The Internal Model Principle for Systems with Unbounded Control and Observation

In this paper the theory of robust output regulation of distributed parameter systems with infinite-dimensional exosystems is extended for plants with unbounded control and observation. As the main result, we present the internal model principle for linear infinite-dimensional systems with unbounded input and output operators. We do this for two different definitions of an internal model found in the literature, namely, the p-copy internal model and the $\mathcal{G}$-conditions. We also introduce a new way of defining an internal model for infinite-dimensional systems. The theoretic results are illustrated with an example where we consider robust output tracking for a one-dimensional heat equation with boundary control and pointwise measurements.Comment: 38 pages, 2 figures, in revie

Stabilising Model Predictive Control for Discrete-time Fractional-order Systems

In this paper we propose a model predictive control scheme for constrained fractional-order discrete-time systems. We prove that all constraints are satisfied at all time instants and we prescribe conditions for the origin to be an asymptotically stable equilibrium point of the controlled system. We employ a finite-dimensional approximation of the original infinite-dimensional dynamics for which the approximation error can become arbitrarily small. We use the approximate dynamics to design a tube-based model predictive controller which steers the system state to a neighbourhood of the origin of controlled size. We finally derive stability conditions for the MPC-controlled system which are computationally tractable and account for the infinite dimensional nature of the fractional-order system and the state and input constraints. The proposed control methodology guarantees asymptotic stability of the discrete-time fractional order system, satisfaction of the prescribed constraints and recursive feasibility