Variable Time Impulse System Optimization with Continuous Control and Impulse Control

Abstract

Optimal control of a variable time impulse system is considered in this study. Besides impulse control, the system is assumed to operate with continuous control also. Necessary conditions for the optimization of such system are derived using the calculus of variations. A reinforcement based solution technique called a single network adaptive critic (SNAC) method is developed in this paper to obtain an optimal solution. Details of the SNAC-based algorithm are presented. Simulation examples are also presented for illustrative purposes.

Optimal two-impulse space interception with multiple constraints

“…In control theory, such an optimization problem is called an impulse control problem, in which there are state or control jumps (see, for example, Wang et al (2014) and references therein). Indeed there is no traditional continuous-time control variable in Problem 1, but instead, the unknown velocity impulses can be viewed as control input parameters defined at discrete-time instants.…”

“…Indeed there is no traditional continuous-time control variable in Problem 1, but instead, the unknown velocity impulses can be viewed as control input parameters defined at discrete-time instants. It can also be considered as an example of switched or hybrid systems with interior point constraints (see, for example, Bryson and Ho (1975), Sigal and Ben-Asher (2014), Wang et al (2014), and references therein). Next we consider a two-impulse space interception problem with a terminal position constraint on r M (t).…”

Online adaptive dynamic programming algorithm for linear fixed-time impulse hybrid systems

“…The methods of dynamic programming [3] and maximum principle [4] have been studied in the literature. Necessary conditions based on variational method are also presented [5], [6], [7] Adaptive dynamic programming(ADP) algorithm is evolving fast recently [8]. Two general categories of ADP method based on value iteration [9] and policy iteration [10] have been extensively studied.…”

Global Exponential Stability of Almost Periodic Solution for Neutral-Type Cohen-Grossberg Shunting Inhibitory Cellular Neural Networks with Distributed Delays and Impulses

“…Systems with short-term perturbations are often naturally described by impulsive differential equations. Owing to its theoretical and practical significance, the theory of impulsive differential equations has undergone a rapid development in the last couple of decades [ 29 – 33 ].…”