Stabilising properties of constrained predictive control

Standard generalised predictive control (GPC) and constrained receding-horizon predictive control (CRHPC) stability results have traditionally been derived in the state-space, using the properties of the solution of the Riccati equation associated with the control law. Unfortunately this type of study does not readily extend to constrained control laws which are nonlinear. By invoking the monotonicity, with respect to time, of the receding-horizon cost function, however, an extension of the stability properties of a subclass of GPC, termed GPC ^∞, and of CRHPC may be obtained, when inequality constraints are added to the control objective. The problem of feasibility (i.e. the compatibility of the constraints) is also becoming a major area of interest in predictive control. In GPC^∞ and CRHPC, the feasibility problem is compounded by the use of end-point equality constraints on the tracking error. A new concept called setpoint conditioning is introduced here, which may be used to resolve the incompatibilities between the inequality and the end-point equality constraints, without compromising stability