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27
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 22 (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.
Backstepping Controller Design For Nonlinear Stochastic Systems Under A RiskSensitive Cost Criterion
, 1999
"... . This paper develops a methodology for recursive construction of optimal and nearoptimal controllers for strictfeedback stochastic nonlinear systems under a risksensitive cost function criterion. The design procedure follows the integrator backstepping methodology, and the controllers ..."
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Cited by 19 (1 self)
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.<F3.778e+05> This paper develops a methodology for recursive construction of optimal and nearoptimal controllers for strictfeedback stochastic nonlinear systems under a risksensitive cost function criterion. The design procedure follows the integrator backstepping methodology, and the controllers obtained guarantee any desired achievable level of longterm average cost for a given risksensitivity parameter<F3.473e+05><F3.778e+05> #. Furthermore, they lead to closedloop system trajectories that are bounded in probability, and in some cases asymptotically stable in the large. These results also generalize to nonlinear systems with strongly stabilizable zero dynamics. A numerical example included in the paper illustrates the analytical results.<F4.005e+05> Key words.<F3.778e+05> stochastic di#erential equation, stochastic stability, risksensitive control, integrator backstepping, zero dynamics<F4.005e+05> AMS subject classifications.<F3.778e+05> 93E15, 93E20, 90D25, 93C10, 90A46<F4....
Backstepping Design with Local Optimality Matching
 IEEE Transactions on Automatic Control
, 2001
"... In this study of the nonlinearoptimal control design for strictfeedback nonlinear systems, our objective is to construct globally stabilizing control laws to match the optimal control law up to any desired order, and to be inverse optimal with respect to some computable cost functional. Our recurs ..."
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Cited by 8 (1 self)
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In this study of the nonlinearoptimal control design for strictfeedback nonlinear systems, our objective is to construct globally stabilizing control laws to match the optimal control law up to any desired order, and to be inverse optimal with respect to some computable cost functional. Our recursive construction of a cost functional and the corresponding solution to the HamiltonJacobiIsaacs (HJI) equation employs a new concept of nonlinear Cholesky factorization. When the value function for the system has a nonlinear Cholesky factorization, we show that the backstepping design procedure can be tuned to yield the optimal control law.
Robust Nonlinear System Identification Using Neural Network Models
 IEEE Transactions on Neural Networks
, 1998
"... We study the problem of identification for nonlinear systems in the presence of unknown driving noise, using both feedforward multilayer neural network and radial basis function network models. Our objective is to resolve the difficulty associated with the Persistency of Excitation condition inheren ..."
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Cited by 6 (1 self)
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We study the problem of identification for nonlinear systems in the presence of unknown driving noise, using both feedforward multilayer neural network and radial basis function network models. Our objective is to resolve the difficulty associated with the Persistency of Excitation condition inherent to the standard schemes in the neural identification literature. This difficulty is circumvented here by a novel formulation and by using a new class of identification algorithms recently obtained in [1]. We show how these algorithms can be exploited to successfully identify the nonlinearity in the system using neural network models. By embedding the original problem in one with noiseperturbed state measurements, we present a class of identifiers (under L1 and L2 cost criteria) which secure a good approximant for the system nonlinearity provided that some global optimization technique is used. In this respect, many available learning algorithms in the current neural network literature, e....
Backstepping control of linear timevarying systems with known and unknown parameters
 IEEE Trans. Automat. Control
, 1908
"... Abstract—The backstepping control design procedure has been used to develop stabilizing controllers for time invariant plants that are linear or belong to some class of nonlinear systems. The use of such a procedure to design stabilizing controllers for plants with time varying parameters has been a ..."
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Cited by 3 (0 self)
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Abstract—The backstepping control design procedure has been used to develop stabilizing controllers for time invariant plants that are linear or belong to some class of nonlinear systems. The use of such a procedure to design stabilizing controllers for plants with time varying parameters has been an open problem. In this paper we consider the backstepping design procedure for linear time varying (LTV) plants with known and unknown parameters. We first show that a backstepping controller can be designed for an LTV plant by following the same steps as in the linear timeinvariant (LTI) case and treating the plant parameters as constants at each time. Its stability properties however cannot be established by using the same Lyapunov function and techniques as in the LTI case. We then introduce a new parametrization and filter structure that takes into account the plant parameter variations leading to a new backstepping controller. The new
Nonlinearities Enhance Parameter Convergence in StrictFeedback Systems
 IEEE Transactions on Automatic Control
, 1998
"... Following the development of a parameter convergence analysis procedure for outputfeedback nonlinear systems, we shift our attention to strictfeedback nonlinear systems in this paper. We develop an analytic procedure which allows us, given a specific nonlinear system and a specific reference signa ..."
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Cited by 3 (0 self)
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Following the development of a parameter convergence analysis procedure for outputfeedback nonlinear systems, we shift our attention to strictfeedback nonlinear systems in this paper. We develop an analytic procedure which allows us, given a specific nonlinear system and a specific reference signal, to determine a priori whether or not the parameter estimates will converge to their true values, simply by checking the linear independence of the rows of a constant real matrix. Moreover, we show that this convergence is exponential. Finally, we prove that even if the rows of this constant matrix are not linearly independent, partial parameter convergence is still achieved, in the sense that the parameter error vector converges asymptotically to the left nullspace of this matrix. Index TermsNonlinear systems, adaptive control, parameter convergence, strictfeedback form. I. INTRODUCTION In linear control theory, there exist many results and design methods which deal with the case of ...
Nonlinear H∞ almost disturbance decoupling
 Syst. Contr. Lett
, 1994
"... Abstract: The L2gain almost disturbance decoupling problem for SISO nonlinear systems is formulated. Sufficient conditions are identified for the existence of a parametrized state feedback controller such that the Legain from disturbances to output can be made arbitrarily small by increasing its g ..."
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Cited by 3 (0 self)
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Abstract: The L2gain almost disturbance decoupling problem for SISO nonlinear systems is formulated. Sufficient conditions are identified for the existence of a parametrized state feedback controller such that the Legain from disturbances to output can be made arbitrarily small by increasing its gain. The controller is explicitly constructed using a Lyapunovbased recursive scheme. Sufficient conditions for the solvability of the,,~ ® almost disturbance decoupling problem and the explicit construction of the controller are given for a more restrictive class of nonlinear systems. Keywords: Disturbance decoupling; Lzgain; highgain; Lyapunov functions; ~,~f~ ® control. 1.
Nonlinearities Enhance Parameter Convergence in OutputFeedback Systems
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 1998
"... While the parameter convergence properties of standard adaptive algorithms for linear systems are well established, there are no similar results on the parameter convergence of adaptive controllers for nonlinear systems, which have gained popularity in recent years. In this paper we focus on a recen ..."
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Cited by 2 (1 self)
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While the parameter convergence properties of standard adaptive algorithms for linear systems are well established, there are no similar results on the parameter convergence of adaptive controllers for nonlinear systems, which have gained popularity in recent years. In this paper we focus on a recently developed class of adaptive schemes for outputfeedback nonlinear systems and show that parameter convergence is guaranteed if and only if an appropriately defined signal vector, which does not depend on closedloop signals, is persistently exciting. Then we develop an analytic procedure which allows us, given a specific nonlinear system and a specific reference signal, to determine a priori whether or not this vector is persistently exciting (PE), and, hence, whether or not the parameter estimates will converge. In the process we show that the presence of nonlinearities usually reduces the sufficient richness (SR) requirements on the reference signals, and hence enhances parameter conver...
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 2 (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...