H∞ Tracking Control for a Class of Nonlinear Systems

Develops the theory for tracking control using the nonlinear H∞ control design methodology for a class of nonlinear input affine systems. The authors use a two-step process of first designing the feedforward part of the controller to design for perfect trajectory following and then design the feedback part of the controller using nonlinear H∞ regulator theory. Results for infinite-time and finite-time horizons are presente

On the order of singular optimal control problems

In singular optimal control problems, the functional form of the optimal control function is usually determined by solving the algebraic equation which results by successively differentiating the switching function until the control appears explicitly. This process defines the order of the singular problem. Order-related results are developed for singular linear-quadratic problems and for a bilinear example which gives new insights into the relationship between singular problem order and singular are order.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45218/1/10957_2004_Article_BF00934035.pd

Controllability on infinite-dimensional manifolds

Following the unified approach of A. Kriegl and P.W. Michor (1997) for a treatment of global analysis on a class of locally convex spaces known as convenient, we give a generalization of Rashevsky-Chow's theorem for control systems in regular connected manifolds modelled on convenient (infinite-dimensional) locally convex spaces which are not necessarily normable.Comment: 19 pages, 1 figur

Second-order necessary conditions in optimal control: Accessory-problem results without normality conditions

An optimal control problem, which includes restrictions on the controls and equality/inequality constraints on the terminal states, is formulated. Second-order necessary conditions of the accessory-problem type are obtained in the absence of normality conditions. It is shown that the necessary conditions generalize and simplify prior results due to Hestenes (Ref. 5) and Warga (Refs. 6 and 7).Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45219/1/10957_2004_Article_BF00934437.pd

Generalized Isoperimetric Problem

In this paper the differential equations describing the minimal length curves satisfying the integral constraining relations of a general type are obtained. Moreover, an additional necessary condition supplementing Pontryagin maximum principle for the generalized isoperimetric problem is established. All results are illustrated by the analysis of generalized Dido's problem

Distinguishing Causal and Acausal Temporal Relations

Abstract. In this paper we propose a solution to the problem of distinguishing between causal and acausal temporal sets of rules. The method, called the Temporal Investigation Method for Enregistered Record Sequences (TIMERS), is explained and introduced formally. The input to TIMERS consists of a sequence of records, where each record is observed at regular intervals. Sets of rules are generated from the input data using different window sizes and directions of time. The set of rules may describe an instantaneous relationship, where the decision attribute depends on condition attributes seen at the same time instant. We investigate the temporal characteristics of the system by changing the direction of time when generating temporal rules to see whether a set of rules is causal or acausal. The results are used to declare a verdict as to the nature of the system: instantaneous, causal, or acausal. 1