离散时间系统混合l1/H∞-控制问题

研究MIMO离散时间系统混合l₁/H_∞控制问题. 通过引入辅助优化问题, 证明了目标优化值关于约束H_∞指标的连续依赖性及其辅助问题最优化解的存在性, 同时证明了辅助优化问题的截断序列问题解的收敛性, 且其极限为混合l₁/H_∞_控制优化的辅助问题的最优化解. 还给出了优化目标值的上下界逼近.

Mixed l-one/H-infinity control problem for discrete-time systems

This paper is concerned with mixed l-one/H-infinity-control problem of MIMO discrete_time systems where l-one-performance objective is minimized subject to an H-infinity constraint. By introducing an auxiliary optimal problem, we prove the continuous_dependence of optimal objective with respect to the constrainted H-infinity-performance objective. The existence of the solution of the auxiliary optimal problem is also proved. We present the convergence of the solutions of a series of the truncation problems of the auxiliary optimal problem, and show that its limit is the optimal solution of the auxiliary optimal problem. Particularly, we give an approach to obtain the converging lower and upper bounds of the mixed l-one/H-infinity-control problem. This approach gives a computationally efficient synthesis procedure which avoid the problem of zero-interpolation techniques. Finally, an example shows that the approach is feasible for designing suboptimal controller of the mixed control problem.