Retrofit Flight Control Using an Adaptive Chebyshev Function Approximator

In this paper, a novel adaptive control approach, named adaptive Chebyshev retrofit control (ACRC), retrofitting an existing baseline controller with an adaptive Chebyshev function approximator is presented. The approximator is composed of a linear combination of a parameter and a basis function. Instead of using neural networks as a function approximator, the new approach utilizes a Chebyshev polynomial as a basis function for function approximation, and a parameter update law is derived via a Lyapunov-like analysis method. The benefits of the proposed method are twofold. First, the computational time is approximately 1.7 times faster than that of the method using the neural network. Second, the implementation is very efficient, because the structure of the approximator is significantly simpler in comparison with those of neural network approaches. Because the complexity of the software is the major contributing factor to software reliability, the high complexity of the implementation of a control algorithm that adopts neural networks could lead to a reduction in software reliability. Therefore, the new adaptive control method is valuable in terms of the improvement in software reliability. In particular, it is important in the field of aerospace control, which requires exceptional reliability for flight control software. Moreover, the short computational time in comparison with neural network approaches is very crucial for small unmanned aerial vehicles that have restricted on-board hardware performance. From simulation results, it is found that the performance of the proposed method in several responses is on par with that of the neural network method in the presence of varying flight conditions. Considering the computation time and simplicity of the proposed method, the authors conclude that the proposed approach is very effective, particularly relative to the neural network method.