All Years Seminars
[INMA] 2012-12-04 (14.00) : A deterministic optimal control problem with a chaotic solution
At Euler building
Speaker :
Roland Hildebrand (CESAME)
Abstract : It is well-known that in continuous-time dynamical systems of dimension greater or equal than 3 chaotic behaviour can occur. Perhaps the most simple, but rather typical example is Smale's Horseshoe, which appears whenever the stable and unstable submanifolds of a hyperbolic fixed point of the two-dimensional Poincare return map in the neighbourhood of a periodic trajectory intersect in a second point.
We present a 4-dimensional, linear-quadratic, deterministic optimal control problem whose optimal solution exhibits a dynamics emanating from a Smale's Horseshoe. Chaotic behaviour was previously not known to occur in optimal control problems.
This is joint work with M.I. Zelikin and L.V. Lokutsievski (Moscow State University).
[INMA] 2012-11-27 (14.00) : Welcome seminar
At Euler building
Speaker :
Young researchers (UCL)
Abstract : In this seminar, a few new Ph.D. students of INMA's team will introduce themselves and their research topic.
[INMA] 2012-11-20 (14.00) : The Interplay of Convexity and Algorithmic Algebra in Optimization and Systems Analysis
At Euler building
Speaker :
Amirali AHMADI (MIT, USA)
Abstract : We present complexity results and algebraic relaxations for two problems of interest in optimization and control theory: (i) recognizing convexity in polynomial optimization, and (ii) proving stability of polynomial differential equations.
(i) We show that deciding convexity of polynomials of degree as low as four is strongly NP-hard. This solves a problem that appeared as one of seven open problems in complexity theory for numerical optimization in 1992. We then introduce an algebraic, semidefinite programming based sufficient condition for convexity known as sum-of-squares-convexity and present a complete characterization of the cases where it is equivalent to convexity. This characterization draws an interesting parallel to a seminal 1888 result of Hilbert in real algebraic geometry.
(ii) We show that deciding asymptotic stability of cubic polynomial vector fields is strongly NP-hard. Currently, one of the most widely used techniques for proving stability of polynomial vector.
[INMA] 2012-11-13 (14.00) : Dissipative Systems Theory and Distributed Control of Interconnected Processes
At Euler building
Speaker :
Nicolas Hudon (UCL)
Abstract : In recent years, as energy and mass integration of chemical processes have been introduced from a process design perspective, many researchers recognized the need for new methods to analyze the dynamics and to design controllers for interconnected chemical process units. On the other hand, the emergence of cheap and reliable communication networks gave a new perspective for the design of distributed controllers, using all information available to increase interconnected processes performance. However, for chemical processes described by nonlinear dynamics, the design and coordination of distributed controllers is still an open problem.
In this talk, we consider an approach to analyze and control interconnected chemical processes. Using a general representation, we use dissipative systems theory as a tool for both the analysis of the global process and for the design of decentralized state and output feedback controllers. The principal objective of the proposed approach is to design distributed feedback controllers to achieve plant-wide stability for a given interconnection structure. At a plant-wide level, extensions of classical results on the stability of large-scale interconnected systems lead to input-output dissipativity constraints for each subsystems, encoded as supply rates from input to output interconnecting ports. Then, for each subsystem, a parameterized nonlinear feedback controller is designed using nonlinear dissipative inequalities to ensure that the aforementioned dissipativity constraints are met in closed-loop. The key advantage of using parameterized controller is the possibility to balance local and global objectives.
This talk also briefly covers new results on the construction of storage functions for control affine systems, as a generalization of physics-based approaches to dissipative systems theory. In particular, it is shown, under a convexity condition, that an approximate storage function candidate can be constructed using a decomposition of the drift vector field. Finally, we discuss some dynamic feedback and robust design extensions obtained recently along those lines. Some open problems around the themes of optimization over networks and analysis of time-varying interconnection structures are discussed within that context.
[INMA] 2012-10-23 (14.00) : Can control theory tell us anything about the brain?
At Euler building
Speaker :
Crevecoeur, Frédéric
Abstract : Understanding how the brain controls movements is a major challenge as most neurological dysfunction result in sensorimotor deficits with an obvious impact on the quality of life. Control theory is a powerful tool to examine whether some components of neural processing can be mapped into computations involved in the control algorithm. In this talk, I will present recent results showing that rapid feedback responses to mechanical perturbations are associated with, and driven by, internal state estimation. We first demonstrated that when we navigate our arm in the vicinity of physical obstacles, straight movements are sometimes rerouted around obstacles following a perturbation. We used optimal control principles to estimate when the controller should switch between strategies and found similar state-dependent switch in the data as predicted from the model. Importantly, this switch was expressed in muscle activity in about 50 ms, which is much faster than voluntary reaction times and decisional processes (> 100 ms). We further examined when the central nervous system updates the estimates of the state of the limb following a perturbation, as ignoring delays as short as 50 ms can cause instability. We reasoned that if limb afferent feedback is extrapolated to estimate the present state, then changing the relationship between the initial perturbation and the current limb motion should result in inadequate motor responses. We found evidence that participants relied on a rapid update in state estimation following the perturbations. This rapid update is adaptive and influences the motor response within 50 ms of perturbation onset according to the expected perturbation profile. In all, these results show that rapid responses traditionally viewed as reflexes, are actually driven by internal state estimation. These results imply that the underlying neural pathway, including primary motor cortex and the cerebellum, implement a state-dependent feedback control policy.
Seminars
Subscribe (ICS)
INMA Contact Info
Mathematical Engineering (INMA)
L4.05.01
Avenue Georges Lemaître, 4
+32 10 47 80 36
secretaire-inma@uclouvain.be
Mon – Fri 9:00A.M. – 5:00P.M.
JOIN US