A model‐and data‐driven predictive control approach for tracking of stochastic nonlinear systems using Gaussian processes

Abstract Nonlinear model predictive control (NMPC) is one of the few control methods that can handle complex nonlinear systems with multi‐objectives and various constraints. However, the performance of NMPC highly depends on the model accuracy and the deterministic solutions may suffer from conservatism, for example, robust MPC only considers the worst‐case scenario, which yields the NMPC not working efficiently in uncertain stochastic cases. To address these issues, a model‐and data‐driven predictive control approach using Gaussian processes (GP‐MDPC) is synthesized in this paper, which copes with the tracking control problems of stochastic nonlinear systems subject to model uncertainties and chance constraints. Because GP has high flexibility to capture complex unknown functions and it inherently handles measurement noise, GP models are employed to approximate the unknowns, the predictions and uncertainty quantification provided by the GPs are then exploited to propagate the uncertainties through the nonlinear model and to formulate a finite‐horizon stochastic optimal control problem (FH‐SOCP). Specifically, given the GP models, closed‐loop simulations are executed offline to generate Monte Carlo samples, from which the back‐offs for constraint tightening are calculated iteratively. The tightened constraints then guarantee the satisfaction of chance constraints online. A tractable GP‐MDPC framework using back‐offs for handling nonlinear chance constrained tracking control problems is yielded, whose advantages include fast online evaluation, consideration of closed‐loop behaviour, and achievable trade‐off between conservatism and constraint violation. Comparisons are carried out to verify the effectiveness and superiority of the proposed GP‐MDPC scheme with back‐offs.