Weak Measurable Optimal Controls for the Problems of Bolza

Two sufficiency theorems for parametric and a nonparametric problems of Bolza in optimal control are derived. The dynamics of the problems are nonlinear, the initial and final states are free, and the main results can be applied when nonlinear mixed time-state-control inequality and equality constraints are presented. The deviation between admissible costs and optimal costs around the optimal control is estimated by functionals playing the role of the square of some norms.

Global Positive Periodic Solutions for Periodic Two-Species Competitive Systems with Multiple Delays and Impulses

A set of easily verifiable sufficient conditions are derived to guarantee the existence and the global stability of positive periodic solutions for two-species competitive systems with multiple delays and impulses, by applying some new analysis techniques. This improves and extends a series of the well-known sufficiency theorems in the literature about the problems mentioned previously.

On the Synthesis of Compensators for Nonovershooting Step Response

A problem of practical and theoretical interest in control is the synthesis of a compensator such that the closed-loop system step response does not overshoot. In this paper we present an approach for synthesizing such compensators for SISO, minimum phase plants. The essential idea of the technique is to appropriately locate the closed loop poles with respect to fixed and added zeros. Admissible pole-zero locations are characterized by two sufficiency theorems.

Isoperimetric Problems in the Calculus of Variations

We are concerned with establishing sufficiency theorems for minima of simple integrals of the parametric type in a class of curves with variable end points and satisfying isoperimetric side conditions. The results which are obtained involve no explicit assumptions of normality. Such results can be derived by transforming our problem to a problem of Bolza and using the latest developments in the theory of that problem. More recently [6] an indirect method of proof has been published. Our object is to present a direct method of proof without transformation of the problem which is based upon a generalization of the classical theory of fields.