There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Data Mining - Concepts and Techniques.

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

This paper describes decentralized control laws for the coordination of multiple vehicles performing spatially distributed tasks. The control laws are based on a gradient descent scheme applied to a class of decentralized utility functions that encode optimal coverage and sensing policies. These utility functions are studied in geographical optimization problems and they arise naturally in vector quantization and in sensor allocation tasks. The approach exploits the computational geometry of spatial structures such as Voronoi diagrams.

/pdf/coverage-control-for-mobile-sensing-networks-3gs75qafnm.pdf

Coverage control for mobile sensing networks

A solution to the problem of disturbance attenuation via measurement feedback with internal stability is presented for an affine nonlinear system. It is shown that the concept of disturbance attenuation, in the sense of truncated L/sub 2/ norms, can be given an interpretation in terms of the response to periodic inputs in the sense of RMS amplitude, even in the nonlinear setup. In the case of state feedback, a family of controllers is also provided. The proofs of all these results are simple and provide deeper insight even in the analysis of the corresponding linear control problem. >

Disturbance attenuation and H/sub infinity /-control via measurement feedback in nonlinear systems

Discontinuous control of nonholonomic systems

A new method to design asymptotically stabilizing and adaptive control laws for nonlinear systems is presented. The method relies upon the notions of system immersion and manifold invariance and, in principle, does not require the knowledge of a (control) Lyapunov function. The construction of the stabilizing control laws resembles the procedure used in nonlinear regulator theory to derive the (invariant) output zeroing manifold and its friend. The method is well suited in situations where we know a stabilizing controller of a nominal reduced order model, which we would like to robustify with respect to higher order dynamics. This is achieved by designing a control law that asymptotically immerses the full system dynamics into the reduced order one. We also show that in adaptive control problems the method yields stabilizing schemes that counter the effect of the uncertain parameters adopting a robustness perspective. Our construction does not invoke certainty equivalence, nor requires a linear parameterization, furthermore, viewed from a Lyapunov perspective, it provides a procedure to add cross terms between the parameter estimates and the plant states. Finally, it is shown that the proposed approach is directly applicable to systems in feedback and feedforward form, yielding new stabilizing control laws. We illustrate the method with several academic and practical examples, including a mechanical system with flexibility modes, an electromechanical system with parasitic actuator dynamics and an adaptive nonlinearly parameterized visual servoing application.

http://eprints.imperial.ac.uk/retrieve/2034/license.txt

Immersion and invariance: a new tool for stabilization and adaptive control of nonlinear systems

We introduce two new tools that can be useful in nonlinear observer and output feedback design. The first one is a simple extension of the notion of homogeneous approximation to make it valid both at the origin and at infinity (homogeneity in the bi-limit). Exploiting this extension, we give several results concerning stability and robustness for a homogeneous in the bi-limit vector field. The second tool is a new recursive observer design procedure for a chain of integrator. Combining these two tools, we propose a new global asymptotic stabilization result by output feedback for feedback and feedforward systems.

/pdf/homogeneous-approximation-recursive-observer-design-and-56hy732nsh.pdf

Homogeneous Approximation, Recursive Observer Design, and Output Feedback

"Nonlinear and Adaptive Control with Applications" provides a detailed treatment of the design of robust adaptive controllers for nonlinear systems with uncertainties. The authors employ a new tool based on the ideas of system immersion and manifold invariance. Departing, in part, from the Lyapunov-function approach of classical control, new algorithms are delivered for the construction of robust asymptotically-stabilising and adaptive control laws for nonlinear systems. The methods proposed lead to modular schemes. These algorithms cater for nonlinear systems with both parametric and dynamic uncertainties. This innovative strategy is illustrated with several examples and case studies from real applications. Power converters, electrical machines, mechanical systems, autonomous aircraft and computer vision are among the practical systems dealt with. Researchers working on adaptive and nonlinear control theory or on control applications will find this monograph of conspicuous interest while graduate students in control systems and control engineers working with electrical, mechanical or electromechanical systems can also gain much insight and assistance from the methods and algorithms detailed.

Alessandro Astolfi

Papers

Disturbance attenuation and H/sub infinity /-control via measurement feedback in nonlinear systems

Discontinuous control of nonholonomic systems

Immersion and invariance: a new tool for stabilization and adaptive control of nonlinear systems

Homogeneous Approximation, Recursive Observer Design, and Output Feedback

Nonlinear and adaptive control with applications