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This paper proposes Runge-Kutta neural disturbance observer to enhance the robustness of PID control of a system with general multicompartment lung mechanics. It is designed to observe the states of a particular type continous time, single-input single-output system where the states cannot be measured but can be observed through the single output and there exists parametric uncertainity or disturbance affecting the underlying system. It utilizes artificial neural network to estimate the disturbance online. Once an accurate disturbance estimation is obtained, it is incorporated in the system state equation and passed through the well-known Runge-Kutta integrator to predict the state values. Hence, the predicted states are obtained considering the disturbance and more robust state observation is achieved. The proposed observer is simple and easy to implement. Adaptation of the neural network is performed using gradient descent with an adaptive learning rate which guarantees convergence. The simulation results demonstrate that the proposed observer gains a significant success in enhancing the robustness of PID control at even high level of disturbance. Note that, multicompartment lung mechanics system is a stand-in model that can mimic the behavior of human lung. Thus, it is appropriate for hardware-in-the-loop simulation which opens a path to the real-patient-tests of mechanical respiratory systems in the future. Copyright (C) 2020 The Authors.

Hemodialysis (HD) is nowadays the most common therapy to treat renal insufficiency. However, despite the improvements made in the last years, HD is still associated with a non-negligible rate of co-morbidities, which could be reduced by means of an appropriate treatment customization. Many differential multi-compartment models have been developed to describe solute kinetics during HD, to optimize treatments, and to prevent intra-dialysis complications; however, they often refer to an average uremic patient. On the contrary, the clinical need for customization requires patient-specific models. In this work, assuming that the customization can be obtained by means of patient-specific model parameters, we propose a Bayesian approach to estimate the patient-specific parameters of a multi-compartment model and to predict the single patient's response to the treatment, in order to prevent intra-dialysis complications. The likelihood function is obtained through a discretized version of a multi-compartment model, where the discretization is in terms of a Runge-Kutta method to guarantee the convergence, and the posterior densities of model parameters are obtained through Markov Chain Monte Carlo simulation.

A numerical method is presented for Runge-Kutta discretization of unconstrained optimal control problems. First, general Runge-Kutta discretization is carried out to obtain a finite-dimensional approximation of the continous-time optimal control problem. Then a recent optimization technique, the inexact restoration (IR) method, due to Martinez and coworkers [E. G. Birgin and J. M. Martinez, J. Optim. Theory Appl., 127 (2005), pp. 229-247; J. M. Martinez and E. A. Pilotta, J. Optim. Theory Appl., 104 (2000), pp. 135-163; J. M. Martinez, J. Optim. Theory Appl., 111 (2001), pp. 39-58], is applied to the discretized problem to find an approximate solution. It is proved that, for optimal control problems, a key sufficiency condition for convergence of the IR method is readily satisfied. Under reasonable assumptions, the IR method for optimal control problems is shown to converge to a solution of the discretized problem. Convergence of a solution of the discretized problem to a solution of the continuous-time problem is also shown. It turns out that optimality phase equations of the IR method emanate from an associated Hamiltonian system, and so general Runge-Kutta discretization induces a symplectic partitioned Runge-Kutta scheme. A computational algorithm is described, and numerical experiments are made to demonstrate the working of the method for optimal control of the van der Pol system, employing the three-stage (order 6) Gauss-Legendre discretization.