Observer-Based Nonlinear Dynamic Inversion Adaptive Control with State Constraints
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Hypersonic vehicle research and development has grown recently in the aerospace industry due to the powerful potential of operating a vehicle that flies at substantially higher speeds than typical aircraft. From a guidance, navigation and control perspective, hypersonic vehicles are particularly interesting due both to inherent vehicle complexities as well as practical concerns that only arise at high Mach numbers. Challenges inherent to the vehicle include nonlinearities, a wide range of operating conditions, high elasticity, high temperatures and parametric uncertainty. Although these challenges have by no means fully been explored in the literature, in the realm of control theory, they are somewhat common. Hypersonic vehicle control is difficult however, because in addition to these more traditional complexities a control designer must also deal with problems very specific to flying at high speeds such as: inlet unstart, overcoming sensing deficiencies at high speeds and creating an implementable digital control framework for a plant with extremely fast dynamics. This dissertation develops three novel theoretical approaches for addressing these challenges through advances in the nonlinear dynamic inversion adaptive control technique. Although hypersonic vehicle control is the motivation and often the application that the control algorithms in this dissertation are tested on, several of the theoretical developments apply to a general class of nonlinear continuous time systems. First, in order to address the problem of inlet unstart, two state constraint mechanisms which integrate into the nonlinear dynamic inversion adaptive control framework are presented. These state constraining control laws require full state feedback and are capable of restricting the outputs of nonlinear systems containing parameter uncertainty to specific regions of the state-space. The first state constraint mechanism achieves this objective using sliding mode control and the second uses bounding functions to smoothly adjust the control and adaptive laws and drive the states toward the origin when constraints are approached. Stability is proven using Lyapunov analysis and these techniques are demonstrated in a nonlinear simulation of a hypersonic vehicle. Second, an observer-based feedback controller is developed that allows for a nonlinear system to track a reference trajectory with bounded errors and without measuring multiple states. Again, the technique used is nonlinear dynamic inversion adaptive control, but because of uncertainty in the system state, it is not assumed that the nonlinear control effectiveness matrix can be canceled perfectly. A nonlinear observer is implemented to estimate the values of the unknown states. This observer allows for the closed-loop stability of the system to be proven through Lyapunov analysis. It is shown that parametric uncertainty can successfully be accounted for using an adaptive mechanism and that all tracking and estimation errors are uniformly ultimately bounded. Finally, a sampled-data nonlinear dynamic inversion adaptive control architecture is introduced. Despite the prevalence of digital controllers in practice, a nonlinear dynamic inversion adaptive control scheme in a sampled-data setting has not previously been developed. The method presented in this dissertation has the capability of extending the benefits of nonlinear dynamic inversion adaptive control - robust control of nonlinear systems with respect to model uncertainty - to more practical platforms.
Nonlinear Dynamic Inversion
Nonlinear Hypersonic Vehicle Control
Famularo, Douglas I. (2017). Observer-Based Nonlinear Dynamic Inversion Adaptive Control with State Constraints. Doctoral dissertation, Texas A & M University. Available electronically from