Hisham Abou-Kandil

ACTIVE VIBRATION DAMPING OF A SMART FLEXIBLE STRUCTURE USING PIEZOELECTRIC TRANSDUCERS: H∞ DESIGN AND EXPERIMENTAL RESULTS

Abstract This paper deals with active vibration control of a plate like smart flexible structure. This plate is equipped with several thin piezoelectric patches. Some of them are used as sensors and the others as actuators. They are optimally positioned and not collocated. The main goal of control is to reduce the most energetic vibrating modes. By using a state-space representation of a MIMO model of the equipped structure, derived from Finite Elements Modeling and modal analysis, a synthesis setup is derived to design an H ∞ controller. The resulting controller is reduced and tested experimentally.

A New Approach for Real-Time Control of Urban Traffic Networks

Abstract Using a new decomposition-coordination approach, an efficient design method for traffic regulation in congested network is presented. A simplified network model is chosen here for testing the proposed two-level structure which alleviates some of the difficulties encountered with classical methods. A local feedback control law is determined which is based on the length of the vehicles queues at each intersection. This law is modified by a coordination term, calculated at the upper level, which takes into consideration the state of the traffic at other intersections. Due to the inherent flexibility of the method, state constraints are treated at the upper level. Only simple calculations are required to determine the control law, leading to short computation time and thus allowing real time control of over saturated networks. The results obtained on various examples confirm the advantages of the proposed technique.

Non-symmetric Riccati theory and applications

The terminology ‘Riccati theory’ is inspired by the book [I0W99] of Ionescu, Oara and Weiss. Therein, Riccati theory stands for the linkage between existence results for stabilizing solutions to the symmetric algebraic Riccati equation, the invertibility of the Toeplitz operator associated with the input-output operator of the underlying Hamiltonian system and the existence of an antianalytic factorization of the Popov function. This theory has been extended in Chapter 7 to cope with the time-varying situation, finding important applications in modern control theory.

Basic results for linear equations

In this section we recall some well-known facts about first order linear systems of differential equations with piecewise continuous, locally bounded coefficients and, in the case of constant coefficients, about the corresponding algebraic equations.

Coupled and generalized Riccati Equations

The purpose of this chapter is to study coupled, non-symmetric and generalized Riccati equations occurring in different control problems. Three main topics are addressed: Dynamic games, linear systems with Markovian jumps and generalized Riccati equations appearing in stochastic control. In all these cases when quadratic criteria have to be minimized the control is expressed in terms of solutions of coupled or generalized Riccati equations. However, all these equations cannot be treated using the same approach. It will be shown that, depending on the nature of these equations, different methods could be employed to analyze and then to solve such Riccati equations.

Hamiltonian Matrices and Algebraic Riccati equations

The main subject of this book is matrix Riccati differential equations; by definition, in this book, these are differential equations which can be written in the form

Symmetric differential Riccati equations: an operator based approach

\dot W = M_{21} (t) + M_{22} (t)W - WM_{11} (t) - WM_{12} (t)W,t \in \mathcal{I},

On a Practical Approach to Real-time Control

(RDE) with W, M 21(t) ∈ ℂmxn, M 22(t) ∈ ℂmxm, M 11(t) ∈ ℂnxn, M 12(t) ∈ ℂnxm for t ∈ \( \mathcal{I} \). Throughout Chapters 2-6 we agree for convenience that all coefficients of matrix Riccati equations are piecewise continuous and locally bounded and that \( \mathcal{I} \) is a non-degenerate interval on the real axis (or maybe an open subset of ℂ). We note that most of our results remain (a.e.) valid if the coefficients are locally integrable and if we understand the solutions in the sense of Caratheodory.