Nonlinear optimal control schemes have achieved remarkable performance in numerous engineering applications; however, they typically require high computational time, which has limited their use in real-world systems with fast dynamics and/or limited computation power. To address this challenge, neighboring extremal (NE) has been developed as an efficient optimal adaption strategy to adapt a pre-computed nominal control solution to perturbations from the nominal trajectory. The resulting control law is a time-varying feedback gain that can be pre-computed along with the original optimization problem, which makes negligible online computation. This thesis focuses on reducing the computational time of the nonlinear optimal control problems using the NE in two parts. In Part I, we tackle model-based nonlinear optimal control and propose an extended neighboring extremal (ENE) to handle model uncertainties and reduce computational time (Chapter 3). Nonlinear Model predictive control (NMPC), which explicitly deals with system constraints, is considered as the case study due to its popularity, but ENE can be easily extended to other model-based nonlinear optimal control schemes. In Part II, we address data-driven nonlinear optimal control and introduce a data-enabled neighboring extremal (DeeNE) to remove parametric model requirement and reduce the computational time (Chapter 4). Data-enabled predictive control (DeePC), which makes a transition from the model-based optimal control to a data-driven one using raw input/output (I/O) data, is considered as the case study due to the attention it has received, but DeeNE can be easily extended to other data-driven nonlinear optimal control approaches. We also compare the control performance of DeeNE and DeePC for KINOVA Gen3 (7-DoF Arm Robot). Moreover, we introduce an adaptive DeePC framework, which can be easily transformed into an adaptive DeeNE, to use real-time informative data and handle time-varying systems (Chapter 5). Finally, we conclude the thesis and discuss the future works in Conclusion (Chapter 6).
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