Third HIT workshop on Mathematics and Control Theory

10:00 17-05-2017
 
 
Third HIT workshop on Mathematics and Control Theory

Organizing comittee: Dr. Yirmeyahu Kaminski  | Dr. Alex Zaslavski | Prof. Ezra Zeheb

Wednesday, May 17, 2017 | 10:00 |  Building 3, Conference Hall
registration

Schedule

Opening: Prof. Eduard Yakubov, HIT President
                 Prof. Ezra Zeheb, Dean of Sciences at HIT

10:00

 Prof. Michael Margaliot, Tel-Aviv University
Monotone dynamical systems and monotone control systems

10:15

Prof. Jean Lévine, MinesParis-Tech, Institut Henri Poincarré
Towards a global analysis of differential flatness, with application to global motion planning

11:00 

Prof. Zvi Artstein, The Weizmann Institute
Controlling coupled slow and fast dynamics
     

11:45 

Lunch break

12:30
 

Prof. Emilia Fridman, Tel-Aviv University
Networked Control Systems: A Time-Delay Approach

14:00

    
14:45
Coffee break
 

15:30

Prof. François Ollivier, CNRS – Ecole Polytechnique
Testing identifiability and computing flat outputs

16:00

 Prof. Ilya Ioslovich, Technion

16:45

 Concluding remarks

17:30




Lecture 1
Prof. Michael Margaliot, Tel-Aviv University
Monotone dynamical systems and monotone control systems
Abstract:
Monotone systems are systems whose flow preserves a partial ordering between the initial conditions. A special case is positive systems, that is, systems whose trajectories evolve on the positive orthant. Monotone systems are recently attracting considerable interest in control theory and systems biology. The talk is a self-contained tutorial on this important issue.
 

Lecture 2
Prof. Jean Lévine, MinesParis-Tech, Institut Henri Poincarré
Towards a global analysis of differential flatness, with application to global motion planning
Joint work with: Yirmeyahu Kaminski and François Ollivier
 
Abstract:
We study the singularities of locally differentially flat systems, in the perspective of providing global or semi-global motion planning solutions for such systems: flat outputs may fail to be globally defined, thus potentially preventing from planning trajectories leaving their domain of definition, the complement of which we call singular. Such singular subsets are classified into two types: apparent and intrinsic.
 
A rigorous defintion of these singularities is introduced in terms of atlas and local charts in the framework of the differential geometry of jets of infinite order and Lie-Bäcklund. isomorphisms. We then give a criterion allowing to effectively compute intrinsic singularities. Finally, we show how our results apply to the global motion planning of the well-known example of non holonomic car.
 

Lecture 3
Prof. Zvi Artstein, The Weizmann Institute
Controlling coupled slow and fast dynamics
 
Abstract:
We review the modeling and analysis, and comment on the computations, of control and optimal control systems, whose dynamics reflect coupled slow and fast behavior.
 

Lecture 4
Prof. Emilia Fridman, Tel-Aviv University
Networked Control Systems: A Time-Delay Approach
 
Abstract:
Networked control systems (NCSs) are systems with spatially distributed sensors, actuators and controller nodes which exchange data via communication network. Compared to traditional feedback control systems, where the components are connected via point-to-point cables, the introduction of communication network media brings great advantages, such as low cost, reduced weight, simple installation/maintenance and long distance control. There are three main approaches to NCSs: the discrete-time, the hybrid system and the time-delay approaches.

Recent results on NCSs via the time-delay approach will be presented.
These results take into account variable sampling intervals, communication delays and scheduling protocols. Differently from the other approaches, the time-delay approach allows treating large communication delays (that may be larger than the sampling intervals). Extensions of the results to large-scale NCSs with asynchronous networks and to parabolic PDEs will be mentioned.
 

Lecture 5
Prof. Per-Olof Gutman, Technion
Optimal Rigid Body Precise Displacement - Minimization of Electrical Energy
Joint work with: Ilya Ioslovich and Shai Moshenberg
 
Abstract:
Precise movement of a rigid body with jerk as the control signal, and with friction compensation is considered. The optimal solution for the minimization of the electrical energy consumption is obtained. The optimal solution was tested numerically.
 

Lecture 6
Prof. François Ollivier, CNRS – Ecole Polytechnique
Monotone dynamical systems and monotone control systems
Joint work with: Brahim Sadik and Guillaume Chèze
 
Abstract:
We focus on flatness criteria that rely on the construction of some involutive system of derivations. Systems linearizable by static feedback, a sufficient flatness condition, enter in this category.
 
Cartan's criterion for driftless systems with two inputs will also produce, if the test is positive, a family of involutive distributions, of which independent pairs of common first integrals will be flat outputs. We provide a new general criterion for systems with two inputs.

We give then methods to test the existence of -"simple" flat outputs, such as polynomial or rational functions of a given low degree. In the case of a family of involutive distributions depending on parameters, one may try to chose them in order to insure the existence of simpler flat outputs.
 

Lecture 7
Prof. Ilya Ioslovich, Technion
Time-Optimal Traffic Control Synthesis for a Signalized Isolated Intersection
Joint work with: Per-Olof Gutman and Michael Borshchevsky
 
Abstract:
The minimum time optimal control problem for an oversaturated signalized intersection is defined as finding the green split that dissolves all initial non-zero queue lengths in minimum time. Here, the optimal minimum time control for an isolated intersection is found in explicit state feedback form, where the state is defined as the queue lengths, by the use of a continuous differential model, and the Pontryagin Maximum Principle.

The closed form feedback solution is presented for all types of constraints on the maximal green split values, and on the queue lengths, i.e. with constrained control and state variables. In general, the minimum time optimal solutions are non-unique. It is also demonstrated that the known contribution by D. Gazis, 1964, alleged to solve the minimal "total delay” problem is in fact a minimal time solution in a particular region of the state space.
 
 

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