Risk Sensitive Control of Hybrid Systems

ECS-9629866 Runolfsson动态系统依赖于表征系统运行模式的辅助参数，在许多应用中出现。在一些应用中，这个参数可以被测量，在另一些应用中，它可以被估计，而在另一些应用中，它是完全未知的，可能除了关于其大小的某种先验估计之外。在控制系统设计中引入辅助参数时所选择的方法取决于参数的特性。如果参数是确定性的并且可以测量，则在实际系统的设计中经常采用增益调度方法。如果参数是(确定性的)未知且不可测量，则通常使用稳健设计方法。另一方面，如果参数是随机的，且具有已知的统计量，则通常采用随机方法。这种情况的一个特例是辅助参数可以被建模为有限状态连续时间马尔可夫链的情况。这样的系统出现在各种应用和系统配方中，例如电力系统、制造系统和容错控制系统。在这项研究中，我们研究具有马尔可夫跳跃参数的混杂系统的风险敏感控制。具体地说，控制的目标是使无限远期风险敏感成本泛函最小化。初步研究表明，对于混杂系统，H_控制、线性微分对策和风险敏感控制之间的关系不成立。其主要原因似乎是，风险敏感度成本函数衡量的是系统对随机跳跃参数和噪声输入引起的转变的风险敏感度。代价泛函对跳跃参数引起的转变的风险敏感性在系统设计中可能具有很大的价值，其中希望使系统性能对跳跃参数的影响尽可能地不敏感。在这项研究中，我们将发展混杂随机系统的风险敏感控制，并详细研究这类系统的理论性质和设计技巧。此外，还将评估所开发技术对上述应用的益处。

ECS-9629866 Runolfsson Dynamic systems that depend on a auxiliary parameter that characterizes the mode of operation of the system arise in many applications. In some applications this parameter can be measured, in others it can be estimated and in still others it is completely unknown except for, perhaps, some apriori estimate about its size. The methods that are chosen in incorporating the auxiliary parameter in the design of a control systems depends on the characteristic of the parameter. If the parameter is deterministic and can be measured, gain scheduling methods are frequently employed in the design of real systems. If the parameter is (deterministic) unknown and not measurable, robust design methods are usually used. If, on the other hand, the parameter is stochastic with known statistic, stochastic methods are usually employed. A particular case of this situation is the case when the auxiliary parameter can be modelled as finite state continuous time Markov chain. Such systems arise in various applications and system formulations such as power systems, manufacturing systems and fault-tolerant control system. In this research we study risk-sensitive control for hybrid systems with a Markovian jump parameter. In particular, the objective of the control is to minimize the infinite-horizon risk-sensitive cost functional. Preliminary investigations show that the relationship between H(_ control, linear differential games and risk-sensitive control does not hold for hybrid systems. The main reason for this appears to be that the risk sensitivity cost functional measures the risk sensitivity of the system to transitions caused by the random jump parameter as well as the noise input. The risk sensitivity of the cost functional to transitions induced by the jump parameter may be of a great value in the design of systems where it is desired to make the system performance as insensitive to the effects of the jump parameter as possible. In this research we will develop risk sen sitive control of hybrid stochastic systems and study in detail both system theoretic properties and design techniques for such systems. Furthermore, the benefits of the developed techniques will be evaluated for the applications described above.