Polyhedral functions and multiparametric linear programming
Journal of Optimization Theory and Applications
On the parametric linear complementarity problem
Journal of Optimization Theory and Applications
Journal of Optimization Theory and Applications
An Algorithm for Approximate Multiparametric Convex Programming
Computational Optimization and Applications
Survey Constrained model predictive control: Stability and optimality
Automatica (Journal of IFAC)
Brief Equivalence of hybrid dynamical models
Automatica (Journal of IFAC)
The explicit linear quadratic regulator for constrained systems
Automatica (Journal of IFAC)
Brief An algorithm for multi-parametric quadratic programming and explicit MPC solutions
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
Expert Systems with Applications: An International Journal
Stability of multiobjective predictive control: A utopia-tracking approach
Automatica (Journal of IFAC)
Hi-index | 22.15 |
This paper proposes a novel model predictive control (MPC) scheme based on multiobjective optimization. At each sampling time, the MPC control action is chosen among the set of Pareto optimal solutions based on a time-varying, state-dependent decision criterion. Compared to standard single-objective MPC formulations, such a criterion allows one to take into account several, often irreconcilable, control specifications, such as high bandwidth (closed-loop promptness) when the state vector is far away from the equilibrium and low bandwidth (good noise rejection properties) near the equilibrium. After recasting the optimization problem associated with the multiobjective MPC controller as a multiparametric multiobjective linear or quadratic program, we show that it is possible to compute each Pareto optimal solution as an explicit piecewise affine function of the state vector and of the vector of weights to be assigned to the different objectives in order to get that particular Pareto optimal solution. Furthermore, we provide conditions for selecting Pareto optimal solutions so that the MPC control loop is asymptotically stable, and show the effectiveness of the approach in simulation examples.