A method for reducing controllers for systems described by partial differential equations (PDEs) is applied to Burgers' equation with periodic boundary conditions. This approach differs from the typical approach of reducing the model and then designing the controller, and has developed over the past several years into its current form. In earlier work it was shown that functional gains for the feedback control law served well as a dataset for reduced order basis generation via the proper orthogonal...

The paper applies the pseudo-linear algebra to unify the results on reducibility, reduction and transfer equivalence for continuous- and discrete-time nonlinear control systems. The necessary and sufficient condition for reducibility of nonlinear input-output equation is presented in terms of the greatest common left factor of two polynomials describing the behaviour of the ‘tangent linearized system’ equation. The procedure is given to find the reduced (irreducible) system equation that is transfer...

Fuzzy logic controller performance depends on the fuzzy control rule set. This set can be obtained either by an expert or from a learning algorithm through a set of examples. Recently, we have developed SLAVE an inductive learning algorithm capable of identifying fuzzy systems. The refinement of the rules proposed by SLAVE (or by an expert) can be very important in order to improve the accuracy of the model and in order to simplify the description of the system. The refinement algorithm is based...

In this paper we review the concept of regional boundary observability, developed in (Michelitti, 1976), by means of sensor structures. This leads to the so-called boundary strategic sensors. A characterization of such sensors which guarantees regional boundary observability is given. The results obtained are applied to a two-dimensional system, and various cases of sensors are considered. We also describe an approach which leads to the estimation of the initial boundary state, which is illustrated...

The purpose of this paper is to study the problem of regional detection, to characterize internal or boundary regionally detectable sources and regionally spy sensors, and to establish a relationship between these sensors and regionally strategic sensors. It is shown how to reconstruct a regionally detectable internal or a boundary source from a given output, with an extension to the case when the output is affected by an observation error. Numerical results are given in the case of a diffusion...

The purpose of this short paper is to provide original results related to the choice of the number of sensors and their supports for general distributed parameter systems. We introduce the notion of extended sensors and we show that the observation error decreases when the support of a sensor is widened. We also show that the observation error decreases when the number of sensors increases.

In this paper we analyze several concepts of solution to discontinuous ODEs in relation to feedbacks generated by optimal syntheses. Optimal trajectories are called Stratified Solutions in case of regular synthesis in the sense of Boltyanskii–Brunovsky. We introduce a concept of solution called Krasowskii Cone Robust that characterizes optimal trajectories for minimum time on the plane and for general problems under suitable assumptions.

In this paper we analyze several concepts of solution to discontinuous ODEs in relation to feedbacks generated by optimal syntheses. Optimal trajectories are called Stratified Solutions in case of regular synthesis in the sense of Boltyanskii-Brunovsky. We introduce a concept of solution called Krasowskii Cone Robust that characterizes optimal trajectories for minimum time on the plane and for general problems under suitable assumptions.

The regularity of solutions of various dynamical equations (wave, Euler-Bernoulli, Kirchhoff, Schrödinger) in a bounded open domain $\mathrm{\Omega }$ in ${\mathbb{R}}^N$, subject to the action of a point control at some point of $\mathrm{\Omega }$, is studied. Detailed proofs of the results are contained in the references [8-10].

Ionizing radiation activates a large variety of intracellular mechanisms responsible for maintaining appropriate cell functionality or activation of apoptosis which eliminates damaged cells from the population. The mechanism of such induced cellular death is widely used in radiotherapy in order to eliminate cancer cells, although in some cases it is highly limited by increased cellular radio-resistance due to aberrations in molecular regulation mechanisms of malignant cells. Despite the positive...

Performance evaluation of classifiers is a crucial step for selecting the best classifier or the best set of parameters for a classifier. Receiver Operating Characteristic (ROC) curves and Area Under the ROC Curve (AUC) are widely used to analyse performance of a classifier. However, the approach does not take into account that misclassification for different classes might have more or less serious consequences. On the other hand, it is often difficult to specify exactly the consequences or costs...

This paper proposes new stability conditions for interval type-2 fuzzy-model-based (FMB) control systems. The type-1 T-S fuzzy model has been widely studied because it can represent a wide class of nonlinear systems. Many favorable results for type-1 T-S fuzzy model have been reported. However, most of conclusions for type-1 T-S fuzzy model can not be applied to nonlinear systems subject to parameter uncertainties. In fact, Most of the practical applications are subject to parameters uncertainties....

This paper is devoted to path planning when the safety of the system considered has to be guaranteed in the presence of bounded uncertainty affecting its model. A new path planner addresses this problem by combining Rapidly-exploring Random Trees (RRT) and a set representation of uncertain states. An idealized algorithm is presented first, before a description of one of its possible implementations, where compact sets are wrapped into boxes. The resulting path planner is then used for nonholonomic...

The problem of energy transfer in an -ladder network is considered. Using the maximum principle, an algorithm for constructing optimal control is proposed, where the cost function is the energy delivered to the network. In the case considered, optimal control exists. Numerical simulations were performed using Matlab.

We study the local exact controllability problem for the Navier-Stokes equations that describe an incompressible fluid flow in a bounded domain $\Omega$ with control distributed in a subdomain $\omega \subset \Omega \subset {ℝ}^n,n\in \{2,3\}$. The result that we obtained in this paper is as follows. Suppose that $\widehat{v}(t,x)$ is a given solution of the Navier-Stokes equations. Let $v_0\left(x\right)$ be a given initial condition and $\parallel \widehat{v}(0,·)-v_0\parallel \<\epsilon$ where $\epsilon$ is small enough. Then there exists a locally distributed control $u,\text{supp}u\subset (0,T)\times \omega$ such that the solution $v(t,x)$ of the Navier-Stokes equations:$${\partial }_{t}v-\Delta v+(v,\nabla )v=\nabla p+u+f,\text{div}v=0,v{{|}_{\partial \Omega }=0,v|}_{t=0}=v_0$$coincides with...

We study the local exact controllability problem for the Navier-Stokes equations that describe an incompressible fluid flow in a bounded domain Ω with control distributed in a subdomain $\omega \subset \Omega \subset {ℝ}^n,n\in \{2,3\}$. The result that we obtained in this paper is as follows. Suppose that $\widehat{v}(t,x)$ is a given solution of the Navier-Stokes equations. Let $v_0\left(x\right)$ be a given initial condition and $\parallel \widehat{v}(0,·)-v_0\parallel <\epsilon$ where ε is small enough. Then there exists a locally distributed control $u,\text{supp}u\subset (0,T)\times \omega$ such that the solution v(t,x) of the Navier-Stokes equations: $${\partial }_{t}v-\Delta v+(v,\nabla )v=\nabla p+u+f,\text{div}v=0,v{{|}_{\partial \Omega }=0,v|}_{t=0}=v_0$$ coincides...