Dipak M. Adhyaru

Bounded robust control of nonlinear systems using neural network–based HJB solution

In this paper, a Hamilton–Jacobi–Bellman (HJB) equation–based optimal control algorithm for robust controller design is proposed for nonlinear systems. The HJB equation is formulated using a suitable nonquadratic term in the performance functional to tackle constraints on the control input. Utilizing the direct method of Lyapunov stability, the controller is shown to be optimal with respect to a cost functional, which includes penalty on the control effort and the maximum bound on system uncertainty. The bounded controller requires the knowledge of the upper bound of system uncertainty. In the proposed algorithm, neural network is used to approximate the solution of HJB equation using least squares method. Proposed algorithm has been applied on the nonlinear system with matched and unmatched type system uncertainties and uncertainties in the input matrix. Necessary theoretical and simulation results are presented to validate proposed algorithm.

Survey of model reference adaptive control

This paper presents the survey of latest research on Model Reference Adaptive Control (MRAC). Effort is to present state of the art, find challenges, limitations and further scope of research on MRAC. Due to recent orientation towards soft computing research, publications with fuzzy logic and neural network have accelerated. Considering this point a section has been allocated to it. A section of variable structure MRAC has been included as variable structure control (VSC) is considered to be recent potential area. Many advanced techniques in MRAC have been surveyed and compiled in paper. Founded with focus on flight control and other aerospace applications, now MRAC has been designed and implemented for diverse application. Different applications of MRAC also have been reviewed here.

State observer design for nonlinear systems using neural network

In this paper, an observer design is proposed for nonlinear systems. The Hamilton-Jacobi-Bellman (HJB) equation based formulation has been developed. The HJB equation is formulated using a suitable non-quadratic term in the performance functional to tackle magnitude constraints on the observer gain. Utilizing Lyapunovs direct method, observer is proved to be optimal with respect to meaningful cost. In the present algorithm, neural network (NN) is used to approximate value function to find approximate solution of HJB equation using least squares method. With time-varying HJB solution, we proposed a dynamic optimal observer for the nonlinear system. Proposed algorithm has been applied on nonlinear systems with finite-time-horizon and infinite-time-horizon. Necessary theoretical and simulation results are presented to validate proposed algorithm.

Fuzzy based selection of PWARX model for the nonlinear hybrid dynamical systems

The Nonlinear Hybrid Dynamical Systems (NHDS) represent discrete event dynamics along with continuous dynamics. This paper is focused identification of the NHDS based on fuzzy c-means clustering approach for the open loop data classification according to its discrete dynamics. In the present work, a novel fuzzy function based selection of PWARX model algorithm applied for validation of identified parameters of the PieceWise affine Auto Regressive eXogeneous (PWARX) models which are separable and linear in the discrete space. The performance of the proposed selection method is demonstrated using the physical application.

Adaptive Neuro-Fuzzy Inference System based control of robotic manipulators

Robot manipulators have become increasingly important in the field of flexible automation. Through the years considerable research effort has been made in their controller design. In order to achieve accurate trajectory tracking and good control performance, a number of control schemes have been developed. Amongst these, ANFIS (Adaptive Neuro-Fuzzy Inference System) has provided best results for control of robotic manipulators as compared to the conventional control strategies.

Robust control of nonlinear systems using neural network based HJB solution

In this paper, a Hamilton-Jacobi-Bellman (HJB) equation based optimal control algorithm for robust controller design is proposed for a nonlinear system. Utilising the Lyapunov direct method, the controller is shown to be optimal with respect to a cost functional, which includes penalty on the control effort, the maximum bound on system uncertainty and cross-coupling between system state and control. The controllers are continuous and require the knowledge of the upper bound of system uncertainty. In the present algorithm, neural network is used to approximate value function to find approximate solution of HJB equation using least squares method. Proposed algorithm has been applied on a nonlinear system with matched uncertainties. It is also applied to the system having uncertainties in input matrix. Results are validated through simulation studies.

Parameter identification of PWARX models using fuzzy distance weighted least squares method

A novel fuzzy distance weight matrix based parameter identification method.Fuzzy clustering based algorithm used to find sub-models of HDS.WLS algorithm is used to identify parameters of sub-models.Results validated through simulation experiments. PieceWise AutoRegressive eXogenous (PWARX) models represent one of the broad classes of the hybrid dynamical systems (HDS). Among many classes of HDS, PWARX model used as an attractive modeling structure due to its equivalence to other classes. This paper presents a novel fuzzy distance weight matrix based parameter identification method for PWARX model. In the first phase of the proposed method estimation for the number of affine submodels present in the HDS is proposed using fuzzy clustering validation based algorithm. For the given set of input-output data points generated by predefined PWARX model fuzzy c-means (FCM) clustering procedure is used to classify the data set according to its affine submodels. The fuzzy distance weight matrix based weighted least squares (WLS) algorithm is proposed to identify the parameters for each PWARX submodel, which minimizes the effect of noise and classification error. In the final phase, fuzzy validity function based model selection method is applied to validate the identified PWARX model. The effectiveness of the proposed method is demonstrated using three benchmark examples. Simulation experiments show validation of the proposed method.

Constrained optimal control of bilinear systems using neural network based HJB solution

In this paper, a Hamilton-Jacobi-Bellman (HJB) equation based optimal control algorithm is proposed for a bilinear system. Utilizing the Lyapunov direct method, the controller is shown to be optimal with respect to a cost functional, which includes penalty on the control effort and the system states. In the proposed algorithm, Neural Network (NN) is used to find approximate solution of HJB equation using least squares method. Proposed algorithm has been applied on bilinear systems. Necessary theoretical and simulation results are presented to validate proposed algorithm.

Clustering based multiple model control of hybrid dynamical systems using HJB solution

(a) Reference level, eventwise, Model-I and Model-II optimal control response; (b) corresponding variation of input flow rate. Hamilton-Jacobi-Bellman (HJB) equation based stabilized optimal control of hybrid dynamical systems (HDS) is presented.The fuzzy validity based method is used to find the number of linear models present in the HDS.Stability proof for the event wise and generalized HJB solution based optimal control is proposed.The proposed modeling and control algorithm have been applied on two HDSs. This paper deals with Hamilton-Jacobi-Bellman (HJB) equation based stabilized optimal control of hybrid dynamical systems (HDS). This paper presents the fuzzy clustering based event wise multiple linearized modeling approaches for HDS to describe the continuous dynamic in each event. In the present work a fuzzy clustering validation approach is presented for the selection of number of linearized models which span entire HDS. The method also describes how to obtain event wise operating point using fuzzy membership function, which is used to find the event wise model bank by linearizing the first principles model. The event wise linearized models are used for the formulation of the optimal control law. The HJB equation is formulated using a suitable quadratic term in the objective function. By use of the direct method of Lyapunov stability, the control law is shown to be optimal with respect to objective functional and stabilized the event wise linearized models. The global Lyapunov function is proposed with discrete variables which stabilized the HDS. The proposed modeling and control algorithm have been applied on two HDSs. Necessary theoretical and simulation experiments are presented to demonstrate the performance and validation of the proposed algorithm.

Constrained controller design for a class of nonlinear discrete-time uncertain systems

In this paper, constrained controller design is proposed for a class of nonlinear discrete-time uncertain system having matched type system uncertainties, using the solution of HJB (Hamilton-Jaccobi-Bellman) equation. The discrete-time HJB equation is formulated using a suitable non-quadratic term in the performance functional to tackle constraints on the control input. Based on the non-quadratic functional, a greedy HDP algorithm is used to obtain the constrained robust-optimal controller. The constrained robust controller requires knowledge of the upper bound of system uncertainties. For facilitating the implementation of the iterative algorithm, two neural networks are used to approximate the value function and to compute the optimal control policy, respectively. Their weights have been tuned using least squares method. Proposed algorithm has been applied on a nonlinear discrete-time system with matched uncertainties.