Pulse-modulated feedback control of nonlinear infinite-dimensional positive systems

Impulsive regulation of infinite-dimensional nonlinear positive plants to a pre-defined periodic solution is studied in this project.

To ensure fast convergence of the controlled output to the desired stationary trajectory, pulse-modulated feedback is implemented.

The continuous plant output measurement modulates the frequency and weights of the instantaneous impulses that impact the plant input.

Continuous Volterra series are employed to model the plant dynamics since they readily account for smooth nonlinearity through multidimensional convolution and allow explicit introduction of pointwise and distributed delays in the convolution kernels.

The resulting closed-loop dynamics are non-smooth and highly nonlinear thus requiring advanced tools for analysis and design. Control of biomedical systems is envisioned as the main application area of the developed control methodology.

Indeed, dynamical models in life sciences are typically positive, essentially nonlinear as well as incorporate infinite-dimensional blocks, such as pointwise and distributed time delays.

To exemplify the theoretical concepts, the proposed research program envisions the development of feedback drug dosing algorithms.

Administration of anesthetic drugs in neuromuscular blockade and general anesthesia are to be addressed in collaboration with a clinical research team in intensive care.