Control Theory In The Plane (lecture Notes In Control And Information Sciences)

This book introduces, presents, and illustrates, the theory of control for systems governed by ordinary differential equations, with special references to the two-dimensional case. These systems are continuous, finite-dimensional, deterministic, with a priori bounds on the admissible controls. Its form is that of a graduate-level textbook, involving motivation, a rather elementary level of exposition, illustrative examples, and extensive problem sections. It is addressed to applied mathematicians and engineers (system, control, electrical, mechanical, chemical) who wish to acquire further mathematical background in order to treat the subject they already know is both fascinating and important. Hopefully, it might also serve those whose interest is in modeling, bio-mathematics, and economics. The special feature of this book is the focused study, in the second part, of control systems whose state space is the phase plane. As with differential equations, where specialisation to the plane provides a far richer theory (the classical results of Poincar? and Bendixson), control theory of two-dimensional systems also has more intuitive and deeper results. This book introduces, presents, and illustrates, the theory of control for systems governed by ordinary differential equations, with special references to the two-dimensional case. These systems are continuous, finite-dimensional, deterministic, with a priori bounds on the admissible controls. Its form is that of a graduate-level textbook, involving motivation, a rather elementary level of exposition, illustrative examples, and extensive problem sections. It is addressed to applied mathematicians and engineers (system, control, electrical, mechanical, chemical) who wish to acquire further mathematical background in order to treat the subject they already know is both fascinating and important. Hopefully, it might also serve those whose interest is in modeling, bio-mathematics, and economics. The special feature of this book is the focused study, in the second part, of control systems whose state space is the phase plane. As with differential equations, where specialisation to the plane provides a far richer theory (the classical results of Poincaré and Bendixson), control theory of two-dimensional systems also has more intuitive and deeper results Examples of control systems....Pages 1-20 Differential equations....Pages 21-75 Control systems....Pages 77-167 Local behavior....Pages 169-194 Controllability, attainability....Pages 195-222 Index theory....Pages 223-244 Optimisation....Pages 245-269 Introduces and illustrates with examples, the theory of control for systems governed by ordinary differential equations, with special reference to the two-dimensional case. Some systems covered are continuous, finite-dimensional and deterministic.