Robust tracking control for magnetic wheeled mobile robots using adaptive dynamic programming

Formation control scheme with reinforcement learning strategy for a group of multiple surface vehicles

“…Therefore, many scholars investigate control designs for each agent with the Euler-Lagrange (EL) dynamic equation, as well as MAS control systems. However, due to the difficulty in unifying the optimal control task and the trajectory tracking problem, there exist a few optimal control approaches, [1][2][3][4] but many typical robust adaptive control schemes [5][6][7][8][9][10] for each agent are represented under the EL dynamic equation. Several authors utilize the description of the Hamiltonian function to find the updating laws of actor/critic (AC) neural networks (NN) [1][2][3][4] after establishing tracking error models under a time-invariant representation for cooperating manipulators, 1,2 surface vehicles (SVs), 3 or wheeled mobile robots (WMRs).…”

“…However, due to the difficulty in unifying the optimal control task and the trajectory tracking problem, there exist a few optimal control approaches, [1][2][3][4] but many typical robust adaptive control schemes [5][6][7][8][9][10] for each agent are represented under the EL dynamic equation. Several authors utilize the description of the Hamiltonian function to find the updating laws of actor/critic (AC) neural networks (NN) [1][2][3][4] after establishing tracking error models under a time-invariant representation for cooperating manipulators, 1,2 surface vehicles (SVs), 3 or wheeled mobile robots (WMRs). 4 On the other hand, based on the foundation of traditional nonlinear control laws, some remarkable progress is mentioned, including the extension of the event-triggered strategy 6 and the development of special transformation functions in adaptive backstepping methods to handle constraint requirements.…”

“…Several authors utilize the description of the Hamiltonian function to find the updating laws of actor/critic (AC) neural networks (NN) [1][2][3][4] after establishing tracking error models under a time-invariant representation for cooperating manipulators, 1,2 surface vehicles (SVs), 3 or wheeled mobile robots (WMRs). 4 On the other hand, based on the foundation of traditional nonlinear control laws, some remarkable progress is mentioned, including the extension of the event-triggered strategy 6 and the development of special transformation functions in adaptive backstepping methods to handle constraint requirements. 5 However, as the objective in robotic control systems involves not only trajectory tracking but also different responses, optimal control strategies are utilized more efficiently.…”

“…From an optimal control standpoint, the objective is to ensure the minimization of a given cost function that corresponds to specific performance requirements. However, due to the complexity of effectively solving the Hamilton-Jacobi-Bellman (HJB) partial derivative equation (PDE) through analytical methods, various researchers have explored reinforcement learning (RL) techniques, including actor/critic architecture, [1][2][3][4]11 sequential learning" 12 and data-driven methods, [13][14][15][16] among others. Differing from traditional methods that approximate the Bellman function and optimal policy after each step, 12 the actor/critic procedure enables simultaneous training by minimizing the square of the Hamiltonian.…”

“…[1][2][3] Additionally, when combined with the sliding mode control (SMC) approach, the training law can be implemented using a single NN. 4 Modified Hamiltonian and corresponding adaptation law can be designed using a distinct cost function with a discount factor. 16 On the other hand, the data-driven approach involves data collection at regular time intervals to handle uncertain models.…”