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1. Invariant set theory for predicting potential failure of antibiotic cycling

   https://doi.org/10.1016/j.idm.2025.04.001  

   Anderson, Alejandro; Kinahan, Matthew W; Gonzalez, Alejandro H; Udekwu, Klas; Hernandez-Vargas, Esteban A (September 2025, Infectious Disease Modelling)

   Collateral sensitivity, where resistance to one drug confers heightened sensitivity to another, offers a promising strategy for combating antimicrobial resistance, yet predicting resultant evolutionary dynamics remains a significant challenge. We propose here a mathematical model that integrates fitness trade-offs and adaptive landscapes to predict the evolution of collateral sensitivity pathways, providing insights into optimizing sequential drug therapies. Our approach embeds collateral information into a network of switched systems, allowing us to abstract the effects of sequential antibiotic exposure on antimicrobial resistance. We analyze the system stability at disease-free equilibrium and employ set-control theory to tailor therapeutic windows. Consequently, we propose a computational algorithm to identify effective sequential therapies to counter antibiotic resistance. By leveraging our theory with data on collateral sensivity interactions, we predict scenarios that may prevent bacterial escape for chronic Pseudomonas aeruginosa infections. 

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2. Computing controlled invariant sets in two moves

   https://doi.org/10.1109/CDC40024.2019.9029610  

   Anevlavis, Tzanis; Tabuada, Paulo (December 2019, 2019 IEEE 58th Conference on Decision and Control (CDC))

   null (Ed.)

   In this paper we revisit the problem of computing controlled invariant sets for controllable discrete-time linear systems. We propose a novel algorithm that does not rely on iterative computations. Instead, controlled invariant sets are computed in two moves: 1) we lift the problem to a higher dimensional space where a controlled invariant set is computed in closed-form; 2) we project the resulting set back to the original domain to obtain the desired controlled invariant set. One of the advantages of the proposed method is the ability to handle larger systems. 

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3. A Switched Systems Approach Based on Changing Muscle Geometry of the Biceps Brachii During Functional Electrical Stimulation

   https://doi.org/10.1109/LCSYS.2017.2734060  

   Rouse, Courtney A.; Duenas, Victor H.; Cousin, Christian; Parikh, Anup; Dixon, Warren E. (January 2018, IEEE Control Systems Letters)

   Functional electrical stimulation (FES) is commonly used for people with neurological conditions. As the muscle geometry changes (i.e., muscle lengthening/ shortening), the force induced by static electrode placement may also change. Experimental results indicate that muscle forces can be increased by spatially switching stimulation as the muscle geometry changes with joint angle. In this letter, an electric field is switched between multiple electrodes placed across the biceps brachii to track a desired trajectory. A switched systems approach is used to develop a position-based switching law, including a switched robust sliding mode controller that successfully tracks the desired angular trajectory about the elbow, despite changes in muscle geometry. Lyapunovbased methods for switched systems are used to prove global exponential tracking. Experimental results from nine able-bodied subjects are presented and the developed control system achieves an average position and velocity error of −0.21 ± 1.17 deg and −0.43 ± 5.38 deg/s, respectively, and, on average, reduces fatigue by 13.6%, as compared to traditional single-electrode methods, demonstrating the performance of the uncertain nonlinear switched control system. 

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4. Polynomial Chaos-Based Controller Design for Uncertain Linear Systems With State and Control Constraints

   https://doi.org/10.1115/1.4038800  

   Nandi, Souransu; Migeon, Victor; Singh, Tarunraj; Singla, Puneet (July 2018, Journal of Dynamic Systems, Measurement, and Control)

   For linear dynamic systems with uncertain parameters, design of controllers which drive a system from an initial condition to a desired final state, limited by state constraints during the transition is a nontrivial problem. This paper presents a methodology to design a state constrained controller, which is robust to time invariant uncertain variables. Polynomial chaos (PC) expansion, a spectral expansion, is used to parameterize the uncertain variables permitting the evolution of the uncertain states to be written as a polynomial function of the uncertain variables. The coefficients of the truncated PC expansion are determined using the Galerkin projection resulting in a set of deterministic equations. A transformation of PC polynomial space to the Bernstein polynomial space permits determination of bounds on the evolving states of interest. Linear programming (LP) is then used on the deterministic set of equations with constraints on the bounds of the states to determine the controller. Numerical examples are used to illustrate the benefit of the proposed technique for the design of a rest-to-rest controller subject to deformation constraints and which are robust to uncertainties in the stiffness coefficient for the benchmark spring-mass-damper system. 

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5. Strategy synthesis for partially-known switched stochastic systems

   https://doi.org/10.1145/3447928.3456649  

   Jackson, John; Laurenti, Luca; Frew, Eric; Lahijanian, Morteza (May 2021, The 24th International Conference on Hybrid Systems: Computation and Control)

   null (Ed.)

   We present a data-driven framework for strategy synthesis for partially-known switched stochastic systems. The properties of the system are specified using linear temporal logic (LTL) over finite traces (LTLf), which is as expressive as LTL and enables interpretations over finite behaviors. The framework first learns the unknown dynamics via Gaussian process regression. Then, it builds a formal abstraction of the switched system in terms of an uncertain Markov model, namely an Interval Markov Decision Process (IMDP), by accounting for both the stochastic behavior of the system and the uncertainty in the learning step. Then, we synthesize a strategy on the resulting IMDP that maximizes the satisfaction probability of the LTLf specification and is robust against all the uncertainties in the abstraction. This strategy is then refined into a switching strategy for the original stochastic system. We show that this strategy is near-optimal and provide a bound on its distance (error) to the optimal strategy. We experimentally validate our framework on various case studies, including both linear and non-linear switched stochastic systems. 

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