Stable auto-tuning of adaptive controllers for nonlinear systems

This dissertation focuses on improving the performance of direct and indirect adaptive control methodologies for nonlinear discrete and continuous-time systems via the use of additional cost functions to achieve stable and hopefully higher performance operation. We will in particular focus on adjusting the parameters of the adaptive laws by optimizing some cost functions of interest (e.g., instantaneous control energy). In this dissertation, the adaptation gain and the direction of descent for discrete-time systems are updated on-line to optimize some cost function. The auto-tuning is performed in such a way that stability is maintained for any value of the adaptation gain within the feasible range. We show that auto-tuning the adaptation gain can be viewed as a special case of auto-tuning the direction of descent. Based on simulation results, we find that the lower bound of the adaptation gain tends to be used when the output error is very small. In the case where the output error is fairly large, a large adaptation gain tends to be used. Also, for one example in the direct case the auto-tuning algorithm is able to achieve a mean squared error (MSE) that is smaller in magnitude than the MSE that can be achieved using any fixed adaptation gain, with a relatively small control energy. In the indirect case, however, for this example the auto-tuning algorithm is only able to achieve an acceptable MSE with a relatively small control energy. Based on simulation results, we find that adapting the direction of descent can be used to trade-off between the tracking performance and control energy.; Next, the adaptation gain for continuous-time systems is updated on-line to minimize the instantaneous control energy. For this purpose, a gradient-based hybrid adaptive law is used for parameter adaptation. Using this update law, some local results are established and boundedness of the control and output variables is provided. Since the hybrid adaptive law only guarantees that a function of the output error (not the output error) is driven to a small value, it may not be always possible to drive the output error to a small value. Based on simulation results, it is found in the direct case that it is possible to drive the output error to a small value. Unfortunately, this is not feasible in the indirect case.