DF-MRAC baseado em redes neurais para controle de veiculos lançadores: um estudo comparativo dos modelos RBF, WNN e ELM

Abstract

The pitch-axis attitude control of finless launch vehicles with Thrust Vector Control features continuous variation of mass, moment of inertia, and aerodynamic coefficients along the atmospheric trajectory — conditions that compromise the performance of fixed-gain linear controllers. The Derivative-Free Model Reference Adaptive Control employs an algebraic update law with time delay that handles time-varying weight uncertainties and guarantees uniform boundedness of both tracking and parametric errors at steady state through a Lyapunov–Krasovskii functional, without integrating derivatives of the Lyapunov function. To compensate for the matched dynamic uncertainties present in the plant, this control architecture requires neural networks due to their property as universal function approximators, which is essential for uncertainty estimation and compensation. The choice of neural network influences both the estimation accuracy and the closed-loop stability of the system under parametric variations. This dissertation evaluates and compares seven activation function architectures of single-hidden-layer neural networks integrated into the aforementioned adaptive controller for the pitch-axis attitude control problem of a finless launch vehicle with Thrust Vector Control. The investigated architectures are: radial basis function networks with Gaussian and inverse multiquadratic activation, wavelet neural networks with Morlet and Mexican hat functions, and extreme learning machines with sigmoid, hyperbolic tangent, and exponential functions. The nominal controller is designed via Linear Quadratic Regulator with state feedback. The performance evaluation of the estimators is carried out through computational simulation under three matched uncertainty profiles: constant weights, squarewave modulation, and sinusoidal modulation. The comparison metrics adopted are the mean squared error, the mean absolute error, and the coefficient of determination, obtained by exhaustive hyperparameter search over the number of neurons and the adaptation rate. The robustness of the optimal configurations is assessed by Monte Carlo simulation with dispersion of physical plant parameters between five and twenty-five percent. The results indicate that extreme learning machines, in the hyperbolic tangent and exponential variants, produce the lowest mean squared error values under nominal operating conditions. However, for parametric dispersions equal to or greater than ten percent, these architectures exhibit closed-loop system divergence in at least one Monte Carlo run, with numerical divergence recorded at fifteen percent variation. Radial basis function networks maintain stability up to fifteen percent dispersion for the static uncertainty profile, but lose maximum error boundedness at variations exceeding twenty percent. The Morlet wavelet network is the only architecture that maintains low parametric sensitivity of the tracking error across all uncertainty profiles throughout the entire evaluated parametric dispersion range, with a standard deviation of mean squared error below one hundredth of one thousandth of a radian for the sinusoidal disturbance at twenty-five percent variation, with no occurrence of numerical divergence. These results, obtained under linearized single-point model conditions and an isolated pitch channel, characterize a structural trade-off between approximation accuracy under nominal conditions and global stability under high parametric uncertainty, establishing the Morlet wavelet network as the recommended architecture for application to the attitude control of finless rockets under the investigated operational conditions.