Optimal control of nonlinear discrete time-varying systems using a new neural network approximation structure

A reinforcement learning-based near-optimal hierarchical approach for motion control: Design and experiment

As a data-driven design method, model-free optimal control based on reinforcement learning provides an effective way to find optimal control strategies. The design of model-free optimal control is sensitive to system data because it relies on data rather than detailed dynamic models. A prerequisite for generating applicable data is that the system must be open-loop stable (with a stable equilibrium point), which restricts the data-based control design methods in actual control problems and leads to rare experimental studies or verification in the literature. To improve this situation and enrich its applications, we propose a pre-stabilized mechanism and apply it to the motion control of a mechanical system together with a reinforcement learning-based model-free optimal control method, which constitutes a so-called hierarchical control structure. We design two real-time control experiments on an underactuated system to verify its effectiveness. The control results show that the proposed hierarchical control is quite promising in controlling this mechanical system, even though it is open-loop unstable with unknown dynamics.

Neural network based asynchronous synchronization for fuzzy hidden Markov jump complex dynamical networks

This paper investigates the drive-response synchronization problem of Takagi–Sugeno fuzzy hidden Markov jump complex dynamical networks. More precisely, a novel asynchronous synchronization control strategy is developed for coping with mismatched hidden jumping modes. Furthermore, the neural network is adopted with online learning laws for unknown function approximation. By taking advantage of Lyapunov method, sufficient conditions are established to ensure mean-square synchronization performance with disturbances. Based on the synchronization criterion, asynchronous controller gains are designed in terms of linear matrix inequalities. An illustrative example is finally given to validate the effectiveness of the proposed synchronization techniques.

Neural-Network-Based Output-Feedback Control Under Round-Robin Scheduling Protocols

The neural-network (NN)-based output-feedback control is considered for a class of stochastic nonlinear systems under round-Robin (RR) scheduling protocols. For the purpose of effectively mitigating data congestions and saving energies, the RR protocols are implemented and the resulting nonlinear systems become the so-called protocol-induced periodic ones. Taking such a periodic characteristic into account, an NN-based observer is first proposed to reconstruct the system states where a novel adaptive tuning law on NN weights is adopted to cater to the requirement of performance analysis. In addition, with the established boundedness of the periodic systems in the mean-square sense, the desired observer gain is obtained by solving a set of matrix inequalities. Then, an actor-critic NN scheme with a time-varying step length in adaptive law is developed to handle the considered control problem with terminal constraints over finite-horizon. Some sufficient conditions are derived to guarantee the boundedness of estimation errors of critic and actor NN weights. In view of these conditions, some key parameters in adaptive tuning laws are easily determined via elementary algebraic operations. Furthermore, the stability in the mean-square sense is investigated for the discussed issue in infinite horizon. Finally, a simulation example is utilized to illustrate the applicability of the proposed control scheme.

Output-Feedback Control of Unknown Linear Discrete-Time Systems With Stochastic Measurement and Process Noise via Approximate Dynamic Programming

This paper studies the optimal output-feedback control problem for unknown linear discrete-time systems with stochastic measurement and process noise. A dithered Bellman equation with the innovation covariance matrix is constructed via the expectation operator given in the form of a finite summation. On this basis, an output-feedback-based approximate dynamic programming method is developed, where the terms depending on the innovation covariance matrix are available with the aid of the innovation covariance matrix identified beforehand. Therefore, by iterating the Bellman equation, the resulting value function can converge to the optimal one in the presence of the aforementioned noise, and the nearly optimal control laws are delivered. To show the effectiveness and the advantages of the proposed approach, a simulation example and a velocity control experiment on a dc machine are employed.

Pattern-Based NN Control of a Class of Uncertain Nonlinear Systems

This paper presents a pattern-based neural network (NN) control approach for a class of uncertain nonlinear systems. The approach consists of two phases of identification and another two phases of recognition and control. First, in the phase (i) of identification, adaptive NN controllers are designed to achieve closed-loop stability and tracking performance of nonlinear systems for different control situations, and the corresponding closed-loop control system dynamics are identified via deterministic learning. The identified control system dynamics are stored in constant radial basis function (RBF) NNs, and a set of constant NN controllers are constructed by using the obtained constant RBF networks. Second, in the phase (ii) of identification, when the plant is operated under different or abnormal conditions, the system dynamics under normal control are identified via deterministic learning. A bank of dynamical estimators is constructed for all the abnormal conditions and the learned knowledge is embedded in the estimators. Third, in the phase of recognition, when one identified control situation recurs, by using the constructed estimators, the recurred control situation will be rapidly recognized. Finally, in the phase of pattern-based control, based on the rapid recognition, the constant NN controller corresponding to the current control situation is selected, and both closed-loop stability and improved control performance can be achieved. The results presented show that the pattern-based control realizes a humanlike control process, and will provide a new framework for fast decision and control in dynamic environments. A simulation example is included to demonstrate the effectiveness of the approach.

Quantization-Based Adaptive Actor-Critic Tracking Control With Tracking Error Constraints

In this paper, the problem of adaptive actor-critic (AC) tracking control is investigated for a class of continuous-time nonlinear systems with unknown nonlinearities and quantized inputs. Different from the existing results based on reinforcement learning, the tracking error constraints are considered and new critic functions are constructed to improve the performance further. To ensure that the tracking errors keep within the predefined time-varying boundaries, a tracking error transformation technique is used to constitute an augmented error system. Specific critic functions, rather than the long-term cost function, are introduced to supervise the tracking performance and tune the weights of the AC neural networks (NNs). A novel adaptive controller with a special structure is designed to reduce the effect of the NN reconstruction errors, input quantization, and disturbances. Based on the Lyapunov stability theory, the boundedness of the closed-loop signals and the desired tracking performance can be guaranteed. Finally, simulations on two connected inverted pendulums are given to illustrate the effectiveness of the proposed method.

Actor-Critic Off-Policy Learning for Optimal Control of Multiple-Model Discrete-Time Systems

In this paper, motivated by human neurocognitive experiments, a model-free off-policy reinforcement learning algorithm is developed to solve the optimal tracking control of multiple-model linear discrete-time systems. First, an adaptive self-organizing map neural network is used to determine the system behavior from measured data and to assign a responsibility signal to each of system possible behaviors. A new model is added if a sudden change of system behavior is detected from the measured data and the behavior has not been previously detected. A value function is represented by partially weighted value functions. Then, the off-policy iteration algorithm is generalized to multiple-model learning to find a solution without any knowledge about the system dynamics or reference trajectory dynamics. The off-policy approach helps to increase data efficiency and speed of tuning since a stream of experiences obtained from executing a behavior policy is reused to update several value functions corresponding to different learning policies sequentially. Two numerical examples serve as a demonstration of the off-policy algorithm performance.

Model-Free Optimal Tracking Control via Critic-Only Q-Learning

Model-free control is an important and promising topic in control fields, which has attracted extensive attention in the past few years. In this paper, we aim to solve the model-free optimal tracking control problem of nonaffine nonlinear discrete-time systems. A critic-only Q-learning (CoQL) method is developed, which learns the optimal tracking control from real system data, and thus avoids solving the tracking Hamilton-Jacobi-Bellman equation. First, the Q-learning algorithm is proposed based on the augmented system, and its convergence is established. Using only one neural network for approximating the Q-function, the CoQL method is developed to implement the Q-learning algorithm. Furthermore, the convergence of the CoQL method is proved with the consideration of neural network approximation error. With the convergent Q-function obtained from the CoQL method, the adaptive optimal tracking control is designed based on the gradient descent scheme. Finally, the effectiveness of the developed CoQL method is demonstrated through simulation studies. The developed CoQL method learns with off-policy data and implements with a critic-only structure, thus it is easy to realize and overcome the inadequate exploration problem.

Data-driven output-feedback fault-tolerant L2 control of unknown dynamic systems

This paper studies the data-driven output-feedback fault-tolerant L2-control problem for unknown dynamic systems. In a framework of active fault-tolerant control (FTC), three issues are addressed, including fault detection, controller reconfiguration for optimal guaranteed cost control, and tracking control. According to the data-driven form of observer-based residual generators, the system state is expressed in the form of the measured input-output data. On this basis, a model-free approach to L2 control of unknown linear time-invariant (LTI) discrete-time plants is given. To achieve tracking control, a design method for a pre-filter is also presented. With the aid of the aforementioned results and the input-output data-based time-varying value function approximation structure, a data-driven FTC scheme ensuring L2-gain properties is developed. To illustrate the effectiveness of the proposed methodology, two simulation examples are employed.

Fuzzy Counter Propagation Neural Network Control for a Class of Nonlinear Dynamical Systems

Fuzzy Counter Propagation Neural Network (FCPN) controller design is developed, for a class of nonlinear dynamical systems. In this process, the weight connecting between the instar and outstar, that is, input-hidden and hidden-output layer, respectively, is adjusted by using Fuzzy Competitive Learning (FCL). FCL paradigm adopts the principle of learning, which is used to calculate Best Matched Node (BMN) which is proposed. This strategy offers a robust control of nonlinear dynamical systems. FCPN is compared with the existing network like Dynamic Network (DN) and Back Propagation Network (BPN) on the basis of Mean Absolute Error (MAE), Mean Square Error (MSE), Best Fit Rate (BFR), and so forth. It envisages that the proposed FCPN gives better results than DN and BPN. The effectiveness of the proposed FCPN algorithms is demonstrated through simulations of four nonlinear dynamical systems and multiple input and single output (MISO) and a single input and single output (SISO) gas furnace Box-Jenkins time series data.