Controlled contractive sets for low-complexity constrained control

Sarmad Munir 1 Morten Hovd 1 Guillaume Sandou 2, 3 Sorin Olaru 2, 3
2 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
Abstract : Explicit constrained control is relatively simple when a controlled contractive set is available. However, the complexity of the explicit controller will depend on the complexity of the controlled contractive set. The ability to design a low complexity controlled contractive set is therefore desirable. Most methods for finding controlled contractive sets either assume the use of a constant linear state feedback, or is based on reachable set computations. In the first case, the assumption of a constant linear state feedback is restrictive (as MPC controllers for linear systems are typically piecewise affine), and in the second case the complexity of the controlled contractive set may be very high. Initial results on the construction of low complexity controlled contractive sets without assuming linear state feedback were reported at the IFAC World Congress in 2014. The present paper addresses shortcomings in the previous results, including the ability to handle identical modes in series (corresponding to a non-diagonalizable A matrix) and oscillatory modes. The paper suggests a method to find a flexible complexity controlled contractive set.
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Sarmad Munir, Morten Hovd, Guillaume Sandou, Sorin Olaru. Controlled contractive sets for low-complexity constrained control. IEEE Multi-Conference on Systems and Control (MSC 2016), Sep 2016, Buenos Aires, Argentina. ⟨10.1109/cacsd.2016.7602546⟩. ⟨hal-01381706⟩

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