Robust analysis for data-driven model predictive control

Abstract

Here the idea of data driven is introduced in model predictive control to establish our proposed data-driven model predictive control. Considering one first-order discrete time nonlinear dynamical system, the main essence of data driven means the actual output value in cost function for model predictive control is identified through input–output observed data in case of unknown but bounded noise and martingale difference sequence. After substituting the identified actual output in cost function, the total cost function in model predictive control is reformulated as its standard form, i.e. one quadratic program problem with input and output constraints. Then semidefinite relaxation scheme is used to derive a lower bound for its optimal value, and the robust counterpart of an uncertain quadratic program is reduced to one conic quadratic problem. The above semidefinite relaxation scheme and conic quadratic problem correspond to the similar robust analysis based on convex optimization theory. Finally, one simulation example is used to prove the efficiency of our proposed theory.