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Adaptive controller design for tracking and disturbance attenuation in parametricstrictfeedback nonlinear systems
 IEEE Transactions on Automatic Control
, 1996
"... Abstract — The authors develop a systematic procedure for obtaining robust adaptive controllers that achieve asymptotic tracking and disturbance attenuation for a class of nonlinear systems that are described in the parametric strictfeedback form and are subject to additional exogenous disturbance ..."
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Cited by 32 (4 self)
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Abstract — The authors develop a systematic procedure for obtaining robust adaptive controllers that achieve asymptotic tracking and disturbance attenuation for a class of nonlinear systems that are described in the parametric strictfeedback form and are subject to additional exogenous disturbance inputs. Their approach to adaptive control is performancebased, where the objective for the controller design is not only to find an adaptive controller, but also to construct an appropriate cost functional, compatible with desired asymptotic tracking and disturbance attenuation specifications, with respect to which the adaptive controller is “worst case optimal. ” In this respect, they also depart from the standard worst case (robust) controller design paradigm where the performance index is fixed priori. Three main ingredients of the paper are the backstepping methodology, worst case identification schemes, and singular perturbations analysis. Under full state measurements, closedform expressions have been obtained for an adaptive controller and the corresponding value function, where the latter satisfies a Hamilton–Jacobi–Isaacs equation (or inequality) associated with the underlying cost function, thereby leading to satisfaction of a dissipation inequality for the former. An important byproduct of the analysis is the finding that the adaptive controllers that meet the dual specifications of asymptotic tracking and disturbance attenuation are generally not certaintyequivalent, but are asymptotically so as the measure quantifying the designer’s confidence in the parameter estimate goes to infinity. To illustrate the main results, the authors include a numerical example involving a thirdorder system. Index Terms—Adaptive control, backstepping, disturbance attenuation, nonlinear systems, tracking. I.
Design and analysis of a novel L1 adaptive control architeture with guaranteed transient performance
 IEEE Trans. on Auto. Control
, 2008
"... Conventional Model Reference Adaptive Controller (MRAC), while providing an architecture for control of systems in the presence of parametric uncertainties, offers no means for characterizing the system’s input/output performance during the transient phase. Application of adaptive controllers was th ..."
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Cited by 23 (8 self)
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Conventional Model Reference Adaptive Controller (MRAC), while providing an architecture for control of systems in the presence of parametric uncertainties, offers no means for characterizing the system’s input/output performance during the transient phase. Application of adaptive controllers was therefore largely restricted due to the fact that the system uncertainties during the transient have led to unpredictable/undesirebale situations, involving control signals of highfrequency or large amplitudes, large transient errors or slow convergence rate of tracking errors, to name a few. In this paper, we develop a novel adaptive control architecture that ensures that the input and the output of an uncertain linear system track the input and output of a desired linear system during the transient phase, in addition to the asymptotic tracking. This new architecture has a lowpass filter in the feedbackloop that enables to enforce the desired transient performance by increasing the adaptation gain. For the proof of asymptotic stability, the L1 gain of a cascaded system, comprised of this filter and the closedloop desired reference model, is required to be less than the inverse of the upper bound of the norm of unknown parameters used in projection
Guaranteed transient performance with L1 adaptive controller for systems with unknown timevarying parameters
 Part I. Conf. on Decision and Control, Submitted
, 2006
"... This paper presents a novel adaptive control methodology for uncertain systems with timevarying unknown parameters and timevarying bounded disturbance. The adaptive controller ensures uniformly bounded transient and asymptotic tracking for system’s both signals, input and output, simultaneously. Th ..."
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Cited by 18 (8 self)
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This paper presents a novel adaptive control methodology for uncertain systems with timevarying unknown parameters and timevarying bounded disturbance. The adaptive controller ensures uniformly bounded transient and asymptotic tracking for system’s both signals, input and output, simultaneously. The performance bounds can be systematically improved by increasing the adaptation gain. Simulations of a robotic arm with timevarying friction verify the theoretical findings. 1
Neural Network based Adaptive Algorithms for Nonlinear Control
 He joined the School of Aerospace Engineering at the Georgia Institute of Technology in
, 1995
"... this paper, backstepping control, has become a very popular and powerful tool in nonlinear adaptive control. A complete account for such methods can be found in [59, 73, 121]. An extension to non linearizable systems was proposed in [107]. The combination of adaptive control and feedback linearizat ..."
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Cited by 4 (0 self)
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this paper, backstepping control, has become a very popular and powerful tool in nonlinear adaptive control. A complete account for such methods can be found in [59, 73, 121]. An extension to non linearizable systems was proposed in [107]. The combination of adaptive control and feedback linearization applied to flight control can be found in [126]. In most of the classical adaptive control literature it is common to assume the unknown dynamics to have a known structure with unknown parameters entering linearly in the dynamics. The linear parameterization of unknown dynamics poses serious obstacles in adopting adaptive control algorithms in practical applications, because it is di#cult to fix the structure of the unknown nonlinearities. This fact has been the motivating factor behind the interest in online function approximators to estimate and learn the unknown function. The most common function approximators used in adaptive control are artificial neural network and fuzzy logic structures. On line control algorithms that do not require knowledge of the system dynamics (except its dimension and relative degree) have been made possible by employing artificial neural networks in the feedback loop [34]. The ability of neural networks to approximate uniformly continuous functions has been proven in several articles [21, 27, 38, 28, 40]. An important aspect of neural network control applications is the di#erence between approximation theory results and what is achievable in online adaptive schemes using such approximators. First and most importantly, in o#line applications the neural network weights are updated based on inputoutput matching, 5 whereas in direct adaptive control situations the update of the network parameters is driven by a tracking error, which by it...
L1 adaptive output feedback controller for nonstrictly positive real systems: Missile longitudinal autopilot design
 AIAA Journal of Guidance, Control and Dynamics
, 2009
"... This paper presents an extension of the L1 adaptive output feedback controller to systems of unknown relative degree in the presence of timevarying uncertainties without restricting the rate of their variation. As compared to earlier results in this direction, a new piecewise continuous adaptive l ..."
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Cited by 4 (1 self)
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This paper presents an extension of the L1 adaptive output feedback controller to systems of unknown relative degree in the presence of timevarying uncertainties without restricting the rate of their variation. As compared to earlier results in this direction, a new piecewise continuous adaptive law is introduced along with the lowpass filtered control signal that allows for achieving arbitrarily close tracking of the input and the output signals of the reference system, the transfer function of which is not required to be strictly positive real (SPR). Stability of this reference system is proved using smallgain type argument. The performance bounds between the closedloop reference system and the closedloop L1 adaptive system can be rendered arbitrarily small by reducing the step size of integration. Simulations verify the theoretical findings. I.
An Energy Amplification Condition for Decentralized Adaptive Stabilization
, 1995
"... We are interested here in the problem of global decentralized adaptive regulation (of the plant output to zero) of square multivariable linear timeinvariant systems without any restrictions on relative degrees nor matching assumptions. The first solution to this problem was recently reported by the ..."
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Cited by 3 (0 self)
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We are interested here in the problem of global decentralized adaptive regulation (of the plant output to zero) of square multivariable linear timeinvariant systems without any restrictions on relative degrees nor matching assumptions. The first solution to this problem was recently reported by the author using Morse's new dynamic certainty equivalent adaptive controller to prove that global stabilization is possible if the unmodelled interconnections do not induce "amplification of the energy of the signals in all channels". In this paper we show that, to preserve global convergence, it is actually enough to have only one "non amplifying channel". Instrumental for the establishment of our result is the fundamental Sprocedure losslessness theorem of Megretsky and Treil, together with some basic looptransformations and Dscalings. Keywords: Adaptive Control, Decentralized Control, Passive Systems. 1 Introduction Several fundamental problems in identification and adaptive control of ...
Neural Network Adaptive Control Architecture With Guaranteed Transient Performance
"... Abstract—In this paper, we present a novel neural network (NN) adaptive control architecture with guaranteed transient performance. With this new architecture, both input and output signals of an uncertain nonlinear system follow a desired linear system during the transient phase, in addition to st ..."
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Cited by 1 (0 self)
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Abstract—In this paper, we present a novel neural network (NN) adaptive control architecture with guaranteed transient performance. With this new architecture, both input and output signals of an uncertain nonlinear system follow a desired linear system during the transient phase, in addition to stable tracking. This new architecture uses a lowpass filter in the feedback loop, which consequently enables to enforce the desired transient performance by increasing the adaptation gain. For the guaranteed transient performance of both input and output signals of the uncertain nonlinear system, the 1 gain of a cascaded system, comprised of the lowpass filter and the closedloop desired reference model, is required to be less than the inverse of the Lipschitz constant of the unknown nonlinearities in the system. The tools from this paper can be used to develop a theoretically justified verification and validation framework for NN adaptive controllers. Simulation results illustrate the theoretical findings. Index Terms—Adaptive control, approximation region, neural network (NN), radial basis function (RBF), transient. I.
INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, VOL. 11, 501—517 (1997) DISCRETETIME COMBINED MODEL REFERENCE ADAPTIVE CONTROL
"... The discretetime version of continuoustime combined model reference adaptive control (CMRAC) is presented in this paper. A global stability proof of the overall adaptive scheme is given using arguments similar to those used in discretetime direct model reference adaptive control (DMRAC) but prope ..."
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The discretetime version of continuoustime combined model reference adaptive control (CMRAC) is presented in this paper. A global stability proof of the overall adaptive scheme is given using arguments similar to those used in discretetime direct model reference adaptive control (DMRAC) but properly
Performance index for quality response of dynamical systems
 ISA TRANSACTIONS
, 2004
"... The use of performance indices to measure the quality response of dynamical systems is studied in this paper. A definition of a general performance index is proposed which is easy to compute, easy to interpret, and flexible enough to account for different cases commonly presented in practice. The in ..."
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The use of performance indices to measure the quality response of dynamical systems is studied in this paper. A definition of a general performance index is proposed which is easy to compute, easy to interpret, and flexible enough to account for different cases commonly presented in practice. The index is tested over several dynamical responses obtained from different systems obtaining good results, in the sense that it is able to rank the behaviors from best to worse, compared with a pattern response.
NorthHolland Transientperformance
, 1992
"... improvement with a new class of adaptive controllers* ..."