Basil Kouvaritakis

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.

Nonlinear predictive control : theory and practice

* Part I * Chapter 1: Review of nonlinear model predictive control applications * Chapter 2: Nonlinear model predictive control: issues and applications * Part II * Chapter 3: Model predictive control: output feedback and tracking of nonlinear systems * Chapter 4: Model predictive control of nonlinear parameter varying systems via receding horizon control Lyapunov functions * Chapter 5: Nonlinear model-algorithmic control for multivariable nonminimum-phase processes * Part III * Chapter 6: Open-loop and closed-loop optimality in interpolation MPC * Chapter 7: Closed-loop predictions in model based predictive control linear and nonlinear systems * Chapter 8: Computationally efficient non linear predictive control algorithm for control of constrained nonlinear systems * Part IV * Chapter 9: Long-prediction-horizon nonlinear model predictive control * Chapter 10: Nonlinear control of industrial processes * Chapter 11: Nonlinear model based predictive control using multiple local models * Chapter 12: Neural network control of a gasoline engine with rapid sampling

Brief Robust receding horizon predictive control for systems with uncertain dynamics and input saturation

A receding horizon predictive control method which assures stability for systems with model uncertainty and input saturation is derived by extending earlier work in two important respects: (i) ellipsoidal invariant sets are replaced by polyhedral invariant sets; and (ii) the constraint that the state lie in an invariant set is invoked N steps ahead. The new algorithm allows for a considerable enlargement of the stabilizable set and provides extra degrees of freedom with which to improve performance.

Probabilistic Constrained MPC for Multiplicative and Additive Stochastic Uncertainty

The technical note develops a receding horizon control strategy to guarantee closed-loop convergence and feasibility in respect of soft constraints. Earlier results addressed the case of multiplicative uncertainty only. The present technical note extends these to the more general case of additive and multiplicative uncertainty and proposes a method of handling probabilistic constraints. The results are illustrated by a simple design study considering the control of a wind turbine.

Stochastic Tubes in Model Predictive Control With Probabilistic Constraints

Recent developments in stochastic MPC provided guarantees of closed loop stability and satisfaction of probabilistic and hard constraints. However the required computation can be formidable for anything other than short prediction horizons. This difficulty is removed in the current paper through the use of tubes of fixed cross-section and variable scaling. A model describing the evolution of predicted tube scalings simplifies the computation of stochastic tubes; furthermore this procedure can be performed offline. The resulting MPC scheme has a low online computational load even for long prediction horizons, thus allowing for performance improvements. The approach is illustrated by numerical examples.

Brief Nonlinear model predictive control with polytopic invariant sets

Ellipsoidal invariant sets have been widely used as target sets in model predictive control (MPC). These sets can be computed by constructing appropriate linear difference inclusions together with additional constraints to ensure that the ellipsoid lies within a given inclusion polytope. The choice of inclusion polytope has a significant effect on the size of the target ellipsoid, but the optimal inclusion polytope cannot in general be computed systematically. This paper shows that use of polytopic invariant sets overcomes this difficulty, allowing larger stabilizable sets without loss of performance. In the interests of online efficiency, consideration is focused on interpolation-based MPC.

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.

Brief paper: Explicit use of probabilistic distributions in linear predictive control

The guarantee of feasibility given feasibility at initial time is an issue that has been overlooked by many of the recent papers on stochastic model predictive control. Effective solutions have recently been proposed, but these carry considerable online computational load and a degree of conservativism. For the case that the elements of the random additive disturbance vector are independent, the current paper ensures that probabilistic constraints are met and that a quadratic stability condition is satisfied. A numerical example illustrates the efficacy of the proposed algorithm, which achieves tight satisfaction of constraints and thereby attains near-optimal performance.

Optimizing prediction dynamics for robust MPC

A convex formulation is derived for optimizing dynamic feedback laws for constrained linear systems with polytopic uncertainty. We show that, when it exists, the maximal invariant ellipsoidal set for the plant state under a dynamic feedback law incorporating any chosen static feedback gain is equal to the maximal invariant ellipsoidal set under any linear feedback law. The dynamic controller and its associated invariant set define a computationally efficient robust model predictive control (MPC) law with prediction dynamics belonging to a polytopic uncertainty set.

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.