2 edition of On the optimal control of bilinear systems and its relation to Lie algebras found in the catalog.
On the optimal control of bilinear systems and its relation to Lie algebras
Banks, Stephen P.
|Statement||by S. P. Banks and M. K. Yew.|
|Series||Research report / University of Sheffield. Department of Control Engineering -- no.275, Research report (University of Sheffield. Department of Control Engineering -- no.275.|
|Contributions||Yew, Melvyn Kam Keir.|
Associative algebras, Lie algebras, and bilinear forms November 4, 1 Introduction The most basic and important example of a Lie group is the group GL(n;R) of invertible n nmatrices. This group is very closely related to the asso-ciative algebra M(n;R) of all n nmatrices. In particular, the Lie algebra. Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then is that they can't see the problem. one day, perhaps you will find the final question. G.K. Chesterton. The Scandal of Father Brown 'The point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. van Gulik's The Chinese Maze Murders.
A control system is called bilinear if it is described by linear differential equations in which the control inputs appear as coefficients. The study of bilinear control systems began in the s and has since developed into a fascinating field, vital for the solution of many challenging practical control problems. Introduction --Symmetric systems: Lie theory --Systems with drift --Discrete-time bilinear systems --Systems with outputs --Examples --Linearization --Input structures --Matrix algebra --Lie algebras and groups --Algebraic geometry --Transitive Lie algebras. Series Title: Applied mathematical sciences (Springer-Verlag New York Inc.), v.
Suboptimal control for bilinear systems is discussed by use of an extension of the linear‐quadratic optimal control index. The design method of this bilinear suboptimal control system is presented. Its application to the moisture control of a paper‐making process is given as an example. The simulation results show that this suboptimal control system functions very well. The purpose of this paper is to study the observability of a class of systems for which the state space is a Lie group and the output space is a cosec space. The study of this type of system was initiated by Brockett [SIAM J. Control, 10 (), pp. –]. In this paper, Brockett’s observability results are generalized and necessary and sufficient conditions for observability are obtained.
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On the Optimal Control of Bilinear Systems and its relation to Lie algebras. by P, Banks and M. Yew Department of Con trol Engineering. University of Sheffield, Mappin Street, Sheffield. Sl 3JD. Research Report No The study of bilinear control systems began in the s and has since developed into a fascinating field, vital for the solution of many challenging practical control problems.
Its methods and applications cross inter-disciplinary boundaries, proving useful in areas as diverse as spin control in quantum physics and the study of Lie semigroups. The optimal control of bilinear systems is considered and related to the Lie algebra generated by the system matrices. Interesting results obtain when this Lie algebra is nilpotent.
On the optimal control of bilinear systems and its relation to Lie algebras: International Journal of Control Cited by: Banks S.P. and Yew M.K. On the optimal control of bilinear systems and its relation to Lie algebras. Int. Control ; 43(– CrossRef Google Scholar. The optimal control of bilinear systems is considered and related to the Lie algebra generated by the system matrices.
Interesting results obtain when this Lie algebra is nilpotent. View. from book Optimization and control of bilinear systems. Theory, An optimal control for bilinear systems is considered here to describe the.
control Lie algebra of a problem. The optimal control of bilinear systems is obtained by considering the Lie algebra generated by the system matrices.
It should be noted that we have obtained an open-loop control depending on the. Bourdache-Siguerdinljane has applied the method of Lie algebras to the study of optimal control regulation of satellites. Banks and M. Yew have studied the optimal control of energy consumption minimization for a class of bilinear systems and J.S.
Liu et al., have generalized this result for the class of affine nonlinear systems. The optimal control of bilinear systems to obtain by considering the Lie algebra generated by the system matrices.
Previous article in issue; S.P. Banks, M.K. YewOn the optimal control of linear system and its relation to Lie algebras. Internat. Control, 43 (3) (), p. MCSS is an international journal devoted to mathematical control and system theory, including system theoretic aspects of signal processing.
Its unique feature is its focus on mathematical system theory; it concentrates on the mathematical theory of systems with inputs and/or outputs and dynamics that are typically described by deterministic or stochastic ordinary or partial differential.
This motivates us to solve this problem using different methods to see if possible in the bilinear systems. Recently, Hoo optimal control for disturbance attenuation has received a great deal of attention in the linear systems [8, 17, 20] and nonlinear systems [21, 2, 16].
Focusing on the theory of integrable systems, this book introduces a class of optimal control problems on Lie groups, whose Hamiltonians, obtained through the Maximum Principle of optimality, shed new light on the theory of integrable systems.
These Hamiltonians provide an original and unified account of the existing theory of integrable systems. In particular, switched linear systems are in fact bilinear control systems with the control input representing the switching signal.
Written by one of the pioneers of nonlinear and geometric control theory, this book provides both an expository introduction to this important class of control systems and an up-to-date guide to its vast s: 1.
It is not an isomorphism in general (neither injective nor surjective), for instance for an abelian Lie algebra it is the zero map; Magnin actually checked that the Koszul homomorphism is zero for every nilpotent Lie algebra up to dimension 7.
Magnin also checks that the Koszul homomorphism itself is zero in many cases (this means that the. In example the author wants to derive the optimal system of sub-algebras of the heat equation.
Getting the commutator table and adjoint table is not a problem. But from there on. Control Lie Groups and Lie Algebras The problem of steering a quantum mechanical spin system we are interested in can be formulated as a control problem on a Lie group, or a homogeneous space.
Its solution involves (amongst others) methods from the theory of Lie groups,Lie algebras, andhomogeneousspaces. InthissectionIshall state only. We consider the optimal output tracking control (OOTC) problem for a class of bilinear systems with a quadratic performance index.
Using a successive approximation approach (SAA), the original non-linear optimal problem is transformed into a sequence of linear non-homogeneous two-point boundary value (TPBV) problems. In particular to understand controllability, optimal control, and certain properties of stochastic equations, Lie theoretic ideas are needed.
The framework considered here is probably the most natural departure from the usual linear system/vector space problems which have dominated the control systems. Lie Algebras of Vector Fields and Local Approximation of Attainable Sets.
Related Databases. Web of Science High-order maximum principles for the stability analysis of positive bilinear control systems. Optimal Control Applications and Methods Weakly Coupled Systems and Applications. Author: Zoran Gajic,Myo-Taeg Lim,Dobrila Skataric,Wu-Chung Su,Vojislav Kecman.
Publisher: CRC Press ISBN: Category: Technology & Engineering Page: View: DOWNLOAD NOW» Unique in scope, Optimal Control: Weakly Coupled Systems and Applications provides complete coverage of modern linear, bilinear, and nonlinear optimal control.
Abstract: Recently, attention has been focused on the class of bilinear systems, both for its applicative interest and intrinsic simplicity.
In fact, it appears that many important processes, not only in engineering, but also in biology, socio-economics, and ecology, may be modeled by bilinear systems.The study of bilinear control systems began in the s and has since developed into a fascinating field, vital for the solution of many challenging practical control problems.
Its methods and applications cross inter-disciplinary boundaries, proving useful in areas as diverse as spin control in quantum physics and the study of Lie semigroups Author: David Elliott.• V. Jurdjevic. Geometric Control Theory, Cambridge Univ. Press. (Systems on Lie groups and Homogeneous spaces; classiﬁcation of Lie algebras) • D.
L. Elliott. Bilinear Control Systems. Matrices in Action, Spinger (broad introduction to bilinear systems) • D. Liberzon Switching in Systems and Control, Birkhauser, 2.