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首页> 外文期刊>IEEE Transactions on Automatic Control >An exact solution to general four-block discrete-time mixed ℋ2/ℋ∞ problems via convex optimization
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An exact solution to general four-block discrete-time mixed ℋ2/ℋ∞ problems via convex optimization

机译：通过凸优化解决一般四块离散时间混合＆Hscr; 2 /＆Hscr;∞问题的精确解

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摘要

The mixed ℋ2ℋ∞ control problem can be motivated as a nominal LQG optimal control problem subject to robust stability constraints, expressed in the form of an ℋ∞ norm bound. This paper contains a solution to a general four-block mixed ℋ2/ℋ∞ problem, based upon constructing a family of approximating problems. Each one of these problems consists of a finite-dimensional convex optimization and an unconstrained standard ℋ∞ problem. The set of solutions is such that in the limit the performance of the optimal controller is recovered, allowing one to establish the existence of an optimal solution. Although the optimal controller is not necessarily finite-dimensional, it is shown that a performance arbitrarily close to the optimal can be achieved with rational controllers. Moreover, the computation of a controller yielding a performance ε-away from optimal requires the solution of a single optimization problem, a task that can be accomplished in polynomial time
机译：可以将混合的＆Hscr; 2＆Hscr;∞控制问题作为标称LQG最优控制问题，以鲁棒的稳定性约束为动力，以＆Hscr;∞范数边界的形式表示。本文在构造一系列近似问题的基础上，提供了一个针对一般四块混合＆Hscr; 2 /＆Hscr;∞问题的解决方案。这些问题中的每一个都包括一个有限维凸优化和一个无约束标准＆Hscr;∞问题。该组解决方案使得在极限情况下恢复了最佳控制器的性能，从而使人们能够确定最佳解决方案的存在。尽管最优控制器不一定是有限维的，但它表明，使用理性控制器可以实现任意接近最优性能。此外，要使控制器的性能偏离最优值，需要计算单个优化问题，该任务可以在多项式时间内完成

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