Model predictive control for piecewise affine systems
Project members: B. De Schutter, T.J.J. van den Boom
We have extended our results on model predictive control
(MPC) for discrete event systems (see Project 4.8)
to a class of hybrid systems that can be described by a continuous
piecewiseaffine state space model.
More specifically, we have considered systems of the form
where , and are respectively, the state, the input and
the output vector of the system, and
where the components
of and are
continuous piecewiseaffine (PWA) scalar functions, i.e., functions
that satisfy
the following conditions:
 The domain space of is divided into a finite number
of polyhedral regions;
 In each region can be expressed as an affine function;
 is continuous on any boundary between two regions.
We have shown that continuous PWA systems are equivalent to
maxminplusscaling systems (i.e., systems that can be modeled using
maximization, minimization, addition and scalar multiplication). Next, we
have considered MPC for these systems. In general, this leads to nonlinear
nonconvex optimization problems. However, we have developed a method based on
canonical forms for maxminplusscaling functions to solve these optimization
problems in a more efficient way than by just applying nonlinear optimization
as was done in previous research. More specifically, the proposed algorithm
consists in solving several linear programming problems [20].
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