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Approximate InverseDynamics Based Robust Control Using Static And Dynamic Feedback
, 1997
"... ...rganizing associative neural network architecture that can be used to approximate the inversedynamics in the form of a PositionandDirectiontoAction (PDA) map is also described. Similarities between the basal ganglia  thalamocortical loops and the SDS scheme are discussed and it is argued t ..."
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...rganizing associative neural network architecture that can be used to approximate the inversedynamics in the form of a PositionandDirectiontoAction (PDA) map is also described. Similarities between the basal ganglia  thalamocortical loops and the SDS scheme are discussed and it is argued that the SDS scheme could be viewed as a model of higher order motor functions of these areas.
Estimation and Control for Systems with Nonlinearly Parameterized Perturbations
"... A class of systems influenced by nonlinearly parameterized perturbations is considered. An estimation scheme is developed whereby exponentially stable estimates of the unknown parameters can be obtained with an arbitrarily large region of attraction, provided the states are available for measuremen ..."
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Cited by 3 (1 self)
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A class of systems influenced by nonlinearly parameterized perturbations is considered. An estimation scheme is developed whereby exponentially stable estimates of the unknown parameters can be obtained with an arbitrarily large region of attraction, provided the states are available for measurement. The method applies to a class of perturbations with the property that an exponentially stable estimate of the unknown parameters can be obtained if the whole perturbation is known. Compensation for the perturbations in the system equations is considered for a class of systems which have uniformly globally bounded solutions and for which the origin is globally asymptotically stable when no perturbations are present. Examples with simulations are given in order to illustrate the results.
Observer Design and Parameter Estimation for Linear Systems with Nonlinearly Parameterized Perturbations
, 2009
"... We introduce a method of observer design for systems described by a linear part with a nonlinear perturbation, where the perturbation is parameterized by a vector of unknown, constant parameters. The design is modular, and consists of a modified highgain observer that estimates the states of the sy ..."
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Cited by 1 (0 self)
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We introduce a method of observer design for systems described by a linear part with a nonlinear perturbation, where the perturbation is parameterized by a vector of unknown, constant parameters. The design is modular, and consists of a modified highgain observer that estimates the states of the system together with the full perturbation, and a parameter estimator. The parameter estimator is constructed by the designer to identify the unknown parameters, by dynamically inverting a nonlinear equation. We apply the method to observer design for a DC motor with friction modeled by the dynamic LuGre friction model, estimating the internal state in the friction model and an unknown parameter representing Coloumb friction.
Information Inequalities and Limiting Possibilities of Adaptive Control Strategies in ARX models with a General Quadratic Criterion
"... This paper deals with the analysis of the convergence rate of adaptive asymptotically optimal control strategies when applied to linear, stationary, multidimensional objects belonging to some class which might include a moving average control term. A general type of performance index, which is the s ..."
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This paper deals with the analysis of the convergence rate of adaptive asymptotically optimal control strategies when applied to linear, stationary, multidimensional objects belonging to some class which might include a moving average control term. A general type of performance index, which is the sum of a quadratic form in the output signal plus a quadratic form in the input signal, is considered. Finally, it is shown that for any adaptive control scheme, the corresponding state space trajectories do not differ less than some lower bound, which is sharp, from those corresponding to an optimal control scheme (where full information on the parameters is available). Single input  single output (SISO) and two dimensional case (MIMO) examples are presented. 1 Introduction Many different papers have been devoted to the synthesis and analysis of adaptive control strategies for the class of stationary linear objects, perturbed with stationary (in the wide sense) stochastic noise [1], [2], [...
Parameter Estimation and Compensation in Systems with . . .
, 2009
"... We consider a class of systems influenced by perturbations that are nonlinearly parameterized by unknown constant parameters, and develop a method for estimating the unknown parameters within an arbitrarily large parameter space. The method applies to systems where the states are available for measu ..."
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We consider a class of systems influenced by perturbations that are nonlinearly parameterized by unknown constant parameters, and develop a method for estimating the unknown parameters within an arbitrarily large parameter space. The method applies to systems where the states are available for measurement, and perturbations with the property that an exponentially stable estimate of the unknown parameters can be obtained if the whole perturbation is known. The main contribution is to introduce a conceptually simple, modular design that gives freedom to the designer in accomplishing the main task, which is to construct an update law to asymptotically invert a nonlinear equation. Compensation for the perturbations in the system equations is considered for a class of systems with uniformly globally bounded solutions and for which the origin is uniformly globally asymptotically stable when no perturbations are present. We also consider the case when the parameters can only be estimated when the controlled state is bounded away from the origin, and show that we may still be able to achieve convergence of the controlled state. We illustrate the method through examples, and apply it to the problem of downhole pressure estimation during oil well drilling.
Adaptive Algorithms in Finite Form
, 2003
"... We propose a new method for the design of adaptation algorithms that guarantees a certain prescribed level of performance and applicable to systems with nonconvex parameterization. The main idea behind the method is twofold. First, we augment the tuning error function and design the adaptation sche ..."
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We propose a new method for the design of adaptation algorithms that guarantees a certain prescribed level of performance and applicable to systems with nonconvex parameterization. The main idea behind the method is twofold. First, we augment the tuning error function and design the adaptation scheme in the form of ordinary differential equations. The resulting augmentation is allowed to depend on state derivatives. Second, we find a suitable realization of the designed adaptation scheme in an algebraicintegral form. Due to their explicit dependence on the state of the original system, such adaptation schemes are referred to as adaptive algorithms in finite form, in contrast to (conventional) algorithms in differential form. Sufficient conditions for the existence of finite form realizations are proposed. It is shown that our method to design algorithms in finite form is applicable to a broad class of nonlinear systems including systems with nonconvex parameterization and lowtriangular systems.
State and Parameter Estimation for Linear Systems with Nonlinearly Parameterized Perturbations
"... Abstract — We consider systems that can be described by a linear part with a nonlinear perturbation, where the perturbation is parameterized by a vector of unknown, constant parameters. Under a set of technical assumptions about the perturbation and its relationship to the outputs, we present a modu ..."
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Abstract — We consider systems that can be described by a linear part with a nonlinear perturbation, where the perturbation is parameterized by a vector of unknown, constant parameters. Under a set of technical assumptions about the perturbation and its relationship to the outputs, we present a modular observer design technique. The observers produced by this design technique consist of a modified highgain observer that estimates the states of the system together with the full perturbation, and a parameter estimator. The parameter estimator is constructed by the designer to identify the unknown parameters by dynamically inverting a nonlinear equation. We illustrate the design technique by constructing an observer for a DC motor with friction modeled by the dynamic LuGre friction model. I.
ParameterEstimationandCompensationinSystemswith
"... Weconsideraclassofsystemsinfluencedbyperturbationsthatarenonlinearlyparameterizedbyunknownconstantparameters,anddevelop a method for estimating the unknown parameters. The method applies to systems where the states are available for measurement, and perturbations with the property that an exponentia ..."
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Weconsideraclassofsystemsinfluencedbyperturbationsthatarenonlinearlyparameterizedbyunknownconstantparameters,anddevelop a method for estimating the unknown parameters. The method applies to systems where the states are available for measurement, and perturbations with the property that an exponentially stable estimate of the unknown parameters can be obtained if the whole perturbation is known. The main contribution is to introduce a conceptually simple, modular design that gives freedom to the designer in accomplishing the main task, which is to construct an update law to asymptotically invert a nonlinear equation. Compensation for the perturbations in the system equations is considered for a class of systems with uniformly globally bounded solutions, for which the origin is uniformly globally asymptotically stable when no perturbations are present. We also consider the case when the parameters can only be estimated when the controlled state is bounded away from the origin, and show that we may still be able to achieve convergence of the controlled state. We illustrate the method through examples, and apply it to the problem of downhole pressure estimation during oil well drilling.
State and Parameter Estimation for Nonlinearly Parameterized Systems: An H∞Based Approach ⋆
"... Abstract: We present a framework for estimating states and parameters in systems that can be described by a detectable linear system perturbed by a nonlinear function of the states, exogenous signals, and a vector of unknown, constant parameters. The estimators designed in this framework consist of ..."
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Abstract: We present a framework for estimating states and parameters in systems that can be described by a detectable linear system perturbed by a nonlinear function of the states, exogenous signals, and a vector of unknown, constant parameters. The estimators designed in this framework consist of two interconnected modules: a parameter estimator that is constructed as though the states and the nonlinear perturbation were directly available for measurement; and an observer/perturbation estimator that estimates the states as well as the perturbation. The design methodology is based on satisfying an H ∞ condition, which leaves the designer with a wide range of options for carrying out the design. We discuss the use of LMIbased techniques in particular, and illustrate their application on a simulation example. We also discuss how the results of the paper can be applied to a more general class of cascaded nonlinear systems.