This paper studies the stabilization for a kind of linear and impulse control systems in finite-dimensional spaces, where impulse instants appear periodically. We present several characterizations on the stabilization; show how to design feedback laws; and provide locations for impulse instants to ensure the stabilization. In the proofs of these results, we set up a discrete LQ problem; derived a discrete dynamic programming principle, built up a variant of Riccati's equation; applied repeatedly the Kalman controllability decomposition; and used a controllability result built up in [17].
This paper addresses the problem of impulsive control and optimization for linear dynamical systems. An essential benefit of impulsive control is that such controls may be simpler to implement and involve cheaper control mechanisms. We shall establish some impulsive controllability criteria and obtain some conditions for the existence of optimal solutions. An example is also worked though employing Maple symbolic computation. Optimal control problem of semilinear evolutionary distributed parameter systems with impulse controls is considered. Necessary conditions of optimal controls are derived. The result generalises the usual Pontryagin's maximum principle. We consider the optimal control problem of minimizing some quadratic functional over all possible solutions of an internally controlled multidimensional heat equation with a periodic terminal state constraint. This problem has a unique optimal solution, which can be characterized by an optimality system derived from the Pontryagin maximum principle. We define two approximations of this optimal control problem. The first one is an impulse approximation and consists of considering a system of linear heat equations with impulse control. The second one is obtained by the sample-and-hold procedure applied to the control, resulting in a sampled-data approximation of the controlled heat equation. We prove that both problems have a unique optimal solution, and we establish precise error estimates for the optimal controls and optimal states of the initial problem with respect to its impulse and sampled-data approximations.  This paper is mainly concerned with a class of optimal control problems of systems governed by the nonlinear impulsive differential equation on time scale. The reasonable weak solution of nonlinear impulsive differential equation on time scale is introduced and the existence and uniqueness of the weak solution and its properties are presented. By @math strong @math weak lower semicontinuity of integral functional on time scale, we give the existence of optimal controls. Using integration by parts formula on time scale, the necessary conditions of optimality are derived. An example on mathematical programming is also presented for demonstration.