Tools for mixed logical dynamical and piecewise affine systems based on the model description language HYSDEL are described. They concern various modeling, identification, analysis, control design, and verification tasks. The data exchange format explained in this chapter facilitates the combination of these tools.

This chapter describes MATLAB/Simulink tools for modeling, identifying, simulating, analyzing, and controlling discrete-time hybrid systems with piecewise affine dynamics, described in mixed logical dynamical (MLD) or piecewise affine (PWA) form. Such tools include:

• modeling and identification tools for describing the hybrid model in a high-level user-friendly way, or for identifying hybrid models from data;

• simulation tools for open-loop simulation and validation of hybrid models;

• analysis tools for characterization of stability and reachability properties of hybrid models;

• control design tools for designing hybrid model-predictive controllers, simulating closed-loop performances, and generating real-time control code.

(Section 10.1) describes the modeling language HYSDEL, which ease the process of formulating a hybrid model. Sections 10.2 and 10.3 describe two toolboxes for analysis, simulation, and control of hybrid systems, the Multi-Parametric Toolbox and the Hybrid Toolbox. (Section 10.4) describes two tools for identification of hybrid piecewise-affine models from data, the Hybrid Identification Toolbox and the PieceWise Affine Identification Toolbox. Finally, (Section 10.5) describes an interchange format for transferring models among all the aforementioned tools.

HYSDEL

Modeling aim

HYSDEL (HYbrid System DEscription Language) [632] allows modeling a class of hybrid systems described by interconnections of linear dynamical systems, finitestate automata, IF-THEN-ELSE rules, and propositional logic statements.

Energy management is an issue in many applications ranging from consumer electronics to power systems. The operation of energy management systems involves many severe hybrid phenomena, mostly due to the presence of switches. As a consequence, control and optimization play a crucial role to enable increased performance and reliability, as illustrated by two examples: the control of DC-DC converters and the model-predictive supervision of the voltage stability of power networks.

Introduction to energy management

Three different categories of applications can be distinguished in the area of energy management depending on the time scale at which these systems evolve:

• Power generation involves rotating machines that are used for electricity generation and for which the physical phenomena that determine the system behavior occur in the millisecond range for the magnetic part of the machine and in the range of a second for its mechanical part.

• Power transmission is done through a network and the state of the system is characterized by the voltages at the nodes and active and reactive power flows between the nodes. Such a system typically evolves at time scales varying from seconds to minutes.

• Power conversion involves power electronics devices for which the switching frequency is typically between kilohertz and megahertz.

The first category is not considered in this chapter, the focus will be on the last two.