Geometric Methods in System Theory: Proceedings of the NATO Advanced Study Institute held at London, England, August 27-September 7, 1973

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D.Q. Mayne, R.W. Brockett
Springer Science & Business Media, Dec 31, 1973 - Science - 314 pages
Geometric Methods in System Theory In automatic control there are a large number of applications of a fairly simple type for which the motion of the state variables is not free to evolve in a vector space but rather must satisfy some constraints. Examples are numerous; in a switched, lossless electrical network energy is conserved and the state evolves on an ellipsoid surface defined by x'Qx equals a constant; in the control of finite state, continuous time, Markov processes the state evolves on the set x'x = 1, xi ~ O. The control of rigid body motions and trajectory control leads to problems of this type. There has been under way now for some time an effort to build up enough control theory to enable one to treat these problems in a more or less routine way. It is important to emphasise that the ordinary vector space-linear theory often gives the wrong insight and thus should not be relied upon.
 

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Contents

DYNAMICAL POLYSYSTEMS and CONTROL THEORY
1
LIE ALGEBRAS AND LIE GROUPS IN CONTROL THEORY
43
REALIZATION THEORY OF BILINEAR SYSTEMS
83
AN INTRODUCTION TO STOCHASTIC DIFFERENTIAL EQUATIONS ON MANIFOLDS
131
GENERAL THEORY OF GLOBAL DIFFERENTIAL DYNAMICS
150
TWO PROOFS OF CHOWS THEOREM
159
On Necessary and Sufficient Conditions for Local Controllability Along a Reference Trajectory
165
THE HIGH ORDER MAXIMAL PRINCIPLE
174
CONTROL THEORY IN TRANSFORMATION SEMIGROUPS
215
THE IMBEDDING PROBLEM FOR FINITE MARKOV CHAINS
227
Sane remarks on the geometry of systems
237
MINIMAL REALIZATIONS OF NONLINEAR SYSTEMS
243
IRREDUCIBLE REALIZATIONS
253
ON THE INTERNAL STRUCTURE OP BILINEAR INPUTOUTPUT MAPS
263
OPTIMAL CONTROL OF DISCRETE BILINEAR SYSTEMS
275
DIFFUSIONS ON MANIFOLDS ARISING FROM CONTROLLABLE SYSTEMS
285

OPTIMAL CONTROL ON MANIFOLDS
185
PROBLEMS IN GEODESIC CONTROL
194
CONTROLLABILITY IN NONLINEAR SYSTEMS
205
SIGNAL DETECTION ON LIE GROUPS
295
SOME ESTIMATION PROBLEMS ON LIE GROUPS
305
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