This article addresses the design of therapeutic procedures for cancer using a control based on the Gompertz model, that describes the nonlinear dynamics of tumor growth. The aim is to reduce the tumor size according to a decreasing target reference. The approach presented on this work uses a control Lyapunov function and yields an adaptive PI strategy that results from the exact linearization....

This note investigates the problem of plasma glucose regulation by means of subcutaneous insulin administration. A discrete delay differential equation model of the glucoseinsulin regulatory system has been considered, which properly takes into account also the pancreatic insulin release, in such a way to allow insulin therapies for both Type I and Type II diabetes (in this latter case the endo...

Quantum mechanics abounds in models with Hamiltonian operators which are energy-dependent. A linearization of the underlying Schrödinger equation with H = H(E) is proposed here via an introduction of a doublet of separate energyindependent representatives K and L of the respective right and left action of H(E). Both these new operators are non-Hermitian so that our formalism admits a natural ex...

In this paper some adaptive nonlinear multivariable techniques used in the control of robotic manipulators are presented. The nonlinear control law and state feedback are used in achieving a linear inputoutput behavior for the controlled system. For the design of the adaptive nonlinear control, the exact feedback input-output linearization and the method of gradient are used. The nonlinear cont...

The paper presents a new control method which achieves autonomous obstacle avoidance for manipulators with rate constraints. More precisely, in order to achieve the autonomous obstacle avoidance, we exploit the freedom of the coordinate transformation for exact linearization of nonlinear systems. At the same time, we cope with the rate constraints by adopting the statedependent time scale trans...

We consider the maximum feasible subsystem problem in which, given an infeasible system of linear inequalities, one wishes to determine a largest feasible subsystem. The focus is on the version with bounded variables that naturally arises in several fields of application. To tackle this NP-hard problem, we propose a simple but efficient two-phase relaxation-based heuristic. First a feasible sub...

According to nonlinear operation of STATCOM, nonlinear controller has a better performance in comparison with linear controller. Regulating the DC capacitor voltage in STATCOM is a common task and can improve the system dynamic. The nonlinear control is based on exact linearization via feedback. A PI controller exists in this control system to regulate the capacitor voltage. In conventional sch...

This paper addresses the problem of stabilization non-minimum phase switched nonlinear systems where internal dynamics with symmetries or non-symmetries each mode may be unstable. The authors initially build a stabilizing Lyapunov controller for in order to stabilize its own unstable dynamics. proposed approach is based on exact input-output feedback linearization technique and stability theory...

This paper studies polyhedral methods for the quadratic assignment problem. Bounds on the objective value are obtained using mixed 0–1 linear representations that result from a reformulation–linearization technique (rlt). The rlt provides different “levels” of representations that give increasing strength. Prior studies have shown that even the weakest level-1 form yields very tight bounds, whi...

Accurate solutions of the porous media equation that usually occurs in nonlinear problems of heat and mass transfer and in biological systems are obtained using a compact finite difference method in space and a low-storage total variation diminishing third-order Runge-Kutta scheme in time. In the calculation of the numerical derivatives, only a tridiagonal band matrix algorithm is encountered. ...