[Show abstract][Hide abstract]ABSTRACT: A solution for the Differential Riccati Equation arises from the N-Players LQ differential game is presented. The game solution corresponds to a Nash-equilibrium point of this game. The approach is based on extending the state vector that allows to present the classical result (N Coupled Riccati Equations) as a single Extended Coupled Riccati Differential Equation that can be solved by standard methods. Thus the Nash equilibrium is found in an easier way. The effectiveness of the designed strategy is illustrated by two examples.
[Show abstract][Hide abstract]ABSTRACT: An original linear time-varying system with unmatched disturbances and uncertainties is replaced by a finite set of dynamic models such that each one describes a particular uncertain case including exact realizations of possible dynamic equations as well as external bounded disturbances. Such a tradeoff between an original uncertain linear time varying dynamic system and a corresponding higher order multimodel system with a complete knowledge leads to a linear multi-model system with known bounded disturbances. Each model from a given finite set is characterized by a quadratic performance index. The developed min-max sliding-mode control strategy gives an optimal robust sliding-surface design algorithm, which is reduced to a solution of an equivalent linear quadratic problem that corresponds to the weighted performance indices with weights from a finite dimensional simplex. An illustrative numerical example is presented.
Full-text Article · Jan 2004 · IEEE Transactions on Automatic Control
[Show abstract][Hide abstract]ABSTRACT: A two person prey-predator (evader-pursuit) dynamic linear quadratic game is considered. In general, this problem belongs to the class of non-zero sum dynamic games. An original dynamic linear time varying system with additive disturbances or uncertainties is replaced by a finite set of dynamic models such that each one describes a particular uncertain case including exact realizations of possible dynamic equations as well as external bounded disturbances. Each model from a given finite set is characterized by a quadratic performance index. The developed minimax LG control strategy provides a Nash equilibrium in the given mini-max differential game. This problem is shown to be reduced to finding of a Nash equilibrium point in a finite dimensional simplex.