This book focuses on Model Predictive Control (MPC) of discrete-time hybrid systems. Hybrid
systems contain continuous and discrete valued components and are located at the intersection
between the fields of control theory and computer science. MPC uses an internal model of the
controlled plant to predict the future evolution of the controlled variables over a prediction
horizon. A cost function is minimized to obtain the optimal control input sequence which is
applied to the plant by means of a receding horizon policy. The latter implies that only the
first control input of the input sequence is implemented the horizon is shifted by one
time-step and the above procedure is repeated at the next sampling instant. Most importantly
theory and tools are available to off-line derive the piecewise affine (PWA) state-feedback
control law. Hence any time-consuming on-line computation of the control input is avoided and
plants with high sampling frequencies can be controlled. The book is divided into two parts:
The first part is devoted to theory and algorithms whereas the second part tackles
applications in the fields of power electronics and power systems. In the first part using the
notion of cell enumeration in hyperplane arrangements from computational geometry we propose
an algorithm that efficiently enumerates all feasible modes of a composition of hybrid systems.
This technique allows the designer to evaluate the complexity of the compound model to
efficiently translate the model into a PWA representation and to reduce the computational
burden of optimal control schemes by adding cuts that prune infeasible modes from the model.
With respect to implementation an important issue is the complexity reduction of PWA
state-feedback controllers. Hence we propose two algorithms that solve the problem of deriving
a PWA representation that is both equivalent to the given one and minimal in the number of
regions. As both algorithms refrain from solving additional Linear Programs they are not only
optimal but also computationally feasible. In many cases the optimal complexity reduction
constitutes an enabling technique when implementing the optimal controllers as look-up tables
in hardware. In the second part of the book we consider the field of power electronics that is
intrinsically hybrid since the positions of semiconductor switches are described by binary
variables. %Furthermore hard constraints and nonlinearities are often present. The fact that
the methodologies of MPC and hybrid systems are basically unknown in the power electronics
community has motivated us to consider such problems namely switch-mode DC-DC converters and
induction machines driven by three-phase inverters using the notion of Direct Torque Control
(DTC). For these problems we propose novel modelling and control schemes that are conceptually
simple easy to devise understand and tune and most importantly implementable. Specifically
for DTC we present a low complexity modelling approach of the induction machine based on
which we propose three novel Model Predictive Control (MPC) approaches to tackle the DTC
problem namely MPC based on Priority Levels MPC based on Feasibility and Move Blocking and
MPC based on Extrapolation. In particular the third control scheme is expected to be
implementable what has motivated our industrial partner to protect the scheme by a patent.
Considering the synchronous step-down DC-DC converter as an illustrative example for DC-DC
converters we derive a hybrid model of the converter that is valid for the whole operating
regime and for which we formulate and solve off-line an MPC problem leading to a
state-feedback control law parameterized over the whole state-space. The analysis of the
controller shows that the considered state-space is control invariant and that the nominal
closed-loop system is globally exponentially stable what is proved by a piecewise quadratic
(PWQ) Lyapunov function. Moreover the controller rejects large disturbances in the input
voltage and the load. Alike power electronics power systems possess many hybrid features
including integer manipulated variables such as load-shedding and capacitor switching and
internal controllers based on logic and finite state machines such as tap changers in
transformers. Motivated by the recent severe blackouts in the US and Europe we propose an
emergency voltage control scheme that stabilizes the voltages in spite of major outages in
order to prevent a voltage collapse and a blackout. To avoid unnecessary disruptive control
actions the control moves are classified into nominal and emergency control actions and
corresponding penalty levels are used in the objective function triggering disruptive control
moves such as load-shedding only if absolutely necessary.
