Characterisation of receding horizon control for constrained linear systems

This paper characterises the geometric structure of receding horizon control (RHC) of linear, discrete-time systems, subject to a quadratic performance index and linear constraints. The geometric insights so obtained are exploited to derive a closed-form solution for the case where the total number of constraints is less than or equal to the number of degrees of freedom, represented by the number of control moves. The solution is shown to be a partition of the state space into regions for which an analytic expression is given for the corresponding control law. Both the regions and the control law are characterised in terms of the parameters of the open-loop optimal control problem that underlies RHC and can be computed off line. The solution for the case where the total number of constraints is greater than the number of degrees of freedom is addressed via an algorithm that iteratively uses the off-line solution and avoids on-line optimisation