Infinite time linear quadratic stackelberg game problem for unknown stochastic discrete‐time systems via adaptive dynamic programming approach

Abstract

In this paper, we propose an adaptive dynamic programming (ADP) approach to solve the infinite horizon linear quadratic (LQ) Stackelberg game problem for unknown stochastic discrete‐time systems with multiple decision makers. Firstly, the stochastic LQ Stackelberg game problem is converted into the deterministic problem by system transformation. Next, a value iteration ADP approach is put forword and the convergence is given. Thirdly, in order to implement the iterative method, back propagation neural network (BPNN) is chosen to design model network, critic network and action network to approximate the unknown systems, objective functions and Stackelberg strategies. Finally, simulation results show that the algorithm is effective.

Adaptive critic learning for event‐triggered safe control of nonlinear safety‐critical systems

“…Situation 1: if t ∈ [𝜏 𝑗 , 𝜏 𝑗+1 ), we can get the derivative of (40) when the events are not triggered as follows; substituting (18) and (19)…”

“…This structure is similar to reinforcement learning (RL) and adaptive dynamic programming (ADP), so ACL, ADP, and RL are taken as synonyms. Because of the advantages of ACL technology, it has been widely used in continuous-times control [16,17], discrete-times control [18,19], robust control [20,21], fault-tolerant control [22], and many other fields [23]. Therefore, scholars have adopted ACL-based methods to design optimal security controllers and promoted the rapid development of this field in recent years.…”

Uncertain random linear quadratic control with multiplicative and additive noises

“…Remark Note that when the control system in problem () is only disturbed by random variables or uncertain variables, the uncertain random system becomes stochastic system or uncertain system, and the LQ optimal control problems of the separate system [4,12,13,28] have been tackled in recent years. Compared with previous studies [4,12,13,28], we use the dynamic programming to solve optimal control problems. We study optimal control for uncertain random systems.…”

“…In recent years, most of the researches on optimal control problems with stochastic noises or uncertain noises [27,28]. However, the system in practice is disturbed by not only stochastic noises but also uncertain noises [26].…”

Distributed Nash equilibrium seeking of aggregative games under networked attacks

“…The aim of every player in aggregative games is to find a Nash equilibrium to minimize its payoff function which not only depends its own decision variable but also the aggregate of all players' decision variables. To achieve this, some distributed Nash equilibrium seeking algorithms have been proposed [5][6][7][8][9][10][11][12][13][14][15][16]. The paper [16] proposed distributed consensus-based strategies to seek the Nash equilibrium of the box-constrained aggregative games.…”