nwei Li

Optimal Controls for Dual-Driven Load System with Synchronously Approximate Dynamic Programming Method

This paper applies a synchronously approximate dynamic programming (ADP) scheme to solve the Nash controls of the dual-driven load system (DDLS) with different motor properties based on game theory. First, a neural network (NN) is applied to approximate the dual-driven servo unknown system model. Because the properties of two motors are different, they have different performance indexes. Another NN is used to approximate performance index function of each motor. In order to minimize the performance index, the Hamilton function is constructed to solve the approximate optimal controls of the load system. Based on parameter error information, an adaptive law is designed to estimate NN weights. Finally, the practical DDLS is simulated to demonstrate that the optimal control inputs can be studied by ADP algorithm.

Reconstructed Multi-innovation Gradient Algorithm for the Identification of Sandwich Systems

Inspired by multi-innovation stochastic gradient identification algorithm, a reconstructed multi-innovation stochastic gradient identification algorithm (RMISG) is presented to estimate the parameters of sandwich systems in this paper. Compared with the traditional multi-innovation stochastic gradient identification algorithm, the RMISG is constructed by using the multistep update principle which solves the multi-innovation length problem and improves the performance of the identification algorithm. To decrease the calculation burden of the RMISG, the key-term separation principle is introduced to deal with the identification model of sandwich systems. Finally, simulation example is given to validate the availability of the proposed estimator.

Parameter Estimation for Control of Hammerstein Systems with Dead-Zone Nonlinearity

This paper focuses on the parameter identification and control for Hammerstein systems with dead-zone nonlinearity by using piecewise linear parametric expression method and model predictive control approach (MPC). To linearize the dead-zone nonlinearity, the piecewise linear functions are exploited to deal with dead-zone, and then, a piecewise linear parametric expression (for short, PLPE) algorithm is applied to describe the dead-zone function. Based on the described function, the considered system is transformed to a classical regression form. The parameters of the Hammerstein systems with dead-zone can be easily estimated by using least squares method. Based on dead-zone compensation, an MPC method is introduced to achieve the signal tracking output. Numerical simulation results indicate that the control system not only achieves the tracking output of the reference signal with a small tracking error but also produces an outstanding output response.

\(H\infty \) Tracking Control for Unknown Nonlinear System Based on Augmented Matrix Algorithm

Based on the augmented matrix and approximate dynamic programming algorithms, the (Hinfty ) tracking control problem for unknown nonlinear system is addressed in this paper. An identifier NN is first used to approximate the unknown system. An augmented matrix based on the desired trajectory and system state is then constructed using the identifier, such that the tracking control problem is transformed into the regulation one. We use another NN to approximate the performance index function of the HJI equation, such that (Hinfty ) tracking control pairs are calculated without solving the HJI equation. Moreover, we use an estimation algorithm to estimate unknown parameters in neural network. Finally, a simulation is presented to demonstrate the validity of the proposed method.

Approximate Solution for Three-Player Mixed-Zero-Sum Nonlinear Game via ADP Structure

In this paper, a three-player mixed-zero-sum game situation with nonlinear dynamics is proposed, and an approximate dynamic programming (ADP) learning scheme is used to solve the proposed problem. First, the problem formulation is presented. A value function for player 1 and 2 nonzero-sum game is constructed, another value function for player 1 and 3 zero-sum game is presented for three-player nonlinear game system. Because of the difficulty to solve the nonlinear Hamilton-Jacobi (HJ) equation, the single-layer critic neural networks are used to approximate the optimal value functions. Then the approximated critic neural networks (NNs) are directly used to learn the optimal solutions for three-player mixed-zero-sum nonlinear game. A novel adaptive law with the estimation performance index is proposed to estimate the unknown coefficient vector. Finally, a simulation example is presented to illustrate the proposed methods.

Two-Stage Recursive Least Squares Parameter Identification for Cascade Systems with Dead Zone

In this paper, two-stage recursive least squares algorithm (TS-RLS) is investigated for parameter identification of cascade systems with dead zone. In order to estimate the slopes and endpoints of the dead zone, switching functions are presented to reconstruct the expression of dead zone. All the parameters of linear subsystems and dead zone are separated by using the key term separation principle, which is applied to convert the cascade systems into a quasilinear model. The proposed identification algorithm not only estimates all the parameters of the cascade systems, but also reduces the computation cost of identification process. The result of the simulation illustrates the flexibility and efficiency of proposed identification algorithm.