Intelligent-Critic-Based Tracking Control of Discrete-Time Input-Affine Systems and Approximation Error Analysis With Application Verification
针对函数逼近器存在逼近误差导致系统不稳定问题，提出一种智能评判框架，通过隐式和显式方法证明迭代值函数有界及系统稳定性，并用数值和实际例子验证有效性。
In recent years, the application of function approximators, such as neural networks and polynomials, has ushered in a new stage of development in solving optimal control problems. However, considering the existence of approximation errors, the stability of the controlled system cannot be guaranteed. Therefore, in view of the prevalence of approximation errors, we investigate optimal tracking control problems for discrete-time systems. First, a novel value function is introduced into the intelligent critic framework. Second, an implicit method is utilized to demonstrate the boundedness of the iterative value functions with approximation errors. An explicit method is applied to prove the stability of the system with approximation errors. Furthermore, an evolving policy is designed to iteratively tackle the optimal tracking control problem and demonstrate the stability of the system. Finally, the effectiveness of the developed method is verified through numerical as well as practical examples.