J.A. Rossiter

Model-Based Predictive Control : A Practical Approach

Introduction Common Linear Models Used in Model Predictive Control Prediction in Model Predictive Control Predictive Control-The Basic Algorithm Examples - Tuning Predictive Control and Numerical Conditioning Stability Guarantees and Optimising Performance Closed-Loop Paradigm Constraint Handling and Feasibility Issues in MPC Improving Robustness-The Constraint Free Case The Relationship Between Modelling and the Robustness of MPC Robustness of MPC During Constraint Handling and Invariant Sets Optimisation and Computational Efficiency in Predictive Control Predictive Functional Control Multirate Systems Modelling for Predictive Control Appendices Conclusion

Systems with persistent disturbances: predictive control with restricted constraints

Predictive regulation of linear discrete-time systems subject to unknown but bounded disturbances and to state/control constraints is addressed. An algorithm based on constraint restrictions is presented and its stability properties are analysed.

Efficient robust predictive control

Predictive constrained control of time-varying and/or uncertain linear systems has been effected through the use of ellipsoidal invariant sets (Kothare et al., 1996). Linear matrix inequalities (LMIs) have been used to design a state-dependent state-feedback law that maintains the state vector inside invariant feasible sets. For the purposes of prediction however, at each time instant, the state feedback law is assumed constant. In addition, due to the large number of LMIs involved, online computation becomes intractable for anything other than small dimensional systems. Here we propose an approach that deploys a fixed state-feedback law but introduces extra degrees of freedom through the use of perturbations on the fixed state-feedback law. The problem is so formulated that all demanding computations can be performed offline leaving only a simple optimization problem to be solved online. Over and above the very significant reduction in computational cost, the extra degrees of freedom allow for better performance and wider applicability.

A numerically robust state-space approach to stable-predictive control strategies

Recent work with predictive control strategies has shown that the stable GPC (SGPC) approach has significant computational and numerical advantages. However, SGPC is cast in the transfer function framework which limits its application. Here we develop a means of extending the results to state-space models and show that improved numerical conditioning can be obtained for many stable-predictive control strategies.

The efficient computation of polyhedral invariant sets for linear systems with polytopic uncertainty

In this paper the concept of maximal admissable set (MAS), introduced by Gilbert et al. (1991) for linear time-invariant systems, is extended to linear systems with polytopic uncertainty under linear state feedback. It is shown that by constructing a tree of state predictions using the vertices of the uncertainty polytope and by imposing state and input constraints on these predictions, a polyhedral robust invariant set can be constructed. The resulting set is proven to be the maximal admissable set. The number of constraints defining the invariant set is shown to be finite if the closed loop system is quadratically stable (i.e. has a quadratic Lyapunov function). An algorithm is also proposed that efficiently computes the polyhedral set without exhaustively exploring the entire prediction tree. This is achieved through the formulation of a more general invariance condition than that proposed in Gilbert et al. (1991) and by the removal of redundant constraints in intermediate steps. The efficiency and correctness of the algorithm is demonstrated by means of a numerical example.

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.

Technical Communique: Who needs QP for linear MPC anyway?

Conventional MPC uses quadratic programming (QP) to minimise, on-line, a cost over n linearly constrained control moves. However, stability constraints often require the use of large n thereby increasing the on-line computation, rendering the approach impracticable in the case of fast sampling. Here, we explore an alternative that requires a fraction of the computational cost (which increases only linearly with n), and propose an extension which, in all but a small class of models, matches to within a fraction of a percent point the performance of the optimal solution obtained through QP. The provocative title of the paper is intended to point out that the proposed approach offers a very attractive alternative to QP-based MPC.

Interpolation based MPC for LPV systems using polyhedral invariant sets

Guaranteeing asymptotic stability and recursive constraint satisfaction for a set of initial states that is as large as possible and with both a minimal control cost and computational load can be identified as a common objective in the model predictive control (MPC) community. General interpolation (Rossiter et al., 2004, Bacic et al, 2003) provides a favourable trade oil between these different aspects, however, in the robust case, this requires on-line semi-definite programming (SDP), since one typically employs ellipsoidal invariant sets. Recently, (Pluymers et al., 2005) have proposed an efficient algorithm for constructing the robust polyhedral maximal admissible set (Gilbert et al., 1991) for linear systems with polytopic model uncertainty. In this paper a robust interpolation based MPC method is proposed that makes use of these sets. The algorithm is formulated as a quadratic program (QP) and is shown to have improved feasibility properties, efficiently cope with non-symmetrical constraints and give better control performance than existing interpolation based robust MPC algorithms.

Interpolation based computationally efficient predictive control

This paper investigates interpolation based predictive control and presents a study of the properties and therefore limitations of the approach. This understanding is used to develop an efficient algorithm with guarantees of recursive feasibility and stability.

Modelling and implicit modelling for predictive control

There should be a synergy between model identification and the role of the model in control law design, however this is often ignored in the literature. For the case of a predictive control law, the potential for synergy is quite transparent. The means of utilizing this link are discussed and illustrated and in particular it is shown that a slightly different approach to modelling can support a predictive control design to a far greater extent than conventional methods.