Control Theory in the Plane

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.

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This book introduces and illustrates with examples, the theory of control for systems governed by ordinary differential equations, with special reference to the two-dimensional case. The systems covered are continuous, finite-dimensional, deterministic and those with a priori bounds on the admissible controls. A particular feature of the book is an examination of control systems whose state space is the phase plane. As with differential equations, where specialization to the plane provides a more complex theory (for example, the results of Poincare and Bendixson), control theory of two-dimensional systems also has more meaningful results.