TY - JOUR

T1 - The interpretation of discontinuous state feedback control laws as nonanticipative control strategies in differential games

AU - Vinter, R. B.

AU - Clark, J. M.C.

AU - James, M. R.

PY - 2004/8

Y1 - 2004/8

N2 - In differential games, one player chooses a feedback strategy to maximize a payoff. The other player counters by applying a minimizing open loop control. Classical notions of feedback strategies, based on state feedback control laws for which the corresponding closed loop dynamics uniquely define a state trajectory, are too restrictive for many problems, owing to the absence of minimizing classical feedback strategies or because consideration of classical feedback strategies fails to define, in a useful way, the value of the game. A number of feedback strategy concepts have been proposed to overcome this difficulty. That of Elliot and Kalton, according to which a feedback strategy is a nonanticipative mapping between control functions for the two players, has been widely taken up because it provides a value of the game which connects, via the Hamilton-Jacobi-Isaacs equation, with other fields of systems science. Heuristic analysis of specific games problems often points to discontinuous optimal feedback strategies. These cannot be regarded as classical feedback control strategies because the associated state trajectories are not in general unique. We give general conditions under which they can be interpreted as generalized feedback strategies in the sense of Elliot and Kalton.

AB - In differential games, one player chooses a feedback strategy to maximize a payoff. The other player counters by applying a minimizing open loop control. Classical notions of feedback strategies, based on state feedback control laws for which the corresponding closed loop dynamics uniquely define a state trajectory, are too restrictive for many problems, owing to the absence of minimizing classical feedback strategies or because consideration of classical feedback strategies fails to define, in a useful way, the value of the game. A number of feedback strategy concepts have been proposed to overcome this difficulty. That of Elliot and Kalton, according to which a feedback strategy is a nonanticipative mapping between control functions for the two players, has been widely taken up because it provides a value of the game which connects, via the Hamilton-Jacobi-Isaacs equation, with other fields of systems science. Heuristic analysis of specific games problems often points to discontinuous optimal feedback strategies. These cannot be regarded as classical feedback control strategies because the associated state trajectories are not in general unique. We give general conditions under which they can be interpreted as generalized feedback strategies in the sense of Elliot and Kalton.

UR - http://www.scopus.com/inward/record.url?scp=4344615557&partnerID=8YFLogxK

U2 - 10.1109/TAC.2004.832659

DO - 10.1109/TAC.2004.832659

M3 - Article

SN - 0018-9286

VL - 49

SP - 1360

EP - 1365

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 8

ER -