Title :
Monotone Piecewise Affine Systems
Author :
Aswani, Anil ; Tomlin, Claire
Author_Institution :
Dept. of Electr. Eng. & Comput. Sci., Univ. of California, Berkeley, CA, USA
Abstract :
Piecewise affine (PWA) systems are autonomous systems with discontinuous vector fields which are affine ordinary differential equations at the points of continuity. These systems have applications to many fields of engineering, including systems biology and traffic engineering. We define what it means for a PWA system to be monotone, and we provide a set of sufficient conditions for monotonicity of PWA systems with hyperrectangular invariants. Such sufficient conditions are useful for understanding the dynamics of such PWA systems and for designing controllers for qualitative, reference tracking. We apply these results towards the drug-discovery problem for the cancer-related p53 pathway.
Keywords :
affine transforms; control system synthesis; differential equations; piecewise linear techniques; vectors; affine ordinary differential equations; autonomous systems; cancer-related p53 pathway; designing controllers; discontinuous vector fields; drug-discovery problem; hyperrectangular invariants; monotone piecewise affine systems; reference tracking; sufficient conditions; systems biology; traffic engineering; Control systems; Differential equations; Drugs; Genetics; Multirobot systems; Stability; Sufficient conditions; Systems biology; Systems engineering and theory; Monotone systems; piecewise affine systems; systems biology;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2009.2023771
