Optimal control problem described by impulsive differential equations with nonlocal boundary conditions

We study an optimal control problem in which the plant state is described by impulsive differential equations with nonlocal boundary conditions. By using the contraction mapping principle, we prove the existence and uniqueness of a solution of the nonlocal impulsive boundary value problem for given feasible controls. We compute the first and second variations of the performance functional and use them to obtain various necessary second-order optimality conditions.     

Controllability of impulsive differential systems with nonlocal conditions

The paper is concerned with the controllability of impulsive functional differential equations with nonlocal conditions. Using the measure of noncompactness and Mönch fixed-point theorem, we establish some sufficient conditions for controllability. Firstly, we require the equicontinuity of evolution system, and next we only suppose that the evolution system is strongly continuous. Since we do not assume that the evolution system generates a compact semigroup, our theorems extend some analogous results of (impulsive) control systems.     

Nonlinear hyperbolic systems with nonlocal boundary conditions

A system of nonlinear hyperbolic equations with boundary conditions of renewal type is studied as a general mathematical model for structured biological populations.     

Optimal control of impulsive hybrid systems

In this paper, we deal with optimization techniques for a class of hybrid systems that comprise continuous controllable dynamics and impulses (jumps) in the state. Using the mathematical techniques of distributional derivatives and impulse differential equations, we rewrite the original hybrid control system as a system with autonomous location transitions. For the obtained auxiliary dynamical system and the corresponding optimal control problem (OCP), we apply the Lagrange approach and derive the reduced gradient formulas. Moreover, we formulate necessary optimality conditions for the above hybrid OCPs, and discuss the newly elaborated Pontryagin-type Maximum Principle for impulsive OCPs. As in the case of the conventional OCPs, the proposed first order optimization techniques provide a basis for constructive computational algorithms.     

Optimal control problems with two-point boundary conditions

We study convex as well as some nonconvex optimal control problems for infinite-dimensional first-order linear differential systems with two-point boundary conditions of antiperiodic type. The main advance of this paper over existing related papers consists in the fact that the domains of the possible nonlinear operators involved in the boundary conditions have empty interior. Applications to boundary control systems governed by partial differential equations describing incompressible flows with fading memory and steering a temperature field are given.This work was supported in part by the National Science Foundation under Grant No. DMS-91-11794.     

Optimal control computation for parabolic systems with boundary conditions involving time delays

In this paper, we consider a class of optimal control problems involving a second-order, linear parabolic partial differential equation with Neumann boundary conditions. The time-delayed arguments are assumed to appear in the boundary conditions. A necessary and sufficient condition for optimality is derived, and an iterative method for solving this optimal control problem is proposed. The convergence property of this iterative method is also investigated.On the basis of a finite-element Galerkin's scheme, we convert the original distributed optimal control problem into a sequence of approximate problems involving only lumped-parameter systems. A computational algorithm is then developed for each of these approximate problems. For illustration, a one-dimensional example is solved.     

Optimal control of impulsive switched systems with minimum subsystem durations

This paper presents a new computational approach for solving optimal control problems governed by impulsive switched systems. Such systems consist of multiple subsystems operating in succession, with possible instantaneous state jumps occurring when the system switches from one subsystem to another. The control variables are the subsystem durations and a set of system parameters influencing the state jumps. In contrast with most other papers on the control of impulsive switched systems, we do not require every potential subsystem to be active during the time horizon (it may be optimal to delete certain subsystems, especially when the optimal number of switches is unknown). However, any active subsystem must be active for a minimum non-negligible duration of time. This restriction leads to a disjoint feasible region for the subsystem durations. The problem of choosing the subsystem durations and the system parameters to minimize a given cost function is a non-standard optimal control problem that cannot be solved using conventional techniques. By combining a time-scaling transformation and an exact penalty method, we develop a computational algorithm for solving this problem. We then demonstrate the effectiveness of this algorithm by considering a numerical example on the optimization of shrimp harvesting operations.     

Some sufficient conditions for oscillation of impulsive delay hyperbolic systems with Robin boundary conditions

This paper deals with the oscillation problems of delay hyperbolic systems with impulses. Some sufficient conditions for oscillations of impulsive delay hyperbolic systems with Robin boundary conditions are obtained and the criteria of oscillation of the systems are established.     

Existence for neutral impulsive differential inclusions with nonlocal conditions

In this paper, by using a fixed point theorem for condensing multi-valued maps, we have investigated the existence of mild solutions for a class of semilinear impulsive neutral functional differential inclusions with nonlocal conditions. As an application, an example has been presented to illustrate the results obtained.     

Existence results for impulsive differential inclusions with nonlocal conditions

In this paper, we investigate the existence of mild solutions for first order impulsive differential inclusions with nonlocal condition in Banach spaces. Our result is obtained using another nonlinear alternative of Leray-Schauder type. An example is also presented.     

Nondensely defined evolution impulsive differential inclusions with nonlocal conditions

In this paper, we shall establish sufficient conditions for the existence of integral solutions for some nondensely defined evolution impulsive differential inclusions in Banach spaces with nonlocal conditions.     

Existence for neutral impulsive functional differential equations with nonlocal conditions

In this paper, we study a class of neutral impulsive functional differential equations with nonlocal conditions. We suppose that the linear part satisfies the Hille-Yosida condition on a Banach space and it is not necessarily densely defined. We give some sufficient conditions ensuring the existence of integral solutions and strict solutions. To illustrate our abstract results, we conclude this work by an example.     

Solvability of the -Laplacian with nonlocal boundary conditions

Rather mild sufficient conditions are provided for the existence of positive solutions of a boundary value problem of the form

which unify several cases discussed in the literature. In order to formulate these conditions one needs to know only properties of the homeomorphism and have information about the level of growth of the response operator F. No metric information concerning the linear operators L₀,L₁ in the boundary conditions is used, except that they are positive and continuous and such that L_j(1)<1 j{0,1}.     

Optimal control of stochastic differential equations with dynamical boundary conditions

In this paper we investigate the optimal control problem for a class of stochastic Cauchy evolution problems with nonstandard boundary dynamic and control. The model is composed by an infinite dimensional dynamical system coupled with a finite dimensional dynamics, which describes the boundary conditions of the internal system. In other terms, we are concerned with nonstandard boundary conditions, as the value at the boundary is governed by a different stochastic differential equation.