Problem statement: This study developed a new application for the output model reference adaptive control of linear continuous systems based on the concepts of hyper-stability. Approach: The main idea is to design a non-linear controller which will ensure the minimal error between the reference model and the plant outputs. Results: Therefore, the synthesis of adaptive control with a model of reference was done either using the theory of Lyapunov or from the concept of hyper- stability. The proposed approach was developed and applied to a lateral motion of aircraft, in order to determine the lateral and directional control angles required for trim under steady turns and sideslips. Also, this application is based on the directional and lateral static stability derivatives of the aircraft. Conclusion/Recommendations: Simulation results showed the effectiveness of the proposed application method.

background

Hyperstability and average hyperstability conditions for a broad class of gaussian stochastic systems

Applying Model Reference Adaptive Controller for Lateral Motion of Aircraft

This book presents a unified treatment of linear and nonlinear filtering theory for engineers, with sufficient emphasis on applications to enable the reader to use the theory. The need for this book is twofold. First, although linear estimation theory is relatively well known, it is largely scattered in the journal literature and has not been collected in a single source. Second, available literature on the continuous nonlinear theory is quite esoteric and controversial, and thus inaccessible to engineers uninitiated in measure theory and stochastic differential equations. Furthermore, it is not clear from the available literature whether the nonlinear theory can be applied to practical engineering problems. In attempting to fill the stated needs, the author has retained as much mathematical rigor as he felt was consistent with the prime objective" to explain the theory to engineers. Thus, the author has avoided measure theory in this book by using mean square convergence, on the premise that everyone knows how to average. As a result, the author only requires of the reader background in advanced calculus, theory of ordinary differential equations, and matrix analysis.

Stochastic Processes and Filtering Theory

As a newly minted Ph.D., Paul Halmos came to the Institute for Advanced Study in 1938--even though he did not have a fellowship--to study among the many giants of mathematics who had recently joined the faculty. He eventually became John von Neumann's research assistant, and it was one of von Neumann's inspiring lectures that spurred Halmos to write Finite Dimensional Vector Spaces. The book brought him instant fame as an expositor of mathematics. Finite Dimensional Vector Spaces combines algebra and geometry to discuss the three-dimensional area where vectors can be plotted. The book broke ground as the first formal introduction to linear algebra, a branch of modern mathematics that studies vectors and vector spaces. The book continues to exert its influence sixty years after publication, as linear algebra is now widely used, not only in mathematics but also in the natural and social sciences, for studying such subjects as weather problems, traffic flow, electronic circuits, and population genetics. In 1983 Halmos received the coveted Steele Prize for exposition from the American Mathematical Society for "his many graduate texts in mathematics dealing with finite dimensional vector spaces, measure theory, ergodic theory, and Hilbert space."

Hyperstability and average hyperstability conditions for a broad class of gaussian stochastic systems

Citations

Applying Model Reference Adaptive Controller for Lateral Motion of Aircraft

References

Stochastic Processes and Filtering Theory

Finite-Dimensional Vector Spaces

Bemerkungen zur Theorie der beschränkten Bilinearformen mit unendlich vielen Veränderlichen.

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