The Dubins interval problem aims to find the shortest path of bounded curvature between two targets such that the departure angle from the first target and the arrival angle at the second target are constrained to two respective intervals. We propose a new and a simple algorithm to this problem based on the minimum principle of Pontryagin.

In “Dynamics and Control of DNA Sequence Amplification”, we have formulated the PCR optimal control problem and discussed the strategies for solving it. In this chapter, we implement those strategies and solve a simple PCR optimal control problem. The foundational concepts of Optimal Control were developed as early as the 1750s in classical mechanics as the principle of least action, a variatio...

In the present paper we deal with fully nonlinear two-dimensional smooth control systems with scalar input q̇ = f(q, u), q ∈ M , u ∈ U , where M and U are differentiable smooth manifolds of respective dimensions two and one. For such systems, we provide two microlocal normal forms, i.e., local in the state-input space, using the fundamental necessary condition of optimality for optimal control p...

In this paper, we investigate the minimal time problem for the guidance of a rocket, whose motion is described by its attitude kinematics and dynamics but also by its orbit dynamics. Our approach is based on a refined geometric study of the extremals coming from the application of the Pontryagin maximum principle. Our analysis reveals the existence of singular arcs of higher-order in the optima...

We consider a firm that sells seasonal goods. The firm seeks to reach a fixed level of goodwill at the end of the selling period, with the minimum total expenditure in promotional activities. We consider the linear optimal control problem faced by the firm which can only control the communication expenditure rate; communication is performed by means of advertising and sales promotion. Goodwill ...

1. Intoduction. In this paper, we discuss a class of optimal control problems on Lie groups, focusing on the special Euclidean groups SE(n). The models we discuss arise in the dynamics and control of unmanned aerial vehicles (Justh & Krishnaprasad 2002, 2004, 2005), in continuum models in biophysics (Wiggins 2001) and in fluid mechanics (Newton 2001). In his Ph.D. thesis (Baillieul 1975, 1978),...

To minimize fuel consumption in hybrid electric vehicles it is necessary to define a strategy for the management of the power flows within the vehicle. Under the assumption that the velocity to be developed by the vehicle is known a priori, this problem may be posed as a non linear optimal control problem with control and state constraints. We find the solution to this problem using the optimal...

We built and investigated analytically numerically a differential game model of Cournot oligopoly with consideration pollution for the general case symmetrical agents. conducted comparative analysis selfish agents’ behavior (a in normal form), their hierarchical organization (differential Stackelberg games), cooperation (optimal control problem) using individual collective indices relative effi...

The theory of control analyzes the proprieties of commanded systems. Problems of optimal control OC have been intensively investigated in the world literature for over forty years. During this period, series of fundamental results have been obtained, among which should be noted the maximum principle Pontryagin et al., 1962 and dynamic programming Bellman, 1963 . For many of the problems of the ...

We describe a generalization to Optimal Control of the theory of envelopes of the classical Calculus of Variations. This generalization extends our previous work, by allowing the use of \quasi-extremal" trajectories, i.e. trajectories that satisfy all the conditions of the Pontryagin Maximum Principle except for the fact that the sign of the constant 0 that appears in the Hamiltonian multiplyin...