This paper is devoted to exploring personalized applications of cellular immunotherapy as a control strategy for the treatment of chronic myelogenous leukemia described by a dynamical system of three first-order ordinary differential equations. The latter was achieved by applying both the Localization of Compact Invariant Sets and Lyapunov’s stability theory. Combination of these two approaches allows us to establish sufficient conditions on the immunotherapy treatment parameter to ensure the complete eradication of the leukemia cancer cells. These conditions are given in terms of the system parameters and by performing several in silico experimentations, we formulated a protocol for the therapy application that completely eradicates the leukemia cancer cells population for different initial tumour concentrations. The formulated protocol does not dangerously increase the effector T cells population. Further, complete eradication is considered when solutions go below a finite critical value below which cancer cells cannot longer persist; i.e., one cancer cell. Numerical simulations are consistent with our analytical results.

In this paper, we explore the application of Chimeric Antigen Receptor (CAR) T cell therapy for the treatment of Acute Lymphocytic Leukaemia (ALL) by means of in silico experimentation, mathematical modelling through first-order Ordinary Differential Equations and nonlinear systems theory. By combining the latter with systems biology on cancer evolution we were able to establish a sufficient condition on the therapy dose to ensure complete response. The latter is illustrated across multiple numerical simulations when comparing three mathematically formulated administration protocols with one of a phase 1 dose-escalation trial on CAR-T cells for the treatment of ALL on children and young adults. Therefore, both our analytical and in silico results are consistent with real-life scenarios. Finally, our research indicates that tumour cells growth rate and the killing efficacy of the therapy are key factors in the designing of personalised strategies for cancer treatment.

Hyperchaotic systems have applications in multiple areas of science and engineering. The study and development of these type of systems helps to solve diverse problems related to encryption and decryption of information. In order to solve the chaos synchronization problem for a hyperchaotic Lorenz-type system, we propose an observer based synchronization under a master-slave configuration. The proposed methodology consists of designing a sliding-mode observer (SMO) for the hyperchaotic system. In contrast, this type of methodology exhibits high-frequency oscillations, commonly known as chattering. To solve this problem, a fuzzy-based SMO system was designed. Numerical simulations illustrate the effectiveness of the synchronization between the hyperchaotic system obtained and the proposed observer.

Cancer with all its more than 200 variants continues to be a major health problem around the world with nearly 10 million deaths recorded in 2020, and leukemia accounted for more than 300,000 cases according to the Global Cancer Observatory. Although new treatment strategies are currently being developed in several ongoing clinical trials, the high complexity of cancer evolution and its survival mechanisms remain as an open problem that needs to be addressed to further enhanced the application of therapies. In this work, we aim to explore cancer growth, particularly chronic lymphocytic leukemia, under the combined application of CAR-T cells and chlorambucil as a nonlinear dynamical system in the form of first-order Ordinary Differential Equations. Therefore, by means of nonlinear theories, sufficient conditions are established for the eradication of leukemia cells, as well as necessary conditions for the long-term persistence of both CAR-T and cancer cells. Persistence conditions are important in treatment protocol design as these provide a threshold below which the dose will not be enough to produce a cytotoxic effect in the tumour population. In silico experimentations allowed us to design therapy administration protocols to ensure the complete eradication of leukemia cells in the system under study when considering only the infusion of CAR-T cells and for the combined application of chemoimmunotherapy. All results are illustrated through numerical simulations. Further, equations to estimate cytotoxicity of chlorambucil and CAR-T cells to leukemia cancer cells were formulated and thoroughly discussed with a $95\%$ confidence interval for the parameters involved in each formula.

This paper is devoted to designing a sensorless high-speed tracking control for surface-mount permanent-magnet synchronous motors, considering a time-varying load torque. This proposal consists of an extended-state observer interconnected with a PI-compensated controller, considering only the measurement of electrical variables for feedback. First, to design the extended-state observer, a rotary coordinate model of the motor is extended in one state to estimate the load torque and the rotor’s position and speed. Later, the estimations are fedback to a PI-compensated controller to attenuate the time-varying load torques. Our proposed methodology aims to overcome a restriction regarding the solution of the Riccati equation respecting the Lipschitz condition for observer stability analysis. Therefore, a PI-compensated controller described as a closed-loop provides a sensorless scheme. Lyapunov stability analysis is applied to determine sufficient conditions to ensure that the states of the closed-loop system are ultimately bounded, which is one of our main contributions. The proposed observer-based controller scheme deals with unmeasured load torque fluctuations. Furthermore, we carry out high-precision emulations to provide testing scenarios of the permanent-magnet synchronous motor with some challenging load torque magnitudes and behaviors. Finally, we conduct experiments on the Technosoft${}^{\circledR }$ development platform to corroborate the feasibility of the proposed control scheme in a real-world scenario.