(170c) Effective Dose Delivery in Plasma Medicine Using a Robust MPC Approach for Mixed Stochastic and Deterministic Uncertainty

Cold atmospheric plasma (CAP) is a weakly ionized gas generated in ambient conditions via application of modulated electric field to gases such as helium, argon, and air. CAPs have recently gained increasing attention for treatment of heat and pressure sensitive (bio)materials in surface etching/functionalization, environmental, and biomedical applications [1,2]. An attractive feature of CAPs is that they are non-thermal plasma discharges, that is, the electrons have a high temperature (∼10,000 K) while the temperature of the background gas remains near to room temperature. The high-temperature, energetic electrons in a CAP discharge can generate reactive chemical species through a plethora of excitation and chemical reactions with the background gas and species diffusing in from the ambient air. The reactive chemical species, along with other plasma effects such as UV photons, thermal energy, and electric fields have been postulated to induce therapeutic effects such as tissue disinfection, healing of chronic wounds, shrinkage of cancerous tumors, and regulation of multidrug resistant bacteria [2].

The notion of plasma medicine generally relies on evoking a desired response in a living system through the delivery of a multitude of plasma effects. The highly nonlinear, spatially distributed dynamics of CAP discharges, the cumulative (i.e., “non-retractable”) response of a living system to plasma effects, and the development of instabilities and plasma mode transitions to arc or spark due to variations in plasma properties are some of the key challenges to safe, consistent, and effective dose delivery in plasma medicine. Recently, we have demonstrated the promise of model predictive control (MPC) for effective dose delivery in atmospheric pressure plasma jets (APPJs) [3,4]. APPJs have been identified as a promising class of CAP discharges for plasma medicine due to their operational flexibility and versatile discharge chemistry [2]. A key challenge in applying MPC to APPJs arises from uncertain knowledge of the plasma behavior, which is intrinsically stochastic. Incomplete representations of the complex plasma dynamics can lead to inadequate system models for the use in MPC, possibly affecting the MPC performance for dose delivery. In addition, unmeasured system disturbances, which are typically ubiquitous in APPJ applications, cannot be systematically handled in the standard MPC framework, possibly compromising the safety, consistency, and efficacy of the plasma dose delivery.

In this work, we will first present a robust MPC method for offset-free tracking of piece-wise constant references in the presence of bounded deterministic and stochastic uncertainty [5]. The deterministic uncertainty source accounts for the unknown structural/parametric plant-model mismatch (i.e., incomplete knowledge of the plasma dynamics), whereas the stochastic uncertainty source represents exogenous system disturbances (e.g., random variations in properties of the target substrate in an APPJ application). Concepts from robust tube-based and stochastic tube-based MPC [6,7] will be used to derive a tractable MPC formulation, with computational complexity comparable to that of nominal MPC. We will then adopt the proposed robust MPC method for plasma dose delivery in a kilo-hertz APPJ in helium, which is a prototypical medical therapy device. The performance of the robust MPC method for consistent and effective dose delivery in the presence of plant-model mismatch and disturbances will be demonstrated using extensive simulation results performed on a nonlinear APPJ simulator developed in COMSOL.

References

[1] P. Chu, J. Chen, L. Wang, and N. Huang, Plasma-surface modification of biomaterials, Materials Science and Engineering: Reports, 36,143-206, 2002.

[2] M. Laroussi, M. Kong, G. Morfill, and W. Stolz, Plasma Medicine. New York, NY: Cambridge University Press, 2012.

[3] D. Gidon, D.B. Graves, and A. Mesbah, Model predictive control of thermal effects of an atmospheric pressure plasma jet for biomedical applications, In Proc. ACC, 4889-4894, 2016.

[4] D. Gidon, D.B. Graves, and A. Mesbah, Effective dose delivery in atmospheric pressure plasma jets for plasma medicine: A model predictive control approach, Plasma Sources Science and Technology, Under review, 2017.

[5] J.A. Paulson, L. Xie, and A. Mesbah, Robust offset-free MPC of systems with mixed stochastic and deterministic uncertainty. In Proceedings of the IFAC World Congress, 2017, Toulouse.

[6] D.Q. Mayne, M.M. Seron, and S.V. Rakovic, Robust MPC of constrained linear systems with bounded disturbances. Automatica, 41, 219–224, 2005.

[7] B. Kouvaritakis, M. Cannon, S.V. Rakovic, and Q. Cheng, Explicit use of probabilistic distributions in linear predictive control. Automatica, 46, 1719–1724, 2010.