Parameterized polyhedra and their vertices
International Journal of Parallel Programming
Set-Theoretic Methods in Control
Set-Theoretic Methods in Control
Brief paper: On feasible sets for MPC and their approximations
Automatica (Journal of IFAC)
The explicit linear quadratic regulator for constrained systems
Automatica (Journal of IFAC)
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We propose a new approach to controlling a discrete linear stationary system with a polyhedral constraint on the state and input. The basic idea is to use interpolation. The control law has both explicit and implicit forms. In the implicit form, at any moment of time, at most two linear programming problems are solved online. In the explicit form, the control law contains piecewise affine and continuous functions of state. This method can be viewed as an alternative to predictive control. We show proofs of recursive realizability and asymptotic stability.