Finite Dimensional Compensator Research Articles

Finite dimensional controller design for infinite dimensional systems: The circle criterion approach

The Hilbert space generalization of the circle criterion is used for the finite dimensional compensator design for unstable infinite dimensional systems. A design algorithm which generalizes the small gain based algorithm in [5] is presented.

むだ時間を含む系に対する有限次元補償器の設計

むだ時間を含む系に対する有限次元補償器の設計

Finite-dimensional Compensators for Distributed Parameter Systems Using TDP-Package

An easy-to-use, flexible simulator for distributed parameter systems is presented. Systems, described by parabolic partial differential equations, may be controlled with finite-dimensional compensators. Transfer functions may be measured, rational approximations may be done, and a versatile plotting module is available.

Suboptimal Stochastic Control of Discrete-Time Distributed Parameter Systems with Noisy and Partial Measurements

A parabolic type system described by a linear stochastic difference equation in a Hilbert space is considered. Incomplete and noisy measurements are available for the control of the stochastic system. Moreover, the plant dynamics involve uncertainties and randomness in the form of state-dependent, control-dependent, and additive white Gaussian noise with given statistics. The control problem is considered in the infinite-time interval and with a quadratic performance functional. Since under the above mentioned uncertainties the separation principle is not applicable, a suboptimal controller is designed which utilizes a finite-dimensional Kalman-Bucy type filter. The finite dimensional compensator gains are generated through simplified algebraic equations and their relevance to the infinite dimensional situation are briefly discussed

Finite-Dimensional Compensators for Infinite-Dimensional Systems with Unbounded Input Operators

This paper contains a design procedure for constructing finite dimensional compensators for a class of infinite dimensional systems with unbounded input operators. Applications to retarded functional differential systems with delays in the input or the output variable and to partial differential equations with boundary input operators are discussed.

On the existence of finite-dimensional compensators for retarded and neutral systems

In this paper we study a large class of neutral systems containing the class of retarded systems. A necessary and sufficient condition is given for the existence of a finite-dimensional compensator achieving exponential stability.

A self-Tuning Robust Controller for Semilinear Parabolic Systems

Publisher Summary The chapter presents the robust control theory for parabolic semi linear systems and to discuss the automatically tuning of the controller. The main idea in generalizing robust control theory for nonlinear systems is to use linearization technique. If there is a robust controller for the linear part of the system, and the nonlinear term is small enough, then the linear controller is able to stabilize and regulate the nonlinear system as well. To one's knowledge, there has been no work even in finite-dimensional robust control theory to treat nonlinear systems. In infinite-dimensional systems, Curtain presents a generalization of finite-dimensional compensator for semi linear systems. The chapter presents a definition of criterion, and the central idea is to select the controller parameter matrix to give the direction of steep or steepest descent, and ɛ should be fixed as a step length along this direction.

Stabilization of time-delay systems using finite-dimensional compensators

For linear time-invariant systems with one or more noncommensurate time delays, necessary and sufficient conditions are given for the existence of a finite-dimensional stabilizing feedback compensator. In particular, it is shown that a stabilizable time-delay system can always be stabilized using a finite-dimensional compensator. The problem of explicitly constructing finite-dimensional stabilizing compensators is also considered.

Pole assignment for distributed systems by finite-dimensional control

The question of pole assignment for a class of distributed systems by means of finite dimensional control is considered. A finite dimensional compensator is usually designed based on a reduced order model, and it is not a priori known what effect this will have on the original infinite dimensional system. Explicit formulas are derived which enable one to calculate the eigenvalues of the resulting closed loop system. For a certain compensator design, estimates are derived which can be used to guarantee stability a priori. Numerical results are also presented.

Finite Dimensional Compensators for Parabolic Distributed Systems with Unbounded Control and Observation

It is proved that for a class of parabolic distributed parameter systems with unbounded control and observation there exists a finite dimensional compensator using dynamic output feedback. Finite dimensional means here that the dynamics relating the input to the output is finite dimensional. A constructive design algorithm is presented and several examples are considered.

Compensator Design for Distributed Parameter Systems

Stabilization of linear finite dimensional systems is an important design problem in systems control theory and continues to receive much atten tion in the literature. The problem of stabilization of infinite dimensional linear systems is a much harder problem and the results are less complete. While results on state feedback stabilization and observers first appeared as early as 1975, the interest in these problems remained theoretical due to the fact that all observers turned out to be infinite dimensional. Of course what one would really like is a finite dimensional compensator scheme (preferably of low order) which could stabilize a given infinite dimensional system based on finite dimensional observations and inputs. The first result in this direc tion was obtained by Schumacher in 1981 and has since been followed by other finite dimensional compensator schemes which work essentially for the class of distributed systems isolated by Triggiani in 1975 in his fundamental result on feedback stabilization. In this survey an account is given of recent results on stabilization of infinite dimensional systems with the emphasis on implementable compensator schemes.

Compensators for infinite dimensional linear systems

The problem of stabilizing linear infinite dimensional systems by dynamic output feedback is discussed. The compensator is an auxiliary dynamic system driven by the current output (assumed finite dimensional) and the original system is controlled by a finite linear dimensional operation on this auxiliary state. The system will be stabilized if the combined original system, together with the auxiliary system, is exponentially stable. For a certain class of systems including parabolic and delay systems it is possible to design finite-dimensional compensators.

A multimodel approach to stochastic nash games

A decentralized filtering and control scheme is presented for obtaining low-order Nash equilibrium strategies for decision makers using different models of the same large-scale system. Multiparameter singular perturbations are employed to capture the multimodel nature of the fast dynamic subsystems interconnected through slow dynamic variables. The small parameters are appropriately scaled so that the variables in both time scales are well defined. The decision makers have decentralized information structures and are constrained to use only finite dimensional compensators of a specified dimension. It is shown that the proposed scheme is in fact the asymptotic limit of the exact solution as the small parameters go to zero.

Finite-dimensional compensator design for parabolic distributed systems with point sensors and boundary input

A compensator design is proposed for a large class of parabolic distributed systems. Basically, it is a modal approach utilizing known finite-dimensional algorithms for observer and stabilizer design. The observer is constructed from observations taken from point or averaging sensors and the compensator is a feedback of this observer and can be a "distributed" or "boundary" implementation. Explicit sufficient conditions are given for the convergence of this scheme.