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We study predictive control in a setting where the dynamics are time-varying and linear, and the costs are time-varying and well-conditioned. At each time step, the controller receives the exact predictions of costs, dynamics, and disturbances for the future k time steps. We show that when the prediction window k is sufficiently large, predictive control is input-to-state stable and achieves a dynamic regret of O(λkT), where λ<1 is a positive constant. This is the first dynamic regret bound on the predictive control of linear time-varying systems. We also show a variation of predictive control obtains the first competitive bound for the control of linear time-varying systems: 1+O(λk). Our results are derived using a novel proof framework based on a perturbation bound that characterizes how a small change to the system parameters impacts the optimal trajectory. 

The efficacy of paclitaxel (PTX) is limited due to its poor solubility, poor bioavailability, and acquired drug resistance mechanisms. Designing paclitaxel prodrugs can improve its anticancer activity and enable formulation of nanoparticles. Overall, the aim of this work is to improve the potency of paclitaxel with prodrug synthesis, nanoparticle formation, and synergistic formulation with lapatinib. Specifically, we improve potency of paclitaxel by conjugating it to α-tocopherol (vitamin E) to produce a hydrophobic prodrug (Pro); this increase in potency is indicated by the 8-fold decrease in half maximal inhibitory concentration (IC50) concentration in ovarian cancer cell line, OVCA-432, used as a model system. The efficacy of the paclitaxel prodrug was further enhanced by encapsulation into pH-labile nanoparticles using Flash NanoPrecipitation (FNP), a rapid, polymer directed self-assembly method. There was an 1100-fold decrease in IC50 concentration upon formulating the prodrug into nanoparticles. Notably, the prodrug formulations were 5-fold more potent than paclitaxel nanoparticles. Finally, the cytotoxic effects were further enhanced by co-encapsulating the prodrug with lapatinib (LAP). Formulating the drug combination resulted in synergistic interactions as indicated by the combination index (CI) of 0.51. Overall, these results demonstrate this prodrug combined with nanoparticle formulation and combination therapy is a promising approach for enhancing paclitaxel potency. 

Taxol, a formulation of paclitaxel (PTX), is one of the most widely used anticancer drugs, particularly for treating recurring ovarian carcinomas following surgery. Clinically, PTX is used in combination with other drugs such as lapatinib (LAP) to increase treatment efficacy. Delivering drug combinations with nanoparticles has the potential to improve chemotherapy outcomes. In this study, we use Flash NanoPrecipitation, a rapid, scalable process to encapsulate weakly hydrophobic drugs (logP < 6) PTX and LAP into polymer nanoparticles with a coordination complex of tannic acid and iron formed during the mixing process. We determine the formulation parameters required to achieve uniform nanoparticles and evaluate the drug release in vitro. The size of the resulting nanoparticles was stable at pH 7.4, facilitating sustained drug release via first-order Fickian diffusion. Encapsulating either PTX or LAP into nanoparticles increases drug potency (as indicated by the decrease in IC-50 concentration); we observe a 1500-fold increase in PTX potency and a six-fold increase in LAP potency. When PTX and LAP are co-loaded in the same nanoparticle, they have a synergistic effect that is greater than treating with two single-drug-loaded nanoparticles as the combination index is 0.23 compared to 0.40, respectively.