One of the most recent model predictive control formulations is the constrained infinite- horizon linear quadratic regulator (CIHLQR). This particular control formulation considers future process evolution over the infinite prediction horizon length while accounting for limiting (inequality) constraints imposed on process variables, both state(s)/ output(s) and input(s). As such, it represents a constrained extension of the standard unconstrained linear quadratic regulator, which has received significant attention in the control community for the past 4 decades and has established itself as a corner stone of modern control technology.
The presence of an infinite- horizon provides this MPC formulation with some sound properties. These include guaranteed nominal stability and feasibility, provided that a given control problem is soluble. Furthermore, if CIHLQR is unable to provide a feasible solution then the control problem is insoluble by any other control formulation. This, in particular, is a unique property for this MPC formulation and may prove to be its key advantage over alternative model predictive controllers that have in the past attempted to satisfy nominal stability/ feasibility by imposing restrictive assumptions on the predicted state and/ or control sequences.
Also, the development of related constrained LQG/ LTR formulation and constrained infinite- horizon Hinf control would seem to be possible in a straightforward manner. This, in turn, would allow model predictive control to be accepted as a general framework within which most of the modern control design methodologies can be cast while addressing an important practical issue of inequality constraints, imposed on system variables. On the other hand, in order to reduce the dimensionality of the corresponding optimisation problem from infinite to finite, a certain condition is imposed on the terminal predicted state, dictating the lower bound on the prediction horizon length required to guarantee equivalence to the infinite- horizon formulation. Some research effort has gone into analysing the level of necessity in imposing such a condition in order to guarantee equivalence with infinite- horizon formulation. Consequently, the attempt has been made to reformulate standard CIHLQR so that it can be implemented by solving optimisation problems of comparatively shorter dimensionality and, therefore, complexity.
This presentation concentrates on three topics. Firstly, the standard CIHLQR formulation is reviewed with some of its sound properties discussed in detail. Secondly, attempts at reducing the prediction horizon length, required to achieve performance equivalent to that of CIHLQR is presented. In other words, the recent efforts of simplifying the CIHLQR formulation are reviewed. Finally, situations during which MPC control policy can be achieved by implementing LQR control "with clipping", i.e. saturated LQR, are analysed.
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