A nearly optimal control for spacecraft rendezvous with constrained controls

Abstract

A neural network Hamilton–Jacobi–Bellman (HJB) approach is introduced to deal with the spacecraft rendezvous problem with target spacecraft in arbitrary elliptical orbit. The Lawden equations are utilized to describe the relative motion of two spacecrafts. A generalized non-quadratic functional is introduced to describe constrained control. An approximate solution to the value function of the HJB equation corresponding to constrained controls is obtained by solving for a sequence of cost functions satisfying a sequence of Lyapunov equations. An inverse optimal controller is introduced to design the initial stabilizing admissible control for successive approximation. Furthermore, an optimal control law is obtained to stabilize the closed-loop system under constrained controls, and the spacecraft rendezvous mission can be accomplished with the nearly optimal controller. In comparison with the existing quadratic-regulation-based approaches used to deal with the rendezvous problem, which requires the value function of the nonlinear differential equations, the optimization factor and constrained control are taken into consideration simultaneously, and an approximate optimal constrained state feedback controller has been tuned a priori off-line. Stability analysis as well as simulation results are provided to illustrate the effectiveness of the presented approach.

Fusion of inverse optimal and model predictive control strategies

“…Therefore, IOC is an alternative approach to solve nonlinear optimal control problem while avoiding the tedious task of solving the HJB equation. In recent years, the inverse optimality approach has been increasingly used for solving the nonlinear optimal control problems in many real-time applications (Deng and Krstić, 1997; Krstic and Tsiotras, 1999; Li et al, 2011; Liao et al, 2016; Ornelas-Tellez et al, 2014). A main theorem related to IOC problem for discrete-time affine-in-input nonlinear systems has been given in Ornelas et al (2011).…”

Schooling for multi-agent systems via impulsive containment control algorithms with quantized information

“…To achieve the objective of collective behaviour a variety of decisions relevant to locally sensed information and limited communications have to be made. In the past decades, there have been a large amount of research on collective behaviours in the framework of multi-agent systems, to name just a few, non-linear systems (He et al, 2017; Yang and Ding, 2017), consensus (Ding et al, 2013a, 2013b, 2015; Jiang et al, 2015; Liu et al, 2012, 2016; Zhang et al, 2016), rendezvous (Bhattacharya et al, 2009; Liao et al, 2016), formation control (Ryan et al, 2004), leader-following consensus (Gao et al, 2016) event-driven consensus (Wen et al, 2016; Wu et al, 2015; Zhang et al, 2016) and flocking (Atrianfar and Haeri, 2013; Guan et al, 2012a; Han et al, 2016; Yu et al, 2016). Thus it can be seen that rudimentary studies on multi-agent behaviour based on cooperative control have been done a lot.…”

Partially independent control scheme for spacecraft rendezvous in near-circular orbits

“…A nearly optimal controller for spacecraft rendezvous with constrained controls was studied in Liao et al. 30 by a neural network Hamilton–Jacobi–Bellman approach. Interested readers can refer to Li et al., 31,32 Yang and Gao, 33 and Wan et al.…”

“…Zhou and Lam 29 designed the optimal and saturated linear feedback controller for spacecraft rendezvous in circular orbits by utilizing Lyapunov functions that were frequently used in the absolute stability theory. A nearly optimal controller for spacecraft rendezvous with constrained controls was studied in Liao et al 30 by a neural network Hamilton-Jacobi-Bellman approach. Interested readers can refer to Li et al, 31,32 Yang and Gao, 33 and Wan et al [34][35][36][37] for more results on this topic.…”