NISE-PE Constraint: Data-Driven Predictive Control with Persistence of Excitation

Persistence of excitation (PE) is an important requirement for the successful operation of data-driven predictive control, as it ensures that the input-output data contains sufficient information about the underlying system dynamics. Nonetheless, this property is usually assumed rather than guaranteed. This paper introduces a novel data-driven predictive control formulation that maintains PE. The technical development that allows this is the characterisation of the nonexciting input set (NIS), i.e., the set of inputs that lead to loss of PE, and the consequent derivation of a pair of disjoint, linear inequality constraints on the input, termed NIS exclusion PE (NIS-PE) constraint, that, if satisfied, maintain PE. When used in a predictive control formulation, these constraints lead to a mixed-integer optimal control problem with a single binary variable or, equivalently, a pair of disjoint quadratic programming problems that can be efficiently and reliably solved. Numerical examples show how these constraints are able to maintain PE during the controller's operation, resulting in improved performance over conventional approaches for both time-invariant and time-varying systems.