Showing papers by "Hassan K. Khalil published in 1991"
TL;DR: In this article, Hoppensteadt's lemma for a parameterized family of systems with slowly varying inputs is restated and applied to the analysis of two-time-scale systems.
Abstract: Systems with slowly varying inputs are discussed as a special class of two-time-scale systems, and singular perturbation results are seen as convenient tools to analyze their properties. A lemma by F.C. Hoppensteadt (Trans. Amer. Math. Soc., vol.123, p.521-35, 1966) for a parameterized family of systems is restated and applied to the analysis of systems with slowly varying inputs. >
68 citations
26 Jun 1991
TL;DR: Layered neural networks are used in a nonlinear adaptive tracking problem where the plant is an unknown feedback-linearizable discrete-time system represented by an input-output model with relative degree higher than one.
Abstract: Layered neural networks are used in a nonlinear adaptive tracking problem. The plant is an unknown feedback-linearizable discrete-time system, represented by an input-output model with relative degree higher than one. A state space model of the plant is obtained to define the zero dynamics, which are assumed to be stable. Layered neural networks are used to model the plant and generate controls. Some error between the model and the plant is allowed. A dead-zone is specified in the updating rule. A local convergence result is given.
53 citations
TL;DR: In this paper, a steady-state optimal control problem is considered for nearly completely decomposable Markov chains, and an aggregation method for the value-determination equation is developed.
Abstract: A steady-state optimal control problem is considered for nearly completely decomposable Markov chains. In order to apply the policy iteration method of R.A. Howard (Dynamic Programming and Markov Processes, Cambridge, MA, MIT Press, 1960), a high-dimensional ill-conditioned system of algebraic equations must be solved in the value-determination step. Although algorithms exist for aggregation of the steady-state probability distribution problem, they only provide methods for computing the cost, not the dual variables. Using a singular perturbation approach, an aggregation method for the value-determination equation is developed. The aggregation method is developed in three steps. First, a class of similarity transformations that transform the system into a singularly perturbed form is developed. Second, an aggregation method to compute the steady-state probability distribution is derived. Third, this aggregation method is applied to the value determination step of Howard's method (1960). >
46 citations