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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.