Neuro-observer controller design for nonlinear dynamical systems

Learning from adaptive neural network control of an underactuated rigid spacecraft

In this chapter, a novel control method using a reinforcement learning (RL) (Sutton and Barto (1998)) with concept of sliding mode control (SMC) (Slotine and Li (1991)) for unknown dynamical system is considered. In designing the control system for unknown dynamical system, there are three approaches. The first one is the conventional model-based controller design, such as optimal control and robust control, each of which is mathematically elegant, however both controller design procedures present a major disadvantage posed by the requirement of the knowledge of the system dynamics to identify and model it. In such cases, it is usually difficult to model the unknown system, especially, the nonlinear dynamical complex system, to make matters worse, almost all real systems are such cases. The second one is the way to use only the soft-computing, such as neural networks, fuzzy systems, evolutionary systems with learning and so on. However, in these cases it is well known that modeling and identification procedures for the dynamics of the given uncertain nonlinear system and controller design procedures often become time consuming iterative approaches during parameter identification and model validation at each step of the iteration, and in addition, the control system designed through such troubles does not guarantee the stability of the system. The last one is the way to use the method combining the above the soft-computing method with the model-based control theory, such as optimal control, sliding mode control (SMC), H∞ control and so on. The control systems designed through such above control theories have some advantages, that is, the good nature which its adopted theory has originally, robustness, less required iterative learning number which is useful for fragile system controller design not allowed a lot of iterative procedure. This chapter concerns with the last one, that is, RL system, a kind of soft-computing method, supported with robust control theory, especially SMC for uncertain nonlinear systems. RL has been extensively developed in the computational intelligence and machine learning societies, generally to find optimal control policies for Markovian systems with discrete state and action space. RL-based solutions to the continuous-time optimal control problem have been given in Doya (Doya (2000). The main advantage of using RL for solving optimal

A stochastic, fuzzy, neural network (SFNN) to model unknown nonlinear dynamic systems is developed. In this network, a non-singleton fuzzifier with Gaussian membership functions instead of the singleton fuzzifier in the fuzzy logic is introduced. Based on these membership functions, an online supervised parameter learning algorithm of the SFNN is proposed to overcome the local minimum of learning process in current neural networks, and an off-line algorithm for the structure learning of the SFNN is presented to reduce the amount of computation of the SFNN. This new network provides a universal approximator and it is also applicable to stochastic control and decision systems and the identification of chaos in nonlinear systems.

Observer-based indirect adaptive fuzzy sliding mode control with state variable filters for unknown nonlinear dynamical systems

Neural networks (NNs) have gained significant popularity for modeling complex, nonlinear systems due to their powerful approximation capabilities. However, designing an appropriate network structure and tuning parameters remains challenging, especially for nonlinear dynamic systems where offline training data are unavailable and poor approximations from badly tuned NNs can cause instability. This article presents a novel adaptive frequency-based constructive wavelet NN (AFBCWNN) for tracking reference trajectories for a class of unknown nonlinear dynamic systems. Using online measurements, the AFBCWNN integrates adaptive weight updating, adjustable network structures, and rigorous stability analysis using Lyapunov techniques. Unlike conventional methods, the proposed AFBCWNN leverages frequency-domain analysis to estimate the energy distribution of the unknown nonlinear mapping from measured data. This frequency-based approach provides a uniform design guideline for network initialization, enabling the network to dynamically add wavelet bases when the desired accuracy is not achieved and prune nonenergy-active (low-energy) bases, reducing computational cost without compromising accuracy. Rigorous stability analysis establishes conditions for uniformly bounded trajectories, and simulation results confirm the AFBCWNN's superior performance in capturing complex, nonlinear dynamics compared to the existing adaptive methods.

In this paper, Dynamic Back Propagation (DBP) is reinvestigated in the context of indirect inverse control of unknown nonlinear dynamic systems using Artificial Neural Networks (ANNs). The overall control scheme includes two networks. The first is used as an approximating model of the unknown nonlinear dynamic behavior of the plant while the second is the controller. The trajectory error is backpropagated through the neural model using DBP algorithm to obtain the control input error. The controller, which is a recurrent ANN, is then adapted also using DBP algorithm. Simulation results obtained with both Standard Back Propagation (SBP) and DBP algorithms for a fourth order nonlinear system clearly show some advantage of DBP.

Recently, a deterministic learning (DL) theory was proposed for accurate modeling or identification of the dynamics of nonlinear dynamical systems. In this paper, we further investigate the problem of modeling or identification of the partial derivative of dynamics for dynamical systems. Based on the locally accurate identification of the unknown system dynamics via deterministic learning, the modeling or identification of its partial derivative of dynamics along the periodic or periodic-like system trajectory is obtained by introducing the mathematical concept of directional derivative. With the accurate identification of the system dynamics and its partial derivative of dynamics, a C1-norm modeling approach is then proposed from the perspective of structural stability. This will provide incentives for further applications in the classification for dynamical systems and patterns as well as the prediction of bifurcation and chaos. Simulation studies are included to demonstrate the effectiveness of this modeling approach.

Single-layer networks for nonlinear system identification

Dynamic event-triggered-based single-network ADP optimal tracking control for the unknown nonlinear system with constrained input

The cerebellar model articulation controller (CMAC) neural network (NN) has advantages over fully connected NNs due to its increased structure. This paper attempts to provide a comprehensive treatment of CMAC NNs in closed-loop control applications. The function approximation capabilities of the CMAC NN are first rigorously established, and novel weight-update laws derived that guarantee the stability of the closed-loop system. The passivity properties of the CMAC under the specified tuning laws are examined and the relationship between passivity and closed-loop stability is derived. The utility of the CMAC NN in controlling a nonlinear system with unknown dynamics is demonstrated through numerical examples.

In this paper, we are dealing with the problem of regulating unknown nonlinear dynamical systems. First a dynamical neural network identifier is employed to perform ‘black box’ identification and then a regular static feedback is developed to regulate the unknown system to zero. Not all the plant states are assumed to be available for measurement.

The paper proposes a new method for identifying orders of input-output models for unknown nonlinear dynamic systems. The approach is based on the continuity property of the nonlinear functions which represent input-output models of continuous dynamic systems. The approach does not depend on any nonlinear function approximation methods and solely depends on the system's input-output data measured in experiments. By evaluating the modification of an index which is defined as Lipschitz number with the successive modification of model orders, the appropriate model orders can be determined simply and reliably. Theoretical background of the present approach is discussed. Several examples from chaotic dynamic systems, nonlinear plant models are presented to demonstrate the effectiveness of the present method.

The control problem of an unknown nonlinear dynamic system which contains the abrupt changes of parameters is concerned. Multiple models based on dynamic neural networks are used to approximate the dynamic character of unknown system. Different controllers based on these models and an effectively switching mechanism are applied to an unknown system to trace a reference trajectory. Further, we propose different switching and turning schemes for adaptive control which combine fixed and adaptive models. From the simulation, it can be shown that the multiple model adaptive control method proposed in this paper can improve the control performance greatly compared with the conventional adaptive control.

On generalized residual network for deep learning of unknown dynamical systems

Since the computed torque or inverse dynamics control techniques are based on a good understanding of the controlled system dynamics and even its environment; the objection for the real-time application is unrealizable for the unknown systems. To tackle this problem, this study developed a robust adaptive fuzzy sliding-mode control system based on the H/sup /spl infin// tracking design technique. The developed control system is comprised of a fuzzy controller and a robust controller. The fuzzy controller is utilized to approximate an ideal controller by the tuning algorithms based on the Lyapunov sense, and the robust controller is designed to achieve H/sup /spl infin// robust tracking performance. To investigate the effectiveness of the developed control system, it is applied to a wing rock motion control system. Simulation results demonstrate that the proposed control system can achieve favorable tracking performances with unknown system dynamics.