L2/L1 L_2/L_1 induced norm and Hankel norm analysis in sampled-data systems

This paper is concerned with the $L_2/L_1$ induced and Hankel norms of sampled-data systems. In defining the Hankel norm, the $h$-periodicity of the input-output relation of sampled-data systems is taken into account, where $h$ denotes the sampling period; past and future are separated by the instant $\Theta\in[0, h)$, and the norm of the operator describing the mapping from the past input in $L_1$ to the future output in $L_2$ is called the quasi $L_2/L_1$ Hankel norm at $\Theta$. The $L_2/L_1$ Hankel norm is defined as the supremum over $\Theta\in[0, h)$ of this norm, and if it is actually attained as the maximum, then a maximum-attaining $\Theta$ is called a critical instant. This paper gives characterization for the $L_2/L_1$ induced norm, the quasi $L_2/L_1$ Hankel norm at $\Theta$ and the $L_2/L_1$ Hankel norm, and it shows that the first and the third ones coincide with each other and a critical instant always exists. The matrix-valued function $H(\varphi)$ on $[0, h)$ plays a key role in the sense that the induced/Hankel norm can be obtained and a critical instant can be detected only through $H(\varphi)$, even though $\varphi$ is a variable that is totally irrelevant to $\Theta$. The relevance of the induced/Hankel norm to the $H_2$ norm of sampled-data systems is also discussed

ロバスト性解析と制御器設計のための離散時間非因果的周期時変スケーリング

京都大学0048新制・課程博士博士(工学)甲第17889号工博第3798号新制||工||1581(附属図書館)30709京都大学大学院工学研究科電気工学専攻(主査)教授 萩原 朋道, 教授 土居 伸二, 准教授 久門 尚史学位規則第4条第1項該当Doctor of Philosophy (Engineering)Kyoto UniversityDFA

On Automation in Anesthesia

The thesis discusses closed-loop control of the hypnotic and the analgesic components of anesthesia. The objective of the work has been to develop a system which independently controls the intravenous infusion rates of the hypnotic drug propofol and analgesic drug remifentanil. The system is designed to track a reference hypnotic depth level, while maintaining adequate analgesia. This is complicated by inter-patient variability in drug sensitivity, disturbances caused foremost by surgical stimulation, and measurement noise. A commercially available monitor is used to measure the hypnotic depth of the patient, while a simple soft sensor estimates the analgesic depth. Both induction and maintenance of anesthesia are closed-loop controlled, using a PID controller for propofol and a P controller for remifentanil. In order to tune the controllers, patient models have been identified from clinical data, with body mass as only biometric parameter. Care has been taken to characterize identifiability and produce models which are safe for the intended application. A scheme for individualizing the controller tuning upon completion of the induction phase of anesthesia is proposed. Practical aspects such as integrator anti-windup and loss of the measurement signal are explicitly addressed. The validity of the performance measures, most commonly reported in closed-loop anesthesia studies, is debated and a new set of measures is proposed. It is shown, both in simulation and clinically, that PID control provides a viable approach. Both results from simulations and clinical trials are presented. These results suggest that closed-loop controlled anesthesia can be provided in a safe and efficient manner, relieving the regulatory and server controller role of the anesthesiologist. However, outlier patient dynamics, unmeasurable disturbances and scenarios which are not considered in the controller synthesis, urge the presence of an anesthesiologist. Closed-loop controlled anesthesia should therefore not be viewed as a replacement of human expertise, but rather as a tool, similar to the cruise controller of a car

Contributions to fuzzy polynomial techniques for stability analysis and control

The present thesis employs fuzzy-polynomial control techniques in order to improve the stability analysis and control of nonlinear systems. Initially, it reviews the more extended techniques in the field of Takagi-Sugeno fuzzy systems, such as the more relevant results about polynomial and fuzzy polynomial systems. The basic framework uses fuzzy polynomial models by Taylor series and sum-of-squares techniques (semidefinite programming) in order to obtain stability guarantees. The contributions of the thesis are: ¿ Improved domain of attraction estimation of nonlinear systems for both continuous-time and discrete-time cases. An iterative methodology based on invariant-set results is presented for obtaining polynomial boundaries of such domain of attraction. ¿ Extension of the above problem to the case with bounded persistent disturbances acting. Different characterizations of inescapable sets with polynomial boundaries are determined. ¿ State estimation: extension of the previous results in literature to the case of fuzzy observers with polynomial gains, guaranteeing stability of the estimation error and inescapability in a subset of the zone where the model is valid. ¿ Proposal of a polynomial Lyapunov function with discrete delay in order to improve some polynomial control designs from literature. Preliminary extension to the fuzzy polynomial case. Last chapters present a preliminary experimental work in order to check and validate the theoretical results on real platforms in the future.Pitarch Pérez, JL. (2013). Contributions to fuzzy polynomial techniques for stability analysis and control [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/34773TESI