In this paper we consider three-tank system as a hybrid system with discrete (on/off) valves and then we use Hybrid System’s Description Language to acquire a Mixed Logical Dynamical model of the system. In order to obtain a relatively accurate model of three-tank system, instead of using straight line approximation method for linearization of valves in whole space, we use Piecewise Affine meth...

We introduce a mixed integer linear modeling approach for the optimization of dynamic transport networks based on the piecewise linearization of nonlinear constraints and we show how to apply this method by two examples, transient gas and water supply network optimization. We state the mixed integer linear programs for both cases and provide numerical evidence for their suitability.

This paper presents a new method for constructing onedimensional electrical conductivity models of the Earth from surface electromagnetic measurements. The construction of these models is a nonlinear inverse problem that can be approached by linearization techniques combined with iterative methods and Tikhonov’s regularization. The standard application of these techniques usually leads to smoot...

In this work, the issue of estimation reachable sets in continuous bimodal piecewise affine systems is studied. A new method proposed, framework ellipsoidal bounding, using quadratic Lyapunov functions. Although can be seen as a special class hybrid systems, reachability methods developed for might inappropriately complex dynamics. This work goes direction exploiting dynamical structure system ...

This paper proposes a servo control system based on a minimal-order state observer for nonlinear systems approximated by piecewise bilinear (PB) models. The design method is capable of designing the state observer and the servo controller of nonlinear systems separately. The approximated system is found to be fully parametric. The input-output (I/O) feedback linearization is applied to stabiliz...

Due to the inherent nonlinear nature of real world systems, one of the most popular ways to deal with nonlinear systems is to find a feedback linearizing input and then deal with the system by using the rich literature on linear control methods. As an alternative, the nonlinear terms in the system model can be piecewise linearized and then the system can be controlled by using various linear co...

This paper deals a tracking trajectory controller design of a tricycle robot as a non-holonomic system with a piecewise multi-linear (PML) model. The approximated model is fully parametric. Input-output (I/O) dynamic feedback linearization is applied to stabilize PML control system. We also apply a method for a tracking control based on PML models to the tricycle robot. Although the controller ...

We present an overview on piecewise linearization methods for MINLPs. This will include the concept of disjunctive constraints, which is necessary to define logarithmic reformulations of the so called disaggregated convex combination method and the convex combination method. For the case of a general univariate quadratic function we also calculate the linearization error and proof that equidist...

One of the commonly used techniques for tackling nonconvex optimization problems in which all nonlinear terms are univariate is piecewise linear approximation by reformulated. The performance linearization technique primarily depends on quantities variables and constraints required formulation a function. state-of-the-art method introduces $$2\lceil \log _2 m\rceil$$ inequality constraints, whe...

This paper centres on the application of the new piecewise successive linearization method PSLM in solving the chaotic and nonchaotic Chen system. Numerical simulations are presented graphically and comparison is made between the PSLM and Runge-Kutta-based methods. The work shows that the proposed method provides good accuracy and can be easily extended to other dynamical systems including thos...