Incentive Stackelberg-Nash Strategy with Disturbance Attenuation for Stochastic LPV Systems

The incentive Stackelberg-Nash strategy with disturbance attenuation for stochastic linear parameter-varying (LPV) systems with multiple decision makers is investigated. After establishing the modified stochastic bounded real lemma, linear quadratic control (LQC) for stochastic LPV systems with time-independent fixed gain is formulated. In order to determine the strategy set of multiple decision makers as followers, the incentive Stackelberg-Nash strategy is introduced for each player and the H-infinity constraint is imposed. The solvability conditions of the problem are established from cross-coupled matrix inequalities (CCMIs). The efficiency of the proposed strategy set is demonstrated using a numerical example.

[1]  Hiroaki Mukaidani,et al.  Gain-scheduled H∞ constraint Pareto optimal strategy for stochastic LPV systems with multiple decision makers , 2017, 2017 American Control Conference (ACC).

[2]  Jose B. Cruz,et al.  Stackelberg strategies and incentives in multiperson deterministic decision problems , 1984, IEEE Transactions on Systems, Man, and Cybernetics.

[3]  Gang Feng,et al.  Nonlinear Stochastic $H_2/H_\infty$ Control with $(x,u,v)$-Dependent Noise: Infinite Horizon Case , 2008, IEEE Transactions on Automatic Control.

[4]  Ricardo Salvador Sánchez Peña,et al.  LPV control of a 6-DOF vehicle , 2002, IEEE Trans. Control. Syst. Technol..

[5]  Bor-Sen Chen,et al.  Stochastic H2/H∞ control with state-dependent noise , 2004, IEEE Trans. Autom. Control..

[6]  Tamer Basar,et al.  Team-optimal closed-loop Stackelberg strategies in hierarchical control problems , 1980, Autom..

[7]  Masayuki Sato,et al.  Gain-scheduled output-feedback controllers depending solely on scheduling parameters via parameter-dependent Lyapunov functions , 2011, Autom..

[8]  O. Gomis-Bellmunt,et al.  Modeling and Validation of DFIG 3-MW Wind Turbine Using Field Test Data of Balanced and Unbalanced Voltage Sags , 2011, IEEE Transactions on Sustainable Energy.

[9]  Cheung-Chieh Ku,et al.  Gain-Scheduled H∞ Control for Linear Parameter Varying Stochastic Systems , 2015 .

[10]  Xun Yu Zhou,et al.  Linear matrix inequalities, Riccati equations, and indefinite stochastic linear quadratic controls , 2000, IEEE Trans. Autom. Control..

[11]  Alessandro N. Vargas,et al.  Optimal Control of DC-DC Buck Converter via Linear Systems With Inaccessible Markovian Jumping Modes , 2016, IEEE Transactions on Control Systems Technology.

[12]  Jose B. Cruz,et al.  An approach to discrete-time incentive feedback Stackelberg games , 2002, IEEE Trans. Syst. Man Cybern. Part A.

[13]  Hiroaki Mukaidani,et al.  Team-optimal Incentive Stackelberg Strategies for Markov Jump Linear Stochastic Systems with H∞ Constraint , 2017 .

[14]  Masayuki Sato.  Robust Gain-Scheduled flight controller using inexact scheduling parameters , 2013, 2013 American Control Conference.

[15]  Hiroaki Mukaidani,et al.  A Stochastic Multiple-Leader-Follower Incentive Stackelberg Strategy for Markov Jump Linear Systems , 2017, IEEE Control Systems Letters.

[16]  Hiroaki Mukaidani,et al.  Gain-Scheduled Nash Games with H∞ Constraint for Stochastic LPV Systems , 2017 .

[17]  Hiroaki Mukaidani,et al.  Robust Incentive Stackelberg Games for Stochastic LPV Systems , 2018, 2018 IEEE Conference on Decision and Control (CDC).