Yanhong Luo

Neural-Network-Based Near-Optimal Control for a Class of Discrete-Time Affine Nonlinear Systems With Control Constraints

In this paper, the near-optimal control problem for a class of nonlinear discrete-time systems with control constraints is solved by iterative adaptive dynamic programming algorithm. First, a novel nonquadratic performance functional is introduced to overcome the control constraints, and then an iterative adaptive dynamic programming algorithm is developed to solve the optimal feedback control problem of the original constrained system with convergence analysis. In the present control scheme, there are three neural networks used as parametric structures for facilitating the implementation of the iterative algorithm. Two examples are given to demonstrate the convergence and feasibility of the proposed optimal control scheme.

Data-Driven Robust Approximate Optimal Tracking Control for Unknown General Nonlinear Systems Using Adaptive Dynamic Programming Method

In this paper, a novel data-driven robust approximate optimal tracking control scheme is proposed for unknown general nonlinear systems by using the adaptive dynamic programming (ADP) method. In the design of the controller, only available input-output data is required instead of known system dynamics. A data-driven model is established by a recurrent neural network (NN) to reconstruct the unknown system dynamics using available input-output data. By adding a novel adjustable term related to the modeling error, the resultant modeling error is first guaranteed to converge to zero. Then, based on the obtained data-driven model, the ADP method is utilized to design the approximate optimal tracking controller, which consists of the steady-state controller and the optimal feedback controller. Further, a robustifying term is developed to compensate for the NN approximation errors introduced by implementing the ADP method. Based on Lyapunov approach, stability analysis of the closed-loop system is performed to show that the proposed controller guarantees the system state asymptotically tracking the desired trajectory. Additionally, the obtained control input is proven to be close to the optimal control input within a small bound. Finally, two numerical examples are used to demonstrate the effectiveness of the proposed control scheme.

Near-Optimal Control for Nonzero-Sum Differential Games of Continuous-Time Nonlinear Systems Using Single-Network ADP

In this paper, a near-optimal control scheme is proposed to solve the nonzero-sum differential games of continuous-time nonlinear systems. The single-network adaptive dynamic programming (ADP) is utilized to obtain the optimal control policies which make the cost functions reach the Nash equilibrium of nonzero-sum differential games, where only one critic network is used for each player instead of the action-critic dual network used in a typical ADP architecture. Furthermore, the novel weight tuning laws for critic neural networks are proposed, which not only ensure the Nash equilibrium to be reached but also guarantee the system to be stable. No initial stabilizing control policy is required for each player. Moreover, Lyapunov theory is utilized to demonstrate the uniform ultimate boundedness of the closed-loop system. Finally, a simulation example is given to verify the effectiveness of the proposed near-optimal control scheme.

Adaptive Dynamic Programming for Control

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Adaptive dynamic programming-based optimal control of unknown nonaffine nonlinear discrete-time systems with proof of convergence

In this paper, a novel neuro-optimal control scheme is proposed for unknown nonaffine nonlinear discrete-time systems by using adaptive dynamic programming (ADP) method. A neuro identifier is established by employing recurrent neural networks (RNNs) model to reconstruct the unknown system dynamics. The convergence of the identification error is proved by using the Lyapunov theory. Then based on the established RNN model, the ADP method is utilized to design the approximate optimal controller. Two neural networks (NNs) are used to implement the iterative algorithm. The convergence of the action NN error and weight estimation errors is demonstrated while considering the NN approximation errors. Finally, two numerical examples are used to demonstrate the effectiveness of the proposed control scheme.

A new fuzzy identification method based on adaptive critic designs

A new fuzzy identification method for unknown nonlinear discrete systems is presented by introducing adaptive critic designs into the generalized fuzzy hyperbolic model (GFHM). This method minimizes the long-time error other than the immediate error to improve the identification effect. We first represent the GFHM with a neural network structure, and then utilize the adaptive critic designs (ACDs) to get the optimal parameters of the network so that the long-time identification error is minimized. Finally, we give a simulation example to verify the effectiveness of this identification method.

Application of BFNN in power flow calculation in smart distribution grid

Power flow study is performed to ensure the whole electricity system operating safely, stably and reliably. A back/forward sweep neural network (BFNN) algorithm is put forward based on numbering all nodes using breadth first search plan. All neurons use the same excitation function. The BFNN has a clear structure with a high approximation speed and high precision. Each neuron acts as the threshold to its adjacent neuron in front. In BFNN method weights adjusting means voltage adjusting, hence, when the learning process according to BP algorithm ended, the desired voltages are acquired. And then the power flow can be derived. In this paper the convergence of BFNN has also been validated. The proposed BFNN algorithm is proved to have a better approximation effect than using conditional back/forward method by computing power flow in Tongliao 16-bus distribution system in Inner Mongolia.

Optimal Tracking Control for Discrete-Time Systems

The aim of this chapter is to present some direct methods for solving the closed-loop optimal tracking control problem for discrete-time systems. Considering the fact that the performance index functions of optimal tracking control problems are quite different from those of optimal state feedback control problems, a new type of performance index function is defined. The methods are mainly based on the iterative HDP and GDHP algorithms. We first study the optimal tracking control problem of affine nonlinear systems, and after that we study the optimal tracking control problem of nonaffine nonlinear systems. It is noticed that most real-world systems need to be effectively controlled within a finite time horizon. Hence, based on the above results, we will further study the finite-horizon optimal tracking control problem, using the ADP approach in the last part of this chapter.

Zero-Sum Games for Discrete-Time Systems Based on Model-Free ADP

In this chapter, zero-sum games are investigated for discrete-time systems based on the model-free ADP method. First, an effective data-based optimal control scheme is developed via the iterative ADP algorithm to find the optimal controller of a class of discrete-time zero-sum games for Roesser type 2-D systems. Since the exact models of many 2-D systems cannot be obtained inherently, the iterative ADP method is expected to avoid the requirement of exact system models. Second, a data-based optimal output feedback controller is developed for solving the zero-sum games of a class of discrete-time systems, whose merit is that not only knowledge of the system model is not required, but neither is information of the system states. Theoretical analysis and a simulation study show the validity of the methods presented.

Optimal Feedback Control for Continuous-Time Systems via ADP

In this chapter, we focus on the design of controllers for continuous-time systems via the ADP approach. Although many ADP methods have been proposed for continuous-time systems, a suitable framework in which the optimal controller can be designed for a class of general unknown continuous-time systems still has not been developed. Therefore, in the first part of this chapter, we develop a new scheme to design the optimal robust tracking controllers for unknown general continuous-time nonlinear systems. The merit of the present method is that we require only the availability of input/output data instead of an exact system model. The obtained control input can be guaranteed to be close to the optimal control input within a small bound. In the second part of this chapter, a novel ADP-based robust neural network controller is developed for a class of continuous-time nonaffine nonlinear systems, which is the first attempt to extend the ADP approach to continuous-time nonaffine nonlinear systems. Numerical simulations have shown that the present methods are effective and can be used for a quite wide class of continuous-time nonlinear systems.