Proceedings ArticleDOI
The linear quadratic optimal control problem for infinite dimensional systems over an infinite horizon: Survey and examples
Alain Bensoussan,Michel C. Delfour,Sanjoy K. Mitter +2 more
- Vol. 15, Iss: 15, pp 746-751
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TLDR
A survey of currently available theory for systems the evolution of which can be described by semigroups of operators of class CO can be found in this paper, where the authors make a connection between the concepts of stabilizability and detectability and the problem of existence and uniqueness of solutions to the Riccati equation.Abstract:
Survey of currently available theory for systems the evolution of which can be described by semigroups of operators of class CO. Connection between the concepts of stabilizability and detectability and the problem of existence and uniqueness of solutions to the operator Riccati equation. Examples and Open problems.read more
Citations
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Journal ArticleDOI
Spline approximation for retarded systems and the Riccati equation
Franz Kappel,Dietmar Salamon +1 more
TL;DR: A new spline approximation scheme for retarded functional differential equations that preserves the product space structure of retarded systems and approximates the adjoint semigroup in a strong sense and guarantees the convergence of the solution operators for the differential Riccati equation.
Journal ArticleDOI
Representation of solutions and stability of linear differential-difference equations in a Banach space
TL;DR: In this article, the theory of linear delay differential equations is extended in three directions: the underlying phase space is allowed to be a Banach space so that equations with unbounded operators may be considered, and the delay is permitted to be effective over an infinite interval.
DissertationDOI
Adaptive observer design for parabolic partial differential equations
TL;DR: In this article, the observer design problem for a class of linear one-dimensional parabolic PDEs is addressed by means of a novel methodology based on polynomial optimization and Sum-of-Squares decomposition.
Journal ArticleDOI
Backstepping PDE Design: A Convex Optimization Approach
TL;DR: Backstepping design for boundary linear partial differential equation (PDE) is formulated as a convex optimization problem, and uniqueness and invertibility of the Fredholm-type transformation are proved for polynomial Kernels in the space of continuous functions.
Journal ArticleDOI
Uniform stability of autonomous linear stochastic functional differential equations in infinite dimensions
TL;DR: In this paper, the existence, uniqueness and continuity of mild solutions are established for stochastic linear functional differential equations in an appropriate Hilbert space which is particularly suitable for stability analysis, and the stability results derived in the retarded case are applied to coping with stability for a large class of neutral linear stochiastic systems.
References
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Book
Functional Analysis And Semi-Groups
Einar Hille,R. S. Phillips +1 more
TL;DR: The theory of semi-groups has been studied extensively in the literature, see as discussed by the authors for a survey of some of the main applications of semi groups in the context of functional analysis.
Journal ArticleDOI
Least squares stationary optimal control and the algebraic Riccati equation
TL;DR: In this paper, the optimal control of linear systems with respect to quadratic performance criteria over an infinite time interval is treated, and the integrand of the performance criterion is allowed to be fully quadratically in the control and the state without necessarily satisfying the definiteness conditions which are usually assumed in the standard regulator problem.
Journal ArticleDOI
On the general theory of control systems
TL;DR: In this paper, a general theory of control systems is outlined which answers many basic questions (what is controllable? why? how?) and gives a highly efficient method of computation.
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