Robust Model Predictive Control via Scenario Optimization

This paper discusses a novel probabilistic approach for the design of robust model predictive control (MPC) laws for discrete-time linear systems affected by parametric uncertainty and additive disturbances. The proposed technique is based on the iterated solution, at each step, of a finite-horizon optimal control problem (FHOCP) that takes into account a suitable number of randomly extracted scenarios of uncertainty and disturbances, followed by a specific command selection rule implemented in a receding horizon fashion. The scenario FHOCP is always convex, also when the uncertain parameters and disturbance belong to non-convex sets, and irrespective of how the model uncertainty influences the system's matrices. Moreover, the computational complexity of the proposed approach does not depend on the uncertainty/disturbance dimensions, and scales quadratically with the control horizon. The main result in this paper is related to the analysis of the closed loop system under receding-horizon implementation of the scenario FHOCP, and essentially states that the devised control law guarantees constraint satisfaction at each step with some a-priori assigned probability p, while the system's state reaches the target set either asymptotically, or in finite time with probability at least p. The proposed method may be a valid alternative when other existing techniques, either deterministic or stochastic, are not directly usable due to excessive conservatism or to numerical intractability caused by lack of convexity of the robust or chance-constrained optimization problem.Comment: This manuscript is a preprint of a paper accepted for publication in the IEEE Transactions on Automatic Control, with DOI: 10.1109/TAC.2012.2203054, and is subject to IEEE copyright. The copy of record will be available at http://ieeexplore.ieee.or

Stochastic model predictive control of LPV systems via scenario optimization

A stochastic receding-horizon control approach for constrained Linear Parameter Varying discrete-time systems is proposed in this paper. It is assumed that the time-varying parameters have stochastic nature and that the system's matrices are bounded but otherwise arbitrary nonlinear functions of these parameters. No specific assumption on the statistics of the parameters is required. By using a randomization approach, a scenario-based finite-horizon optimal control problem is formulated, where only a finite number M of sampled predicted parameter trajectories (‘scenarios') are considered. This problem is convex and its solution is a priori guaranteed to be probabilistically robust, up to a user-defined probability level p. The p level is linked to M by an analytic relationship, which establishes a tradeoff between computational complexity and robustness of the solution. Then, a receding horizon strategy is presented, involving the iterated solution of a scenario-based finite-horizon control problem at each time step. Our key result is to show that the state trajectories of the controlled system reach a terminal positively invariant set in finite time, either deterministically, or with probability no smaller than p. The features of the approach are illustrated by a numerical example

Distribution and composition patterns of plastic pollution in small islands subjected to different human pressures along the highly connected waters of the NW Mediterranean Sea.

One of the tools to protect Mediterranean biodiversity was the creation of an extensive network of Marine Protected Areas. That those areas are not exempt from plastic pollution has extensively been demonstrated whether they are characterized by a specific plastic composition if compared to not protected areas is currently a topic of discussion. This research aims to evaluate plastic spatial distribution and composition patterns along the surface waters of small islands of the Western Mediterranean Basin subjected to different human pressures and protection status. We studied the spatial distribution of floating plastics by performing 65 surface trawls, carried out using a Hydro-bios manta net coupled with a 335-μm mesh, along the coastal waters of a remote protected archipelago, Columbretes Islands (NW Mediterranean Sea), a protected archipelago located in a high anthropized environment, Cabrera MPA (Balearic Sea), and protected and unprotected areas of two touristic Islands, Mallorca and Menorca in the Balearic Sea. 10637 plastics were identified along the study area and a subset was categorized according to shape, size and polymer. Plastics were found at each sampling site and in all samples. No microscale nor mesoscale variability in plastics abundance was encountered throughout the study area where similar values were found in remote protected areas with no local land-based contamination sources [0.04 (±0.03) items/m2] and in anthropized areas [0.04 (±0.07) items/m2]. Results suggest that floating plastics, in a region such as the NW Mediterranean Sea, strongly exposed to human stressors and highly connected waters, are homogeneously distributed regardless of land uses. Differences were found in plastic size, shape, and polymer composition. Remote islands showed the highest number of fragments reaching percentages higher than 90%, the lowest percentage of film summing up to less than 3%, a lower microscale variability, and the presence of small items with sizes ranging from 2900 μm to 163000 μm not detected in the more anthropized areas. The percentage of film and plastic size increase according to the level of human pressure. Small fragments are the product of fragmentation processes, driven by photooxidation, of larger plastics to smaller ones. Films, due to their volume/surface ratio are suitable for biofouling favoring their faster removal from the sea surface to the seafloor. The lower abundance of film observed in the studied remote protected areas combined with a consistent abundance of small fragments suggest that plastics detected within these waters could be more aged and be arriving from distant sources when compared to plastics detected in more anthropized areas, such as of the Balearic Archipelago, closer to potential marine debris sources and previously described as plastics “retention area”. Remote areas showed a different polymer composition, with a higher percentage of polystyrene, extensively used in the fishing industry that could represent an important contamination source for those areas. Finally, data from this research can contribute to consolidating scientific evidence available for the elaboration and monitoring of future management plans focused on the mitigation and prevention of plastic pollution in marine protected areas

BREAKING THE PARADIGM: MARINE SEDIMENTS HOLD TWO-FOLD MICROPLASTICS THAN SEA SURFACE WATERS AND ARE DOMINATED BY FIBERS

Marine compartments are often considered independent environments in studies on plastic pollution (Ali et al., 2021). Consequently, little is known about microplastic (MPs) distribution amongst those habitats closely linked. Here, we perform an interactive assessment of MPs abundance and composition from the pelagic habitat to beaches integrating shallow seafloor sediments of a coastal Mediterranean marine protected area and evaluating MPs ingestion in holothurians, echinoderms, molluscs, and fishes inhabiting the area. We observed a gradient in the accumulation of MPs from the sea surface (0.17 ± 0.39 MPs/m2) to the seafloor (76 ± 108 MPs/m2) and beach sediment (13418 ± 28787 MPs/m2), with a skip of two orders of magnitude. Microplastic abundances fit with those reported for more anthropized Mediterranean areas and suggest coastal environments as potential debris sinking areas. Fibers dominate all the studied habitats. Holothurians showed the highest general MPs and fibers ingestion occurrence (91%), with greater values (9.48 ± 8.05 MPs/individual and 8.24 ± 7.95 fibers/individual) than those reported previously (Bulleri et al., 2021). Considering ecological key role, species distribution, and MPs ingestion values, we suggest Holothuroidea as suitable bioindicators for plastic pollution, particularly for fibers. Fibers are composed primarily of cellulose acetate (29%), whereas styrofoam of polystyrene (64%), and films, fragments, and filaments of a variable percentage of polyethylene and polypropylene. Differences found in the polymer composition amongst plastics´ morphologies are reflected in the variability observed between habitats and marine organisms. Particularly the polymer composition of fibers coincides with that of one of the MPs ingested by invertebrates. Results suggest that shape is a key plastic characteristic in determining polymer distribution patterns along with habitats and in marine species. Finally, this study highlights once again the importance and urgency of local and global actions needed to mitigate plastic pollution and particularly fiber release into the marine environment

Multispecies Assessment of Anthropogenic Particle Ingestion in a Marine Protected Area

We have applied a multispecies ecosystem approach to analyse the ingestion of anthropogenic particles (AP) in the gastrointestinal tract of 313 individuals (17 fish species and 8 invertebrate species) from pelagic, demersal and benthic habitats in a marine protected area off the Western Mediterranean (Cabrera National Park). We have quantified and characterized the ingestion at several taxonomic levels of fish, sea urchins, sea cucumbers, bivalves, and jellyfish in relation to biotic/abiotic factors based on taxonomic groups, trophic guilds (functional groups) and habitats. AP ingestion occurrence ranged from 26 to 100% with no significant differences among taxonomic groups. The fish within the MPA showed an overall ingestion occurrence ranging from 0 to 100%, the echinoderms from 29 to 100%, the bivalves from 72 to 96% and the jellyfish 36% ingestion. The ecosystem approach applied to evaluate overall AP ingestion within the species reported that for trophic guilds, the omnivorous species ingested the highest amounts of anthropogenic items, while herbivores ingested significantly fewer items than all other trophic guilds. Moreover, no significant differences were found amongst habitats, indicating a homogeneous spatial distribution of APs at all studied habitats. The multispecies approach provided insight into the high APs exposure to species within Cabrera MPA, highlighting the potential harm linked with marine litter that threatens marine biodiversity.En prensa5,82