Tracking control of uncertain nonlinear systems via adaptive Gaussian process prediction and real-time optimisation

Control of nonlinear systems in the presence of model mismatch and system constraints is quite challenging. To address the issue, this work proposes an adaptive Gaussian process-based real-time optimisation (AGP-RTO) control framework. Specifically, the control law consists of two components, a feedforward tracking control law and an uncertainty compensation control law. Because GP has high flexibility to capture complex unknown functions by using very few parameters and it inherently handles measurement noise, this work utilises the GP as an alternative to estimate the mismatch between the real plant and the approximated model. During every RTO execution, the GPs adaptively update the predictions of the model mismatch, then the predictions are embedded into a nonlinear optimisation problem for the correction of the model cost and constraint functions, which yields the uncertainty compensation control law. The proposed AGP-RTO framework ensures that the Karush-Kuhn-Tucker (KKT) conditions determined by the model match those of the plant upon convergence. Compared to many direct adaptive control methods, AGP-RTO does not rely on a high gain for fast adaptation and hence it improves the robustness of the closed-loop system. Compared to the modifier adaptation (MA) method, AGP-RTO avoids the plant-gradient estimation by using the finite difference scheme, besides it trains the GP models offline, which speeds up online evaluation and improves the applicability and efficacy of real-time control. Comparisons are carried out to illustrate the superiority of the AGP-RTO.