A given explicit piecewise affine representation of an MPC feedback law is approximated by a single polynomial, computed using linear programming. This polynomial state feedback control law guarantees closed-loop stability and constraint satisfaction. The polynomial feedback can be implemented in real time even on very simple devices with severe limitations on memory storage.

In this paper we will present a theory for simplicial diffeomorphims, that is, diffeomorphims that preserve the incidence relations of a simplicial complex. Simplicial diffeomorphisms can be regarded as curvilinear barycentric coordinates. Using the combination of piecewise linear functions on complexes with simplicial diffeomorphisms, we also propose a new representation of curves and surfaces...

The paper deals with the parameter identification of Hammerstein systems having piecewise-linear nonlinearities with asymmetric dead-zones. A new form of nonlinearity representation provides a special form of Hammerstein model. Parameter estimation is carried out iteratively with measured input and output data records and estimated internal variables. To demonstrate the feasibility of the ident...

Abstract: In this paper the problem of stabilization of a particular class of hybrid systems is approached. For the class of discrete-time hybrid systems with time-delays, it is shown that under some assumption it is possible to express these systems in a common representation: piecewise affine systems. The stability of such systems is proved through Lyapunov theory, more accurate through quadr...

We employ a data-sparse, recursive matrix representation, so-called H 2-matrices, for the efficient treatment of discretized integral operators. We obtained this format using local tensor product interpolants of the kernel function and replacing high-order approximations with piecewise lower-order ones. The scheme has optimal, i.e., linear, complexity in the memory requirement and time for the ...

This paper studies controllability of bimodal systems that consist of two linear dynamics on each side of a given hyperplane. We show that the controllability properties of these systems can be inferred from those of linear systems for which the inputs are constrained in a certain way. Inspired by the earlier work on constrained controllability of linear systems, we derive necessary and suffici...