Singularly perturbed control systems: limit occupational measures sets and averaging


Lunedi' 10 marzo alle ore 12.15 in Aula 2BC/30 della Torre Archimede il professor Vladimir Gaitsgory (University South Australia) terra' un seminario dal titolo "Singularly perturbed control systems: limit occupational measures sets and averaging".

We will discuss an asymptotic approximation of the slow dynamics of a singularly perturbed control system (SPCS) by the solutions of the averaged system in which the controls are measure-valued functions taking values in the set of limit occupational measures defined by the "fast" dynamics. For an important special class of SPCS, we will show that problems of optimal control are reduced to infinite dimension linear programming problems and we will discuss an approach to a numerical olution of such problems. The presentation will be mostly focused on the deterministic case based on results obtained in [1], [2]). However, time permitting, we will also discuss some results about averaging of stochastic SPCS (obtained in [3], [4]).

[1] V. Gaitsgory, "On Representation of the Limit Occupational Measures Set of a Control Systems with Applications to Singularly Perturbed Control Systems", SIAM J. Control and Optimization, 43 (2004), No 1, pp 325-340.
[2] V. Gaitsgory and S. Rossomakhine, "Linear Programming Approach to Deterministic Long Run Average Problems of Optimal Control", SIAM J. Control and Optimization, 44 (2005/2006), No 6, pp. 2006-2037.
[3] V. Borkar and V. Gaitsgory, "On Existence of Limit Occupational Measures Ser of a Controlled Stochastic Differential Equation", SIAM J on Control and Optimization, 44:4 (2005/2006), pp. 1436-1473.
[4] V. Borkar and V. Gaitsgory, "Averaging of Singularly Perturbed Controlled Stochastic Differential Equations", Applied Mathematics and Optimization, 56 (2007), pp 169-209

Rif. int. M. Bardi, A. Cesaroni