Consistent approximations of the zeno behaviour in affine-type switched dynamic systems

This paper proposes a new theoretic approach to a specific interaction of continuous and discrete dynamics in switched control systems known as a Zeno behaviour. We study executions of switched control systems with affine structure that admit infinitely many discrete transitions on a finite time interval. Although the real world processes do not present the corresponding behaviour, mathematical models of many engineering systems may be Zeno due to the used formal abstraction. We propose two useful approximative approaches to the Zeno dynamics, namely, an analytic technique and a variational description of this phenomenon. A generic trajectory associated with the Zeno dynamics can finally be characterized as a result of a specific projection or/and an optimization procedure applied to the original dynamic model. The obtained analytic and variational techniques provide an effective methodology for constructive approximations of the general Zeno-type behaviour. We also discuss shortly some possible applications of the proposed approximation schemes

People on both sides of the aegean sea

International audienceOur contribution is devoted to a constructive overview over the implicit system approach in modern control of switched dynamic models. We study a class of non-stationary autonomous switched systems and formally establish the existence of solution. We next incorporate the implicit systems approach into our consideration. At the beginning of the contribution we also develop a specific system example that is used for illustrations of various system aspects that we consider. Our research involves among others a deep examination of the reachability property in the framework of the implicit system framework that we propose. Based on this methodology we finally propose a resulting robust control design for the switched systems under consideration and the proposed control strategy is implemented in the context of the illustrative example

Stability of differential inclusions: A computational approach

We present a technique for analysis of asymptotic stability for a class of differential inclusions. This technique is based on the Lyapunov-type theorems. The construction of the Lyapunov functions for differential inclusions is reduced to an auxiliary problem of mathematical programming, namely, to the problem of searching saddle points of a suitable function. The computational approach to the auxiliary problem contains a gradient-type algorithm for saddle-point problems. We also extend our main results to systems described by difference inclusions. The obtained numerical schemes are applied to some illustrative examples

Robust structural feedback linearization based on the nonlinearities rejection

International audienceIn this paper, we consider a class of affine control systems and propose a new structural feedback linearization technique. This relatively simple approach involves a generic linear-type control scheme and follows the classic failure detection methodology. The robust linearization idea proposed in this contribution makes it possible an effective rejection of nonlinearities that belong to a specific class of functions. The nonlinearities under consideration are interpreted here as specific signals that affect the initially given systems dynamics. The implementability and efficiency of the proposed robust control methodology is illustrated via the attitude control of a PVTOL

Echoes from the Field

One of the more recent developments in reading education is the programmed material called DIST AR, an acronym for Direct Instructional System for Teaching and Remediation. It was developed by Siegfried Engelmann, University of Oregon, and Elaine C. Bruner, Educational Specialist, Bureau of Educational Research, University of Illinois

Start-Up of a PID Fuzzy Logic-Embedded Control System for the Speed of a DC Motor Using LabVIEW

This work explains the speed control design for a DC motor using fuzzy logic with LabVIEW software. It is also a literature review about the design and the implementation environment and is presented using fuzzy logic to describe the materials and methods used. Various processes on the subject highlight the idea, creation, development, and implementation of intelligent control, and the results considering the application and development for this purpose are presented

Branch-and-lift algorithm for deterministic global optimization in nonlinear optimal control

This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and potentially nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a generic, spatial branch-and-bound algorithm. A new operation, called lifting, is introduced, which refines the control parameterization via a Gram-Schmidt orthogonalization process, while simultaneously eliminating control subregions that are either infeasible or that provably cannot contain any global optima. Conditions are given under which the image of the control parameterization error in the state space contracts exponentially as the parameterization order is increased, thereby making the lifting operation efficient. A computational technique based on ellipsoidal calculus is also developed that satisfies these conditions. The practical applicability of branch-and-lift is illustrated in a numerical example. © 2013 Springer Science+Business Media New York

A constructive method for solving stabilization problems

The problem of asymptotic stabilization for a class of differential inclusions is considered. The problem of choosing the Lyapunov functions from the parametric class of polynomials for differential inclusions is reduced to that of searching saddle points of a suitable function. A numerical algorithm is used for this purpose. All the results thus obtained can be extended to cover the discrete systems described by difference inclusions