Inverse Open-Loop Noncooperative Differential Games and Inverse Optimal Control

The higher goal of rehabilitation robot is to aid a person to achieve a desired functional task (e.g., tracking trajectory) based on assisted-as-needed principle. To this goal, a new adaptive inverse optimal hybrid control (AHC) combining inverse optimal control and actor-critic learning is proposed. Specifically, an uncertain nonlinear rehabilitation robot model is firstly developed that includes human motor behavior dynamics. Then, based on this model, an open-loop error system is formed; thereafter, an inverse optimal control input is designed to minimize the cost functional and a NN-based actor-critic feedforward signal is responsible for the nonlinear dynamic part contaminated by uncertainties. Finally, the AHC controller is proven (through a Lyapunov-based stability analysis) to yield a global uniformly ultimately bounded stability result, and the resulting cost functional is meaningful. Simulation and experiment on rehabilitation robot demonstrate the effectiveness of the proposed control scheme.

Download Full-text

Inverse Optimal Control for Identification in Non-Cooperative Differential Games

IFAC-PapersOnLine ◽

10.1016/j.ifacol.2017.08.2538 ◽

2017 ◽

Vol 50 (1) ◽

pp. 14909-14915 ◽

Cited By ~ 3

Author(s):

Simon Rothfuß ◽

Jairo Inga ◽

Florian Köpf ◽

Michael Flad ◽

Sören Hohmann

Keyword(s):

Optimal Control ◽

Differential Games ◽

Inverse Optimal Control ◽

Cooperative Differential Games

Download Full-text

Stochastic differential games and inverse optimal control and stopper policies

International Journal of Control ◽

10.1080/00207179.2017.1407041 ◽

2017 ◽

Vol 92 (7) ◽

pp. 1692-1706

Author(s):

Tanmay Rajpurohit ◽

Wassim M. Haddad ◽

Wei Sun

Keyword(s):

Optimal Control ◽

Differential Games ◽

Stochastic Differential Games ◽

Inverse Optimal Control

Download Full-text

Stochastic differential games and inverse optimal control and stopper policies

2017 IEEE 56th Annual Conference on Decision and Control (CDC) ◽

10.1109/cdc.2017.8264487 ◽

2017 ◽

Cited By ~ 1

Author(s):

Tanmay Rajpurohit ◽

Wassim M. Haddad

Keyword(s):

Optimal Control ◽

Differential Games ◽

Stochastic Differential Games ◽

Inverse Optimal Control

Download Full-text

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

ESAIM Control Optimisation and Calculus of Variations ◽

10.1051/cocv/2019057 ◽

2020 ◽

Vol 26 ◽

pp. 41

Author(s):

Tianxiao Wang

Keyword(s):

Optimal Control ◽

Closed Loop ◽

Optimal Control Problems ◽

Mean Field ◽

Open Loop ◽

Time Inconsistency ◽

Control Problems ◽

Linear Quadratic ◽

Linear Quadratic Optimal Control ◽

Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

Download Full-text