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 strict-feedback form and are subject to additional exogenous disturbance inputs. Their approach to adaptive control is performance-based, 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 by-product of the analysis is the finding that the adaptive controllers that meet the dual specifications of asymptotic tracking and disturbance attenuation are generally not certainty-equivalent, 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 third-order system. Index Terms—Adaptive control, backstepping, disturbance attenuation, nonlinear systems, tracking. I.

.<F3.778e+05> This paper develops a methodology for recursive construction of optimal and nearoptimal controllers for strict-feedback stochastic nonlinear systems under a risk-sensitive cost function criterion. The design procedure follows the integrator backstepping methodology, and the controllers obtained guarantee any desired achievable level of long-term average cost for a given risk-sensitivity parameter<F3.473e+05><F3.778e+05> #. Furthermore, they lead to closed-loop 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, risk-sensitive control, integrator backstepping, zero dynamics<F4.005e+05> AMS subject classifications.<F3.778e+05> 93E15, 93E20, 90D25, 93C10, 90A46<F4....

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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 noise-perturbed 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....

In this study of the nonlinear-optimal control design for strict-feedback 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 Hamilton--Jacobi--Isaacs (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.

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 time-invariant (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

Following the development of a parameter convergence analysis procedure for output-feedback nonlinear systems, we shift our attention to strict-feedback 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 Terms---Nonlinear 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 ...

We show that an adaptive input/output feedback linearization control scheme for minimum phase nonlinear systems is robust with respect to unstructured plant uncertainties that include such as unmodeled dynamics and disturbances, provided the adaptive law is modified in the same fashion as for linear systems, and the plant nonlinearities satisfies some growth constraints. In the analysis we utilize weighted L 2 -norms analogously to the case with a linear model. Keywords: Adaptive Control, Nonlinear Systems, Robustness, Stability, Feedback Linearization. 1 This work was in part supported by the Research Council of Norway under Grant ST.10.12.221718 given to the first author, and in part by the National Science Foundation (NSF) under Grant ECS-9119722. 2 Present address: SINTEF Automatic Control, 7034 Trondheim, Norway. 1 Introduction For adaptive control of linear systems, the robustness issue has turned out to be very important, since it has been demonstrated that even small mode...

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 closed-loop 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...

Abstract: The L2-gain 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 Le-gain from disturbances to output can be made arbitrarily small by increasing its gain. The controller is explicitly constructed using a Lyapunov-based 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; Lz-gain; high-gain; Lyapunov functions; ~,~f~ ® control. 1.