A Convex Feasibility Approach to Anytime Model Predictive Control

This paper proposes to decouple performance optimization and enforcement of asymptotic convergence in Model Predictive Control (MPC) so that convergence to a given terminal set is achieved independently of how much performance is optimized at each sampling step. By embedding an explicit decreasing condition in the MPC constraints and thanks to a novel and very easy-to-implement convex feasibility solver proposed in the paper, it is possible to run an outer performance optimization algorithm on top of the feasibility solver and optimize for an amount of time that depends on the available CPU resources within the current sampling step (possibly going open-loop at a given sampling step in the extreme case no resources are available) and still guarantee convergence to the terminal set. While the MPC setup and the solver proposed in the paper can deal with quite general classes of functions, we highlight the synthesis method and show numerical results in case of linear MPC and ellipsoidal and polyhedral terminal sets.Comment: 8 page

Risk-Averse Model Predictive Operation Control of Islanded Microgrids

In this paper we present a risk-averse model predictive control (MPC) scheme for the operation of islanded microgrids with very high share of renewable energy sources. The proposed scheme mitigates the effect of errors in the determination of the probability distribution of renewable infeed and load. This allows to use less complex and less accurate forecasting methods and to formulate low-dimensional scenario-based optimisation problems which are suitable for control applications. Additionally, the designer may trade performance for safety by interpolating between the conventional stochastic and worst-case MPC formulations. The presented risk-averse MPC problem is formulated as a mixed-integer quadratically-constrained quadratic problem and its favourable characteristics are demonstrated in a case study. This includes a sensitivity analysis that illustrates the robustness to load and renewable power prediction errors

Stabilizing Model Predictive Control of Stochastic Constrained Linear Systems

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On the Approximation of Constrained Linear Quadratic Regulator Problems and their Application to Model Predictive Control - Supplementary Notes

By parametrizing input and state trajectories with basis functions different approximations to the constrained linear quadratic regulator problem are obtained. These notes present and discuss technical results that are intended to supplement a corresponding journal article. The results can be applied in a model predictive control context.Comment: 19 pages, 1 figur