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Low Complexity Model Predictive Control of Hybrid Systems


T. Geyer

Trondheim, Norway, NTNU

Hybrid systems - loosely defined as systems comprised of continuous and discrete/switched components - are prevalent in all domains of engineering. Over the last few years this system class has attracted much attention and various tools have emerged for studying and affecting its behavior. In particular, Model Predictive Control (MPC) problems can be formulated for discrete-time (linear) hybrid systems by introducing integer variables. Motivated by the fact that the resulting mixed-integer optimization problems are NP-hard, the following three techniques will be presented to reduce the associated problem complexity (and hence the computation time for solving these problems). (i) A temporal decomposition scheme that efficiently derives the control actions by performing Lagrangian decomposition on the prediction horizon. More specifically, the algorithm translates the original MPC problem into a temporal sequence of independent subproblems of smaller dimension, and the solution to the Lagrangian problem yields a sequence of control actions for the full horizon. (ii) Another approach is to compute the set of feasible integer combinations (modes) of the model and to add cuts to the optimization problem that a priori rule out infeasible combinations. (iii) When pre-solving the MPC problem for the whole state-space (using multi-parametric programming), a piecewise affine control law results, i.e. the state-space is partitioned into polyhedra and with each polyhedron a given affine feedback law is associated. To reduce the number of polyhedra, the notion of the hyperplane arrangement and Boolean minimization can be used to derive an equivalent representation of the controller that is minimal in the number of polyhedra. All three approaches greatly reduce the complexity and hence the computational burden. These techniques are applied to applications in the fields of power electronics and power systems.


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