Continuity and Monotonicity of the MPC Value Function with respect to Sampling Time and Prediction Horizon

The digital implementation of model predictive control (MPC) is fundamentally governed by two design parameters; sampling time and prediction horizon. Knowledge of the properties of the value function with respect to the parameters can be used for developing optimisation tools to find optimal system designs. In particular, these properties are continuity and monotonicity. This paper presents analytical results to reveal the smoothness properties of the MPC value function in open- and closed-loop for constrained linear systems. Continuity of the value function and its differentiability for a given number of prediction steps are proven mathematically and confirmed with numerical results. Non-monotonicity is shown from the ensuing numerical investigation. It is shown that increasing sampling rate and/or prediction horizon does not always lead to an improved closedloop performance, particularly at faster sampling rates

Analytical results for the multi-objective design of model-predictive control

In model-predictive control (MPC), achieving the best closed-loop performance under a given computational resource is the underlying design consideration. This paper analyzes the MPC design problem with control performance and required computational resource as competing design objectives. The proposed multi-objective design of MPC (MOD-MPC) approach extends current methods that treat control performance and the computational resource separately -- often with the latter as a fixed constraint -- which requires the implementation hardware to be known a priori. The proposed approach focuses on the tuning of structural MPC parameters, namely sampling time and prediction horizon length, to produce a set of optimal choices available to the practitioner. The posed design problem is then analyzed to reveal key properties, including smoothness of the design objectives and parameter bounds, and establish certain validated guarantees. Founded on these properties, necessary and sufficient conditions for an effective and efficient solver are presented, leading to a specialized multi-objective optimizer for the MOD-MPC being proposed. Finally, two real-world control problems are used to illustrate the results of the design approach and importance of the developed conditions for an effective solver of the MOD-MPC problem

Model Predictive Control meets robust Kalman filtering

Model Predictive Control (MPC) is the principal control technique used in industrial applications. Although it offers distinguishable qualities that make it ideal for industrial applications, it can be questioned its robustness regarding model uncertainties and external noises. In this paper we propose a robust MPC controller that merges the simplicity in the design of MPC with added robustness. In particular, our control system stems from the idea of adding robustness in the prediction phase of the algorithm through a specific robust Kalman filter recently introduced. Notably, the overall result is an algorithm very similar to classic MPC but that also provides the user with the possibility to tune the robustness of the control. To test the ability of the controller to deal with errors in modeling, we consider a servomechanism system characterized by nonlinear dynamics

Can a galaxy redshift survey measure dark energy clustering?

(abridged) A wide-field galaxy redshift survey allows one to probe galaxy clustering at largest spatial scales, which carries an invaluable information on horizon-scale physics complementarily to the cosmic microwave background (CMB). Assuming the planned survey consisting of z~1 and z~3 surveys with areas of 2000 and 300 square degrees, respectively, we study the prospects for probing dark energy clustering from the measured galaxy power spectrum, assuming the dynamical properties of dark energy are specified in terms of the equation of state and the effective sound speed c_e in the context of an adiabatic cold dark matter dominated model. The dark energy clustering adds a power to the galaxy power spectrum amplitude at spatial scales greater than the sound horizon, and the enhancement is sensitive to redshift evolution of the net dark energy density, i.e. the equation of state. We find that the galaxy survey, when combined with Planck, can distinguish dark energy clustering from a smooth dark energy model such as the quintessence model (c_e=1), when c_e<0.04 (0.02) in the case of the constant equation of state w_0=-0.9 (-0.95). An ultimate full-sky survey of z~1 galaxies allows the detection when c_e<0.08 (0.04) for w_0=0.9 (-0.95). We also investigate a degeneracy between the dark energy clustering and the non-relativistic neutrinos implied from the neutrino oscillation experiments, because the two effects both induce a scale-dependent modification in the galaxy power spectrum shape at largest spatial scales accessible from the galaxy survey. It is shown that a wider redshift coverage can efficiently separate the two effects by utilizing the different redshift dependences, where dark energy clustering is apparent only at low redshifts z<1.Comment: 14 pages, 7 figures; minor changes to match the published versio

Reliability-based economic model predictive control for generalized flow-based networks including actuators' health-aware capabilities

This paper proposes a reliability-based economic model predictive control (MPC) strategy for the management of generalized flow-based networks, integrating some ideas on network service reliability, dynamic safety stock planning, and degradation of equipment health. The proposed strategy is based on a single-layer economic optimisation problem with dynamic constraints, which includes two enhancements with respect to existing approaches. The first enhancement considers chance-constraint programming to compute an optimal inventory replenishment policy based on a desired risk acceptability level, leading to dynamically allocate safety stocks in flow-based networks to satisfy non-stationary flow demands. The second enhancement computes a smart distribution of the control effort and maximises actuators’ availability by estimating their degradation and reliability. The proposed approach is illustrated with an application of water transport networks using the Barcelona network as the considered case study.Peer ReviewedPostprint (author's final draft

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

Trajectory planning of autonomous vehicles

Autonomous driving is an emerging technology that is advancing in a very fast way. It is a complex challenge that involves many sections with plenty of different disciplines. One of the more important parts is trajectory planning, where this thesis it has been focused. This project revises the different algorithms of trajectory planning that have been proposed for autonomous cars. The reason why a trajectory planner based on numerical optimization algorithm such that Model Predictive Control (MPC) is proposed is also discussed. The main advantages are the possibility of generating the planning online allowing the replanning if unexpected events occurs (objects in the middle of the road, pedestrians appearing unexpectedly, etc.) and the facility of including several objectives in the optimization problem. This thesis studies different parameter that can define an optimal generated trajectory and how it is structured in the optimization program. Moreover there are several weights that should be tuned to orientate the trajectory planner in the direction that it is desired. All this tuning process is explained providing guidelines on how can be done for future cases. Finally, several testing results were included that are obtained with different parameters and structures of the program. These results are analysed and some conclusions of the efficiency of the MPC-based planning algorithm are obtained highlighting the advantages that it presents