Data-Driven Control of Stochastic Systems: An Innovation Estimation Approach

Recent years have witnessed a booming interest in the data-driven paradigm for predictive control. However, under noisy data ill-conditioned solutions could occur, causing inaccurate predictions and unexpected control behaviours. In this article, we explore a new route toward data-driven control of stochastic systems through active offline learning of innovation data, which gives an answer to the critical question of how to derive an optimal data-driven model from a noise-corrupted dataset. A generalization of the Willems' fundamental lemma is developed for non-parametric representation of input-output-innovation trajectories, provided realizations of innovation are precisely known. This yields a model-agnostic unbiased output predictor and paves the way for data-driven receding horizon control, whose behaviour is identical to the ``oracle" solution of certainty-equivalent model-based control with measurable states. For efficient innovation estimation, a new low-rank subspace identification algorithm is developed. Numerical simulations show that by actively learning innovation from input-output data, remarkable improvement can be made over present formulations, thereby offering a promising framework for data-driven control of stochastic systems

Results on data-driven controllers for unknown nonlinear systems

The big data revolution is deeply changing the way we understand and analyze natural phenomena around us. In the field of control engineering, data-driven control enables researchers to explore new intelligent algorithms to model and control complex dynamical systems. Data-driven control is based on the paradigm of learning controllers of an unknown dynamical system by directly using data. The underlying idea is that information about the model can be gathered from experiments, bypassing completely the identification step, which can be impractical or too costly. This thesis presents data-driven control solutions for different families of unknown dynamical systems, with a focus on both linear and special classes of nonlinear ones. In the first part of the thesis, we consider the linear quadratic regulator problem for linear time-invariant discrete-time systems. The system is assumed to be unknown and information on the system is given by a finite set of data. This allows determining the optimal control law in one shot, with no intermediate identification step. Secondly, we present an online algorithm for learning controllers applied to switched linear systems. By collecting data on the fly, the control mechanism can capture any changes in the dynamics of the plant and adapt itself accordingly to achieve stabilization of the running dynamics. Finally, we derive data-driven methods for a more general class of nonlinear systems via nonlinearity cancellation. To this end, we make use of a "dictionary" of nonlinear terms that includes the nonlinearities of the unknown system