Feasibility in predictive control of constrained linear systems: the output feedback case

Abstract

SUMMARYThis paper addresses model-based predictive regulation for a linear discrete-time system in the presence of unknown but bounded disturbances, partial state information and state/control constraints. The proposed nonlinear dynamic compensator uses a set-valued estimator, which recursively updates the membership set of the plant state, along with a receding-horizon regulator which selects on-line the control variable depending upon the current state membership set. It is shown that the overall scheme preserves feasibility if this is assumed from the outset, and hence guarantees closed-loop stability and constraint ful"lment. These properties rely on exact set-membership estimation. A simple approximation scheme which avoids setmembership estimation but preserves stability is also proposed and the relative performance/complexity tradeo!s are discussed. Simulation results demonstrate the e!ectiveness of the proposed method.

State and Output Feedback Nonlinear Model Predictive Control: An Overview

“…For linear systems, [8] introduces a set membership estimator to obtain quantifiable bounds on the estimation error, which are used in a robust constraint-handling predictive controller. The setup of [8] is taken further in [21], using a more general observer, and considering more effective computational methods. For the same class of systems, [56] does joint estimation and control calculation based on a minimax formulation, however without obtaining stability guarantees.…”

A Method for Robust Receding Horizon Output Feedback Control of Constrained Systems

“…We next characterise two critical properties of the parameterisation (14), which make it attractive in application to control of the system (1), and which parallel the results in [19] for the full state feedback case. …”

“…In this section, we characterise some of the geometric and invariance properties associated with control laws synthesised from the feedback parameterisation (14). We first require the following assumption about the terminal constraint set X f :…”

“…An equivalent convex parameterisation can similarly be defined using the feedback parameterisation (14), so that an admissible pair (K, g) ∈ Π of N, (s, E I ) can be calculated using standard convex optimisation techniques (cf. Remark 3 and Theorem 2), where the optimisation problem to be solved is finite-dimensional, since the set E I can be implicitly characterised by a finite number of inequalities (cf.…”

“…However, in order to ensure that the region of attraction is as large as possible while guaranteeing robust constraint satisfaction, an explicit model of the estimation error seems necessary, and a number of control schemes based on error set membership estimation [7,36] have been proposed [3,14]. When the system dynamics are linear, a common approach is to employ a combination of a fixed linear observer and associated estimation error set with a fixed stabilising linear control law, to which a sequence of input perturbations is calculated at each time instant.…”