J.R. Gossner

Stable generalized predictive control with constraints and bounded disturbances

Disturbances in the presence of constraints can drive predictive control into infeasibility and instability. This problem has attracted little research effort, despite its significant practical importance. Earlier work has given stability conditions, but these are restricted to systems with at most one unstable pole, and do not lead to suitable algorithms because they apply to infinite horizons only. Here we modify the constraint limits and derive an algorithm with guaranteed stability and asymptotic tracking. Available degrees of freedom are given up in order to optimize performance; the results of the paper are illustrated by means of numerical examples.

Infinite horizon stable predictive control

Terminal constraints guarantee the stability of predicted trajectories and form the basis of predictive control algorithms with guaranteed stability. Earlier work in the literature uses terminal constraints which define sufficient but not necessary conditions for the stability of predicted trajectories. In this paper we deploy conditions which are both necessary and sufficient and hence release more degrees of freedom for optimizing performance and/or meeting constraints. Also an alternative means of computing the implied infinite horizon GPC cost, avoiding the need for solving a Lyapunov equation, is presented.

Feasibility and stability results for constrained stable generalized predictive control

Several predictive control strategies that handle input/output constraints have been proposed in the literature. The difficulty with all these approaches is that, in an attempt to optimize output tracking over a finite horizon, they tend to drive the controls to the constraint limits; this can lead to infeasibility, which, in the case of systems with poles and/or zeros outside the unit circle, leads to instability. The aim of this paper is to develop necessary and sufficient conditions for feasibility and stability and to propose an algorithm that overcomes finite-horizon infeasibility and gives stability and asymptotic tracking. Predictive control; constraints; stability; algorithms

Cautious stable predictive control: A guaranteed stable predictive control algorithm with low input activity and good robustness

End-point constraints guarantee the stability of predicted trajectories and form the basis of stable predictive control algorithms. However, the use of end-point constraints that define sufficient but not necessary conditions for the stability of predicted trajectories can lead to highly tuned controllers. These often possess poor robustness properties and result in overactive input trajectories which, in the presence of input constraints, may lead to instability. Here we develop conditions that are both necessary and sufficient and deploy these to derive stable predictive control algorithms with reduced input activity and improved robustness properties. The efficacy of the new algorithms, in respect of their ability to cope with both input constraints and robustness, are illustrated by means of design studies.

A priori stability conditions for an arbitrary number of unstable poles

Necessary and sufficient stability conditions that place bounds on the current inputs are derived that guarantee BIBO stability and retain the control authority needed to asymptotically stabilize a system that is subject to physical input constraints. For open-loop stable systems, the stability conditions coincide with the physical constraints, but for unstable systems, tighter limits may be required. Use of these limits in a supervisory role with controllers that have no stability guarantee is discussed and illustrated.

A Priori Stability Conditions for an Arbitrary Number of Unstable Poles

Abstract Necessary and sufficient stability conditions which place bounds on the current input are derived which guarantee BIBO stability and retain the control authority needed to asymptotically stabilize a system which is subject to physical input constraints. For open-loop stable systems, the stability conditions coincide with the physical constraints, but for unstable systems, tighter limits may be required, Use of these limits in a supervisory role with controllers which have no stability guarantee is discussed and illustrated