Robust Positively Invariant Cylinders in Constrained Variable Structure Control

This paper proposes the use of cylinders as primary invariant sets to be used in certain state-constrained control designs. Following the idea originally introduced by O\u27Dell, the primary invariant set is intersected with the state constraints to yield sets which retain the invariance under some conditions. Although several results presented here apply to fairly general nonlinear systems and primary invariant sets of any shape, the focus is on constrained sliding-mode control (SMC) using infinite cylinders as the primary invariant set. Their use is motivated by a coordinate transformation where the sliding motion is decoupled from the overall convergence to the origin. Robust positive invariance conditions are given for cylinders having convex and compact cross sections. For the case of cylinders with ellipsoidal cross sections, the invariance condition is given in the form of a linear matrix inequality. Further, a decision procedure to qualify each state constraint is given as a tool for the selection of the switching gain. A numerical example for a third-order plant illustrates the method

Robust Positively Invariant Cylinders in Constrained Variable Structure Control

This paper proposes the use of cylinders as primary invariant sets to be used in certain state-constrained control designs. Following the idea originally introduced by O\u27Dell, the primary invariant set is intersected with the state constraints to yield sets which retain the invariance under some conditions. Although several results presented here apply to fairly general nonlinear systems and primary invariant sets of any shape, the focus is on constrained sliding-mode control (SMC) using infinite cylinders as the primary invariant set. Their use is motivated by a coordinate transformation where the sliding motion is decoupled from the overall convergence to the origin. Robust positive invariance conditions are given for cylinders having convex and compact cross sections. For the case of cylinders with ellipsoidal cross sections, the invariance condition is given in the form of a linear matrix inequality. Further, a decision procedure to qualify each state constraint is given as a tool for the selection of the switching gain. A numerical example for a third-order plant illustrates the method

Impacts of colonial waterbirds on vegetation and potential restoration of island habitats

Colonial waterbirds have impacted forested island ecosystems throughout their breeding range, changing vegetation, and soil characteristics and bird communities. Our objectives were to (1) determine effects of three levels of colonial waterbird exclusion on overall vegetation diversity and growth, and survival of a candidate restoration species (black elderberry; Sambucus nigra canadensis); (2) investigate effects of different planting techniques on survival and growth of black elderberry; and (3) determine effects of waterbird colonization on soil chemistry. In 2012, we investigated effects of three levels of waterbird exclusion (none control plots [CON]; partial, which excluded waterbirds larger than gulls [PEX]; and full which excluded all waterbirds [FEX]) on bird use, existing vegetation growth and diversity, and survival of planted black elderberry on three islands in Door County, WI, Lake Michigan. In 2013, we evaluated survival of black elderberry established with four planting treatments within three waterbird exclusion treatments on two islands in 2013.We also compared soil chemistry characteristics between islands with and without nesting waterbirds for 2 years. Overall plant growth was greater in exclosures, but elderberry survival was similar among treatments. Soil replacement and weed suppression planting treatments did not affect survival, but generally increased overall elderberry biomass. Soil from nesting islands was more acidic and had greater nutrient concentrations than reference islands. Exclusion or removal of colonial nesting waterbirds from islands may improve overall vegetation growth, but successful restoration of woody vegetation may require significant soil manipulation and planting

Impacts of colonial waterbirds on vegetation and potential restoration of island habitats

Colonial waterbirds have impacted forested island ecosystems throughout their breeding range, changing vegetation, and soil characteristics and bird communities. Our objectives were to (1) determine effects of three levels of colonial waterbird exclusion on overall vegetation diversity and growth, and survival of a candidate restoration species (black elderberry; Sambucus nigra canadensis); (2) investigate effects of different planting techniques on survival and growth of black elderberry; and (3) determine effects of waterbird colonization on soil chemistry. In 2012, we investigated effects of three levels of waterbird exclusion (none control plots [CON]; partial, which excluded waterbirds larger than gulls [PEX]; and full which excluded all waterbirds [FEX]) on bird use, existing vegetation growth and diversity, and survival of planted black elderberry on three islands in Door County, WI, Lake Michigan. In 2013, we evaluated survival of black elderberry established with four planting treatments within three waterbird exclusion treatments on two islands in 2013.We also compared soil chemistry characteristics between islands with and without nesting waterbirds for 2 years. Overall plant growth was greater in exclosures, but elderberry survival was similar among treatments. Soil replacement and weed suppression planting treatments did not affect survival, but generally increased overall elderberry biomass. Soil from nesting islands was more acidic and had greater nutrient concentrations than reference islands. Exclusion or removal of colonial nesting waterbirds from islands may improve overall vegetation growth, but successful restoration of woody vegetation may require significant soil manipulation and planting