Control Of Linear Time-delay Systems Research Articles

A descriptor system approach to H/sub ∞/ control of linear time-delay systems

The output-feedback H/sub /spl infin// control problem is solved for continuous-time, linear, retarded and neutral-type systems. A delay-dependent solution is obtained in terms of linear matrix inequalities (LMIs) by using a descriptor model transformation of the system and by applying P. Park's inequality (1999) for bounding cross-terms. A state-feedback solution is derived for systems with polytopic parameter uncertainties. An output-feedback controller is then found by solving two LMIs, one of which is associated with a descriptor time-delay "innovation filter". The cases of instantaneous and delayed measurements are considered. Numerical examples are given which illustrate the effectiveness of the new theory.

Delay-dependent robust and reliable H∞ control for uncertain time-delay systems with actuator failures

This paper focuses on the synthesis problem of delay-dependent robust and reliable H ∞ control for linear time-delay systems with norm-bounded time-varying parameter uncertainty in the state and delayed-state matrices and also with actuator failures among a prespecified subset of actuators. Actuator failures are considered as disturbance signals of arbitrary values to the system. An LMI (Linear Matrix Inequality) method is given for the delay-dependent memoryless state feedback synthesis problem to quadratically stabilize the given systems with an H ∞-norm bound constraints on attenuation of augmented disturbances, including failure signals in cases of actuator failures for any admissible uncertainty.

H∞-Control for Linear Time-Delay Systems with Markovian Jumping Parameters

This paper deals with the robust H∞-control problem for uncertain continuous-time linear time-delay systems with Markovian jumping parameters. Based on Lyapunov functional approach, a sufficient condition that assures the robust stochastic stabilizability and preserves the H∞-disturbance attenuation for the uncertain class of linear time-delay systems with Markovian jumping parameters is established. The uncertainties considered in this paper are of the norm-bounded type. A numerical example is given to demonstrate the usefulness of the results.

Discrete-time optimal control for linear time-delay systems with deterministic disturbances

Presents an approach to formulating the optimisation problem of linear discrete-time systems with delays. It is shown that, by properly augmenting the state vector, the optimisation problem of achieving closed-loop poles inside a circular region with centre ( beta , 0) and radius alpha , where alpha + mod beta mod <or=1, and at the same time accommodating deterministic disturbances, can be reduced to a standard discrete quadratic regulator problem with no delays. It is also shown that the dynamical feedback controller, which minimises the performance to achieve poles inside a circular region and accommodate disturbances, can be implemented via an auxiliary linear dynamical system. The implementation scheme is effective in many applications.

Optimal control of linear time-delay systems via general orthogonal polynomials

A Padé approximation is introduced to transform the delay differential equation into an ordinary equation. The optimal control of a linear time delay system with quadratic performance index is then derived via general orthogonal polynomials. The adjoint equation is also extracted using a maximum principle. The state and adjoint equations can be solved by using the general orthogonal polynomials and the difficulty encountered when using a two-point boundary condition is circumvented. Examples are given to demonstrate the usefulness of the proposed method.

Optimal control of linear time-delay systems via general orthogonal polynomials

A Pade approximation is introduced to transform the delay differential equation into an ordinary equation. The optimal control of a linear time delay system with quadratic performance index is then derived via general orthogonal polynomials. The adjoint equation is also extracted using a maximum principle. The state and adjoint equations can be solved by using the general orthogonal polynomials and the difficulty encountered when using a two-point boundary condition is circumvented. Examples are given to demonstrate the usefulness of the proposed method.

Direct approach for the optimal control of linear time-delay systems via shifted Legend re polynomials

The present paper proposes a direct approach to the optimal control of linear time-delay systems. In the first step, both control and state are approximated by shifted Legendre polynomials, and then the Legendre-coefficients vector of states can be expressed in terms of the Legend re-coefficients vector of controls. In the second step, the relation between Legendre-coefficients vectors of states and controls, which satisfies the state equations approximately, is introduced into the performance index. Next, the variational principle is applied to find the Legendre-coefficients vector of near-optimal control that minimizes the performance index directly. In the present approach, the Legendre-coefficients vector of sub-optimal control can be obtained directly from a set of algebraic equations. Thus, both difficulties in solving simultaneous partial differential equations of large dimension, or in solving n sets of ordinary differential equations, are avoided.

Proper stable Bezout factorizations and feedback control of linear time-delay systems†

This paper deals with the existence and construction of proper stable Bezout factorizations of transfer function matrices of linear time-invariant systems with commensurate time delays. Existence of factorizations is characterized in terms of spectral controllability (or spectral observability)of the co-canonical (or canonical) realization of the transfer function matrix. An explicit procedure for computing proper stable Bezout factorizations is given in terms of a specialized ring of pure and distributed time delays. This procedure is utilized to construct finite-dimensional stabilizing compensators and to construct feedback systems which assign the characteristic polynomial of the closed-loop system.

A modified Smith predictor and controller for unstable processes with time delay

An integrated design procedure is developed for a modified Smith predictor and associated controller for linear time-delay systems having transfer functions of the form k 1, A exp (—sT)/B, where A and B are monic polynomials in s of degree n — l and n, respectively. A is Hurwitz and B has a single right-half-plane root at s = λ. For l=1,2,3, an augmented PI controller guarantees asymptotic stability for λT less than an l-dependent limit. The procedure for l = 3 is extended to l = 4 with the introduction of derivative action into the controller. Design arguments are on root locus topology, and on Nyquist analysis applied to an auxiliary system.

Optimal Output-Feedback Controllers for Linear Time-Delay Systems

Optimal control of linear time-delay systems with a quadratic performance criterion is discussed. The optimal strategy is searched among the class of controllers that use only output information. The optimal gains are characterized by certain Riccati-type equations.

On the controllability of linear time-delay systems with piecewise constant inputs †

An important problem in system theory is whether a dynamic system is controllable with inputs from the class of admissible controls. This paper treats the case whore the dynamic system is described by differential-difference equations and the class of admissible control inputs consists of piecewise constant functions. This situation arises in practice in the on-line control of some industrial processes. Euclidean space and function space controllability are studied, and controllability conditions which are both necessary and sufficient are derived for R n and R n null controllability. Simple algebraic conditions are also given for two special cases. In the study of function space null controllability the concept of j-controllability is introduced and a sufficiency theorem is stated in terms of this new concept.

Optimal control of linear time-delay systems

A method is presented whereby an optimal control may be obtained for a linear time-varying system with time delay. The performance criterion is quadratic with a fixed, finite upper limit, and results in a set of differential equations with boundary conditions whose solution yields an optimal feedback control. A numerical technique is developed for the solution of the differential equations, and two examples are worked.