Uniting bounded control and MPC for stabilization of constrained linear systems

  • Authors:

  • Nael H. El-Farra;Prashant Mhaskar;Panagiotis D. Christofides

  • Affiliations:

  • Department of Chemical Engineering, The Henry Samueli School of Engineering and Applied Science, University of California, 405 Hilgard Avenue, Box 951592 Los Angeles, CA 90095-1592, USA;Department of Chemical Engineering, The Henry Samueli School of Engineering and Applied Science, University of California, 405 Hilgard Avenue, Box 951592 Los Angeles, CA 90095-1592, USA;Department of Chemical Engineering, The Henry Samueli School of Engineering and Applied Science, University of California, 405 Hilgard Avenue, Box 951592 Los Angeles, CA 90095-1592, USA

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2004

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Abstract

In this work, a hybrid control scheme, uniting bounded control with model predictive control (MPC), is proposed for the stabilization of linear time-invariant systems with input constraints. The scheme is predicated upon the idea of switching between a model predictive controller, that minimizes a given performance objective subject to constraints, and a bounded controller, for which the region of constrained closed-loop stability is explicitly characterized. Switching laws, implemented by a logic-based supervisor that constantly monitors the plant, are derived to orchestrate the transition between the two controllers in a way that safeguards against any possible instability or infeasibility under MPC, reconciles the stability and optimality properties of both controllers, and guarantees asymptotic closed-loop stability for all initial conditions within the stability region of the bounded controller. The hybrid control scheme is shown to provide, irrespective of the chosen MPC formulation, a safety net for the practical implementation of MPC, for open-loop unstable plants, by providing a priori knowledge, through off-line computations, of a large set of initial conditions for which closed-loop stability is guaranteed. The implementation of the proposed approach is illustrated, through numerical simulations, for an exponentially unstable linear system.