Showing papers by "Hassan K. Khalil published in 1984"
TL;DR: In this paper, the composite feedback control strategy of continuous-time singularly perturbed systems is extended to the new problem and asymptotic behavior of the optimal solution as the perturbation parameter tends to zero is studied.
Abstract: Linear quadratic regulators for singularly perturbed difference equations are considered. Asymptotic behaviour of the optimal solution as the perturbation parameter tends to zero is studied. The composite feedback control strategy of continuous-time singularly perturbed systems is extended to the new problem.
72 citations
TL;DR: In this paper, the Kalman filter is decomposed into separate slow-mode and fast-mode filters via the use of a decoupling transformation, and a near-optimal control law is derived by approximating the coefficients of the optimal control law.
Abstract: This paper presents a new approach to the decomposition and approximation of linear-quadratic-Gaussian estimation and control problems for singularly perturbed systems. The Kalman filter is decomposed into separate slow-mode and fast-mode filters via the use of a decoupling transformation. A near-optimal control law is derived by approximating the coefficients of the optimal control law. The order of approximation of the optimal performance is 0(\mu^{N}) where N is the order of approximation of the coefficients.
51 citations
TL;DR: In this paper, it was shown that the instability phenomenon might take place even when the reduced-order design model is strictly proper, even if the neglected modes are asymptotically stable.
Abstract: In an earlier note it was shown that designing a nonstrictly proper output feedback compensator using a model that neglects parasitic elements might lead to an unstable closed-loop system even when the neglected modes are asymptotically stable. The purpose of this note is to show that this instability phenomenon might take place even when the reduced-order design model is strictly proper.
35 citations
01 Jan 1984
TL;DR: In this paper, the design of stabilizing feedback control of singularly perturbed diserete-time systems is decomposed into slow and fast controllers which are combined to form the composite control.
Abstract: The design of stabilizing feedback control of singularly perturbed diserete-time systems is decomposed into the design of slow and fast controllers which are combined to form the composite control. Composite control strategies are developed for the case of single rate measurements (all variables are measured at the same rate) as well as for the case of multirate measurements (slow variables are measured at a rate slower than that of fast variables).
23 citations
TL;DR: This note presents an algorithm for decomposing the system into a set of isolated subsystems at different time scales to construct a uniform asymptotic approximation to A(\epsilon)t.
Abstract: An implicit singularly perturbed system \dot{x} = A(\epsilon)x , where A(0) is singular, is considered. This note presents an algorithm for decomposing the system into a set of isolated subsystems at different time scales. The decomposed form of the system is used to construct a uniform asymptotic approximation to \exp (A(\epsilon)t) .
16 citations
TL;DR: In this paper, an asymptotic approximation of nonlinear autonomous singularly perturbed systems on the semi-infinite time interval [0, ∞] is considered, and it is shown that the conditions employed in [1] to guarantee stability ensure that the solution of the full system converges uniformly as g3→ 0 to the approximation derived from the reduced and boundary-layer systems.
11 citations
01 Dec 1984
TL;DR: It is shown that the controllability and observability properties of the slow and fast subsystems obtained after applying feedback are invariant with respect to the feedback gain.
Abstract: Feedback control of implicit singularly perturbed linear systems is considered. Under certain conditions, given in the paper, the system equations can be brought into the standard singularly perturbed form via state transformation and/or feedback. It is shown that the controllability and observability properties of the slow and fast subsystems obtained after applying feedback are invariant with respect to the feedback gain.
6 citations
TL;DR: The study reveals that for the well-posedness of multimodel strategies control agents need to communicate their observations and decisions.
1 citations