On the finite horizon Nash equilibrium solution in the differential game approach to formation control

The solvability of the coupled Riccati differential equations appearing in the differential game approach to the formation control problem is vital to the finite horizon Nash equilibrium solution.These equations(if solvable)can be solved numerically by using the terminal value and the backward iteration.To investigate the solvability and solution of these equations the formation control problem as the differential game is replaced by a discrete-time dynamic game.The main contributions of this paper are as follows.First,the existence of Nash equilibrium controls for the discretetime formation control problem is shown.Second,a backward iteration approximate solution to the coupled Riccati differential equations in the continuous-time differential game is developed.An illustrative example is given to justify the models and solution.

Optimal fault detection for a class of discrete-time switched linear systems

This paper deals with the problem of optimal fault detection filter （FDF） design for a class of discrete-time switched linear systems under arbitrary switching. By using an observer-based FDF as a residual generator, the design of the FDF is formulated into an optimization problem through maximizing the H_/H∞ or H∞/H∞ performance index. With the aid of an operator optimization method, it is shown that a mode-dependent unified optimal solution can be derived by solving a coupled Riccati equation. A numerical example is given to show the effectiveness of the proposed method.

Iterative algorithms with the latest update for Riccati matrix equations in Ito Markov jump systems

This study is concerned with the problem to solve the continuous coupled Riccati matrix equations in It?Markov jump systems.A new iterative algorithm is developed by using the latest estimation information and introducing a tuning parameter.The iterative solution obtained by the proposed algorithm with zero initial conditions converges to the unique positive definite solution of the considered equations.The convergence rate of the algorithm is dependent on the adjustable parameter.Furthermore,a numerical example is provided to show the effectiveness of the presented algorithms.

Infinite horizon H-two/H-infinity control for descriptor systems:Nash game approach

This paper studies the infinite time horizon mixed H-two/H-infinity control problem for descriptor systems using Nash game approach. A necessary/sufficient condition for the existence of infinite horizon H-two/H-infinity control is presented in the form of two coupled algebraic Riccati equations, respectively. Finally, a suboptimal H-two/H-infinity controller design is given based on an iterative linear matrix inequality algorithm.