available in the system. Without the need for a fault detection and isolation mechanism, an adaptive sliding mode controller, where the gain of the nonlinear unit vector term is updated automatically to compensate the effects of actuator faults, is designed to guarantee the asymptotic stability and adaptive H_∞ performance of closed‐loop systems. The effectiveness of the proposed design method is illustrated via a B747‐100/200 aircraft model. Copyright © 2014 John Wiley & Sons, Ltd.     

Delay‐dependent adaptive reliable H∞ control of linear time‐varying delay systems

This paper considers the problem of delay‐dependent adaptive reliable H_∞ controller design against actuator faults for linear time‐varying delay systems. Based on the online estimation of eventual faults, the parameters of adaptive reliable H_∞ controller are updating automatically to compensate the fault effects on the system. A new delay‐dependent reliable H_∞ controller is established using a linear matrix inequality technique and an adaptive method, which guarantees the stability and adaptive H_∞ performance of closed‐loop systems in normal and faulty cases. A numerical example and its simulation results illustrate the effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

Adaptive Versus Nonadaptive Attribute-Efficient Learning

We study the complexity of learning arbitrary Boolean functions of n variables by membership queries, if at most r variables are relevant. Problems of this type have important applications in fault searching, e.g. logical circuit testing and generalized group testing. Previous literature concentrates on special classes of such Boolean functions and considers only adaptive strategies. First we give a straightforward adaptive algorithm using O(r2 ^r log n) queries, but actually, most queries are asked nonadaptively. This leads to the problem of purely nonadaptive learning. We give a graph-theoretic characterization of nonadaptive learning families, called r-wise bipartite connected families. By the probabilistic method we show the existence of such families of size O(r2 ^r log n + r ²2 ^r ). This implies that nonadaptive attribute-efficient learning is not essentially more expensive than adaptive learning. We also sketch an explicit pseudopolynomial construction, though with a slightly worse bound. It uses the common derandomization technique of small-biased k-independent sample spaces. For the special case r = 2, we get roughly 2.275 log n adaptive queries, which is fairly close to the obvious lower bound of 2 log n. For the class of monotone functions, we prove that the optimal query number O(2 ^r + r log n) can be already achieved in O(r) stages. On the other hand, (2 ^r log n) is a lower bound on nonadaptive queries.     

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.     

Stability and robustness analysis of MIMO MRAC using Kp = L 2 D 2 S 2 factorization

For a class of MIMO systems with input and output unmodeled dynamics, bounded disturbances and any relative degree, using the idea of K_p = L ₂ D ₂ S ₂ factorization, the design and analysis of robust direct model reference adaptive control are further investigated in this article. By establishing the L_p and L _2δ relationship properties between the input and output, multivariable swapping lemmas and relating all the signals in the closed-loop system with the normalizing signal, stability and robustness of adaptive system are analyzed rigorously. Compared with the existing results, the proof procedure is more compact and simple. A simulation example verifies the effectiveness of the control scheme.     

A Performance Model of Adaptive Wormhole Routing in k-Ary n-Cubes in the Presence of Digit-Reversal Traffic

Several analytical models of fully adaptive routing in wormhole-routed k-ary n-cubes under the uniform traffic pattern have recently been proposed in the literature. Although the uniform reference model has been widely used by researchers, it is not always true in practice as there are many applications that exhibit traffic nonuniformity. There has hardly been any study that describes an analytical model of fully adaptive routing under nonuniform traffic conditions. This paper describes the first analytical model of fully adaptive routing in k-ary n-cubes in the presence of nonuniform traffic generated by the digit-reversal permutation, which is an important communication operation found in many matrix computation problems. Results obtained through simulation experiments confirm that the model predicts message latency with a good degree of accuracy under different working conditions.     

An adaptive collect algorithm with applications

Summary. In a shared-memory distributed system, n independent asynchronous processes communicate by reading and writing to shared variables. An algorithm is adaptive (to total contention) if its step complexity depends only on the actual number, k, of active processes in the execution; this number is unknown in advance and may change in different executions of the algorithm. Adaptive algorithms are inherently wait-free, providing fault-tolerance in the presence of an arbitrary number of crash failures and different processes' speed. A wait-free adaptive collect algorithm with O(k) step complexity is presented, together with its applications in wait-free adaptive alg orithms for atomic snapshots, immediate snapshots and renaming. Received: August 1999 / Accepted: August 2001     

A New Model-free Robust Adaptive Control of Cable-driven Robots

For high performance control of cable-driven robots, a new model-free robust adaptive control is proposed using adaptive proportional-integral-derivative nonsingular fast terminal sliding mode (PID-NFTSM) in this paper. The designed control scheme has three elements, which are time-delay estimation (TDE) and a new PID-NFTSM manifold and a combined adaptive reaching law. The TDE element is applied to achieve the lumped system dynamics and hence founds a practical model-free structure. Meanwhile, a new PID-NFTSM manifold is designed to inherit the advantages of the NFTSM and high-order SM (HOSM) and integral SM (ISM) controls. Because of this design, the PID-NFTSM manifold can effectively ensure the non-singularity and high comprehensive control performance. Then, by combining the fast-TSM-type reaching law and a constant speed one with adaptive gain, we design a new combined adaptive reaching law for performance reinforcement. Benefiting from above three parts, our proposed control is model-free, highly precise and strongly robust. Stability is analyzed using Lyapunov theory. The effectiveness of our control is proved by comparative simulation studies.

     

Adding one power integrator: a tool for global stabilization of high-order lower-triangular systems

In this paper, a new adaptive control technique called adding a power integrator is proposed, for a class of linearly parametrized high-order nonlinear systems that are of a lower-triangular structure, but neither feedback linearizable nor affine in the control input. Using the adaptive adding a power integrator technique as a basic design tool, we show how to explicitly construct, in a recursive manner, a smooth adaptive controller that solves the problem of adaptive regulation with global stability. The development of the adding a power integrator technique leads to a significant relaxation on the system nonlinearities such as feedback linearizability and affineness, which are known to be two standard hypotheses made in the existing nonlinear adaptive control schemes.     

Strongly adaptive token distribution

The token distribution (TD) problem, an abstract static variant of load balancing, is defined as follows: letM be a (parallel processor) network with setP of processors. Initially, each processorP P has a certain amountl(P) of tokens. The goal of a TD algorithm, run onM, is to distribute the tokens evenly among the processors. In this paper we introduce the notion of strongly adaptive TD algorithms, i.e., algorithms whose running times come close to the best possible runtime, the off-line complexity of the TD problem, for each individual initial token distributionl. Until now, only weakly adaptive algorithms have been considered, where the running time is measured in terms of the maximum initial load max{l(P)P P}.We design an almost optimal, strongly adaptive algorithm on mesh-connected networks of arbitrary dimension extended by a single 1-bit bus. This result shows that an on-line TD algorithm can come close to the optimal (off-line) bound for each individual initial load. Furthermore, we exactly characterize the off-line complexity of arbitrary initial token distributions on arbitrary networks. As an intermediate result, we design almost optimal weakly adaptive algorithms for TD on mesh-connected networks of arbitrary dimension.This research was partially supported by DFG-Forschergruppe Effiziente Nutzung massiv paralleler Systeme, Teilprojekt 4, by the ESPRIT Basic Research Action No. 7141 (ALCOM II), and by the Volkswagen-stiftung. A preliminary version was presented at the 20th ICALP, 1993, see [9].     

Adaptive compliant motion control of manipulators without velocity measurements

This article presents two adaptive schemes for compliant motion control of uncertain manipulators. The first strategy is developed using an adaptive impedance control approach and is appropriate for tasks in which the dynamic character of the end-effector/environment interaction must be controlled, while the second scheme is an adaptive position/force controller and is useful for those applications which require independent control of end-effector position and contact force. The proposed controllers are very general and computationally efficient, require virtually no information regarding the manipulator dynamic model or the environment, and are implementable without velocity measurements. It is shown that the schemes ensure semiglobal boundedness of all signals in the presence of bounded disturbances, and that the ultimate size of the system errors can be made arbitrarily small. The capabilities of the proposed control strategies are illustrated through both computer simulations and laboratory experiments with a 6 degree-of-freedom (DOF) IMI Zebra Zero manipulator. ©1997 John Wiley & Sons, Inc.     

Adaptive control of nonlinear systems: A case study of underwater robotic systems

The problem of controlling underwater mobile robots in 6 degrees of freedom (DOF) is addressed. Underwater mobile robots where the number of thrusters and control surfaces exceeds the number of controllable DOF are considered in detail. Unlike robotic manipulators underwater mobile robots should include a velocity dependent thruster configuration matrix B( q ), which modifies the standard manipulator equation to: Mq + C( q ) q + g(x) = B( q ) u where x = J( x ) q . Uncertainties in the thruster configuration matrix due to unmodeled nonlinearities and partly known thruster characteristics are modeled as multiplicative input uncertainty. This article proposes two methods to compensate for the model uncertainties: (1) an adaptive passivity-based control scheme and (2) deriving a hybrid (adaptive and sliding) controller. The hybrid controller combines the adaptive scheme where M, C, and g are estimated on-line with a switching term added to the controller to compensate for uncertainties in the input matrix B. Global stability is ensured by applying Barbalat's Lyapunov-like lemma. The hybrid controller is simulated for the horizontal motion of the Norwegian Experimental Remotely Operated Vehicle (NEROV).     

ADAPTIVE FUZZY‐BASED MIXED H2/H∞ TRACKING CONTROL DESIGN IN UNCERTAIN ROBOTIC SYSTEMS

In this study, an adaptive fuzzy‐based mixed H₂/H_∞ tracking control design is developed in robotic systems under unknown or uncertain plant parameters and external disturbances. The mixed H₂/H_∞ control design has the advantage of both H₂ optimal control performance and H_∞ robust control performance and the fuzzy adaptive control scheme is used to compensate for the plant uncertainties. By virtue of the skew‐symmetric property in the robotic systems and adequate choice of state variable transformation, sufficient conditions are developed for the adaptive fuzzy‐based mixed H₂/H_∞ tracking control problems in terms of a pair of coupled algebraic equations instead of a pair of coupled differential equations. The proposed methods are simple and the coupled algebraic equations can be solved analytically. Simulation results indicate that the desired performance of the proposed adaptive fuzzy‐based mixed H₂/H_∞ tracking control schemes for the uncertain robotic systems can be achieved.