Computer-implemented method for designing a state controller, in particular for a vehicle, with stochastic optimization in the presence of static and time-variant uncertainties

A computer-implemented method for designing a state controller with stochastic optimization, comprising:

• receiving a dynamic model for describing a system to be controlled, wherein the dynamic model is represented by a predefined function (f(zk, p, wk, uk)), wherein the predefined function includes the following time-dependent arguments:
• a state vector (zk) comprising one or more state variables;
• an input vector (uk) comprising one or more input variables and connected to the state vector (zk) by a feedback matrix (K) describing the state controller, and
• a stochastic parameter vector (wk) having at least one component comprising a time-dependent uncertainty parameter describing a stochastic process, wherein the predefined function has a non-linear dependence with respect to the stochastic parameter vector and further includes a time-independent argument given by a static parameter vector (p) with at least one component comprising a static uncertainty parameter;
• forming a discrete-time representation of the dynamic model for describing the system to be controlled by a time discretization of the predefined function;
• decomposing the stochastic parameter vector (wk) into one or more deterministic modes (gj,k), wherein each mode is associated with a respective eigenvalue (λj), wherein the decomposed stochastic parameter vector (wk) is determined based on a random vector comprising one or more random variables (ζj) as components;
• approximating the predefined function to resolve the non-linear dependence with respect to the stochastic parameter vector (wk);
• and
• solving an optimization problem to determine the component of the feedback matrix (K),
• wherein the optimization problem comprises a cost function (J) calculated based on one or more expected values (E(zk);
• E(uk)) and one or more variances (V(zk);
• V(uk)) of the one or more state variables of the state vector (zk) and/or the one or more input variables of the input vector (uk).