Monotonous Parameter Estimation of One Class of Nonlinearly Parameterized Regressions without Overparameterization

The estimation law of unknown parameters vector ${\theta}$ is proposed for one class of nonlinearly parametrized regression equations $y\left( t \right) = \Omega \left( t \right)\Theta \left( \theta \right)$. We restrict our attention to parametrizations that are widely obtained in practical scenarios when polynomials in $\theta$ are used to form $\Theta \left( \theta \right)$. For them we introduce a new 'linearizability' assumption that a mapping from overparametrized vector of parameters $\Theta \left( \theta \right)$ to original one $\theta$ exists in terms of standard algebraic functions. Under such assumption and weak requirement of the regressor finite excitation, on the basis of dynamic regressor extension and mixing technique we propose a procedure to reduce the nonlinear regression equation to the linear parameterization without application of singularity causing operations and the need to identify the overparametrized parameters vector. As a result, an estimation law with exponential convergence rate is derived, which, unlike known solutions, (i) does not require a strict P-monotonicity condition to be met and a priori information about $\theta$ to be known, (ii) ensures elementwise monotonicity for the parameter error vector. The effectiveness of our approach is illustrated with both academic example and 2-DOF robot manipulator control problem.Comment: 7 pages, 2 figure

Nonlinear PI control of uncertain systems: an alternative to parameter adaptation

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Neural feedback linearization adaptive control for affine nonlinear systems based on neural network estimator

In this work, we introduce an adaptive neural network controller for a class of nonlinear systems. The approach uses two Radial Basis Functions, RBF networks. The first RBF network is used to approximate the ideal control law which cannot be implemented since the dynamics of the system are unknown. The second RBF network is used for on-line estimating the control gain which is a nonlinear and unknown function of the states. The updating laws for the combined estimator and controller are derived through Lyapunov analysis. Asymptotic stability is established with the tracking errors converging to a neighborhood of the origin. Finally, the proposed method is applied to control and stabilize the inverted pendulum system