Contracted Product-Based Dynamical Systems

In 2017, Kruppa [IFAC-PapersOnLine] introduced the contracted product-based dynamical system (CPDS) representation, which expresses the system evolution as the contracted product between a dynamic tensor and a monomial state tensor. Unlike TVPDSs, this representation belongs to the class of polynomial dynamical systems. The key strength of the CPDS representation lies in the ability to perform efficient computations using tensor decompositions, including CPD, TD, TTD, and HTD. Notably, it enables the computation of analytically exact arithmetic operations such as derivatives and multiplications, which holds particular significance in developing controller algorithms like feedback linearization or model predictive control. Furthermore, CPDSs can be efficiently linearized without the need to recompute the full tensor representation.