1 2 Abstract---Motivated by the fact that determining a feedback solution for the optimal control problem under constraints is a hard task we introduce the concept of relative optimality, roughly optimality for a specific (nominal) plant initial condition. We consider a generic discrete-time finite-horizon constrained optimal control problem for linear systems, and we seek for a state feedback ...

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 ...

A high order optimal control strategy is proposed in this work, based on the use of differential algebraic techniques. In the frame of orbital mechanics, differential algebra allows to represent, by high order Taylor polynomials, the dependency of the spacecraft state on initial conditions and environmental parameters. The resulting polynomials can be manipulated to obtain the high order expans...

A relatively optimal control is a stabilizing controller that, without initialization nor feedforwarding and tracking the optimal trajectory, produces the optimal (constrained) behavior for the nominal initial condition of the plant. In a previous work, a linear dynamic relatively optimal control, for discrete–time linear systems, was presented. Here a static solution is shown, namely a dead–be...

Almost-global orientation trajectory tracking for a rigid body with external actuation has been well studied in the literature, and in the geometric setting as well. The tracking control law relies on the fact that a rigid body is a simple mechanical system (SMS) on the 3−dimensional group of special orthogonal matrices. However, the problem of designing feedback control laws for tracking using...

Air Traac Management (ATM) of the future allows for the possibility of free ight, in which aircraft choose their own optimal routes, altitudes, and velocities. The safe and fair resolution of trajectory connicts between aircraft is necessary to the success of such a distributed control system. In this paper, we propose a method to synthesize provably safe connict resolution maneuvers. The metho...

The judicious use of buffering capacity is important in the development of future continuous pharmaceutical manufacturing processes. The potential benefits are investigated of using optimal-averaging level control for tanks that have buffering capacity for a section of a continuous pharmaceutical pilot plant involving two crystallizers, a combined filtration and washing stage and a buffer tank....

Hybrid dynamical systems have proven to be a powerful modeling abstraction, yet fundamental questions regarding their dynamical properties remain. In this paper, we develop a novel solution concept for a class of hybrid systems, which is a generalization of Filippov’s solution concept. In the mathematical theory, these hybrid Filippov solutions eliminate the notion of Zeno executions. Building ...

In this paper, a new approach to stability for fractional order control system is proposed. Here a dynamic system whose behavior can be modeled by means of differential equations involving fractional derivatives. Applying Laplace transforms to such equations, and assuming zero initial conditions, causes transfer functions with no integer powers of the Laplace transform variable s to appear. In ...

In this paper, a nonlinear system aiming at reducing the signal transmission rate in a networked control system is constructed by adding nonlinear constraints to a linear feedback control system. Its stability is investigated in detail. It turns out that this nonlinear system exhibits very interesting dynamical behaviors: in addition to local stability, its trajectories may converge to a nonori...