Identification of Piecewise Linear Models of Complex Dynamical Systems

The paper addresses the realization and identification problem or a subclass of piecewise-affine hybrid systems. The paper provides necessary and sufficient conditions for existence of a realization, a characterization of minimality, and an identification algorithm for this subclass of hybrid systems. The considered system class and the identification problem are motivated by applications in systems biology

Model Reduction of Linear Switched Systems by Restricting Discrete Dynamics

We present a procedure for reducing the number of continuous states of discrete-time linear switched systems, such that the reduced system has the same behavior as the original system for a subset of switching sequences. The proposed method is expected to be useful for abstraction based control synthesis methods for hybrid systems

Realization Theory for LPV State-Space Representations with Affine Dependence

In this paper we present a Kalman-style realization theory for linear parameter-varying state-space representations whose matrices depend on the scheduling variables in an affine way (abbreviated as LPV-SSA representations). We deal both with the discrete-time and the continuous-time cases. We show that such a LPV-SSA representation is a minimal (in the sense of having the least number of state-variables) representation of its input-output function, if and only if it is observable and span-reachable. We show that any two minimal LPV-SSA representations of the same input-output function are related by a linear isomorphism, and the isomorphism does not depend on the scheduling variable.We show that an input-output function can be represented by a LPV-SSA representation if and only if the Hankel-matrix of the input-output function has a finite rank. In fact, the rank of the Hankel-matrix gives the dimension of a minimal LPV-SSA representation. Moreover, we can formulate a counterpart of partial realization theory for LPV-SSA representation and prove correctness of the Kalman-Ho algorithm. These results thus represent the basis of systems theory for LPV-SSA representation.Comment: The main difference with respect to the previous version is as follows: typos have been fixe

Commitment and Dispatch of Heat and Power Units via Affinely Adjustable Robust Optimization

The joint management of heat and power systems is believed to be key to the integration of renewables into energy systems with a large penetration of district heating. Determining the day-ahead unit commitment and production schedules for these systems is an optimization problem subject to uncertainty stemming from the unpredictability of demand and prices for heat and electricity. Furthermore, owing to the dynamic features of production and heat storage units as well as to the length and granularity of the optimization horizon (e.g., one whole day with hourly resolution), this problem is in essence a multi-stage one. We propose a formulation based on robust optimization where recourse decisions are approximated as linear or piecewise-linear functions of the uncertain parameters. This approach allows for a rigorous modeling of the uncertainty in multi-stage decision-making without compromising computational tractability. We perform an extensive numerical study based on data from the Copenhagen area in Denmark, which highlights important features of the proposed model. Firstly, we illustrate commitment and dispatch choices that increase conservativeness in the robust optimization approach. Secondly, we appraise the gain obtained by switching from linear to piecewise-linear decision rules within robust optimization. Furthermore, we give directions for selecting the parameters defining the uncertainty set (size, budget) and assess the resulting trade-off between average profit and conservativeness of the solution. Finally, we perform a thorough comparison with competing models based on deterministic optimization and stochastic programming.Comment: 31 page

Hamiltonian and self-adjoint control systems

This paper outlines results recently obtained in the problem of determining when an input-output map has a Hamiltonian realization. The results are obtained in terms of variations of the system trajectories, as in the solution of the Inverse Problem in Classical Mechanics. The variational and adjoint systems are introduced for any given nonlinear system, and self-adjointness defined. Under appropriate conditions self-adjointness characterizes Hamiltonian systems. A further characterization is given directly in terms of variations in the input and output trajectories, proving an earlier conjecture by the first author