Multivariable Nonlinear Dynamical Systems Research Articles

Optimally designed Lyapunov–Krasovskii terminal costs for robust stable–feasible model predictive control of uncertain time-delay nonlinear dynamical systems

This article details a new Model Predictive Control algorithm ensuring robust stability and control feasibility for uncertain nonlinear multi-input multi-output dynamical systems considering uncertain time-delay effects. The proposed control algorithm is based on construction of a Lyapunov–Krasovskii functional as terminal cost. Incorporation of this terminal cost into the Model Predictive Control optimization problem and calculation of the associated admissible set result in robust feasibility and robust stability of closed-loop system in presence of uncertain time-delay effects and bounded disturbance signals. The Lyapunov–Krasovskii functional term is constructed with respect to predicted sliding functions over the prediction horizon and considers the effects of dynamical variations over the prediction horizon in generation of control inputs. As dynamical variations are investigated in a sample-to-sample basis, feasible sliding regions are updated at each sample as well. Finally, based on expression of sliding functions as a combination of dynamical variations and input-based terms, required control inputs are calculated in the admissible bound by the optimization algorithm. Construction of control scheme on this basis permits straightforward calculation of robust stability and feasibility conditions for a general class of uncertain nonlinear system in finite prediction horizon whereas in the previous works, often-restrictive conditions were considered for the investigated dynamical systems. Numerical illustrations indicate precision and efficiency of control algorithm and improved stability and convergence rate for multivariable nonlinear dynamical systems considering uncertain time-delay effects. Finally, hardware-in-the-loop implementation indicates applicability of the proposed scheme in real-time control applications particularly in case appropriate compromises between optimality and calculation speed are considered.

Recurrent-Neural-Network-Based Multivariable Adaptive Control for a Class of Nonlinear Dynamic Systems With Time-Varying Delay.

At the beginning, an approximate nonlinear autoregressive moving average (NARMA) model is employed to represent a class of multivariable nonlinear dynamic systems with time-varying delay. It is known that the disadvantages of robust control for the NARMA model are as follows: 1) suitable control parameters for larger time delay are more sensitive to achieving desirable performance; 2) it only deals with bounded uncertainty; and 3) the nominal NARMA model must be learned in advance. Due to the dynamic feature of the NARMA model, a recurrent neural network (RNN) is online applied to learn it. However, the system performance becomes deteriorated due to the poor learning of the larger variation of system vector functions. In this situation, a simple network is employed to compensate the upper bound of the residue caused by the linear parameterization of the approximation error of RNN. An e -modification learning law with a projection for weight matrix is applied to guarantee its boundedness without persistent excitation. Under suitable conditions, the semiglobally ultimately bounded tracking with the boundedness of estimated weight matrix is obtained by the proposed RNN-based multivariable adaptive control. Finally, simulations are presented to verify the effectiveness and robustness of the proposed control.

Identification of Multivariable Nonlinear Dynamic System Based on PID Neural Network

System identification is the basis for control system design. For linear time-invariant systems have a variety of identification methods, identification methods for nonlinear dynamic system is still in the exploratory stage. Nonlinear identification method based on neural network is a simple and effective general method that does not require too much priori experience about the system to be identified. Through training and learning, the network weights are corrected to achieve the purpose of system identification. The paper is about the identification of multivariable nonlinear dynamic system based on PID neural network. The structure and algorithm of PID neural network are introduced and the properties and characteristics are analyzed. The system identification is completed and the results are fast convergence.

Generalized Mittag-Leffler stability of multi-variables fractional order nonlinear systems

In this paper, the stability of multi-variable fractional order nonlinear dynamic system is investigated. We propose the definition of generalized Mittag-Leffler stability with multi-variable and introduce the fractional Lyapunov direct method with multi-variable. Meanwhile, a novel approach is suggested to study generalized Mittag-Leffler stability in multi-variable fractional order nonlinear dynamic systems. An interesting multi-variable fractional order Lotka–Volterra predator–prey model is used to illustrate the proposed method and its effectiveness.

An IV-QR Algorithm for Neuro-Fuzzy Multivariable Online Identification

In this paper, a new algorithm for neuro-fuzzy identification of multivariable discrete-time nonlinear dynamic systems, more specifically applied to consequent parameters estimation of the neuro-fuzzy inference system, is proposed based on a decomposed form as a set of coupled multiple input and single output (MISO) Takagi-Sugeno (TS) neuro-fuzzy networks. An on-line scheme is formulated for modeling a nonlinear autoregressive with exogenous input (NARX) recurrent neuro-fuzzy structure from input-output samples of a multivariable nonlinear dynamic system in a noisy environment. The adaptive weighted instrumental variable (WIV) algorithm by QR factorization based on the numerically robust orthogonal Householder transformation is developed to modify the consequent parameters of the TS multivariable neuro-fuzzy network

Reinforcement genetic approach to coefficient estimation for multivariable nonlinear discrete-time dynamical systems

In this paper, we propose a novel genetic algorithm (GA) with a multi-crossover fashion to estimate the associated coefficients for a class of nonlinear discrete-time multivariable dynamical systems. Unlike the traditional crossover method of using two chromosomes, the proposed method uses three chromosomes to achieve a crossover. According to the adjusting direction by crossing three chromosomes, more excellent offspring can be produced. To solve the identification problem of multivariable nonlinear discrete-time systems, each of estimated system coefficients represents a gene, and a collection of genes is referred to as a chromosome in the view of GA. The chromosomes in the population are then evolved using the proposed multi-crossover method. An illustrative example of multivariable nonlinear systems is given to demonstrate the effectiveness, as compared with the traditional crossover method, of the proposed method.

New modifying self-organizing fuzzy controller for robotic motion control

The precise motion control of robotic manipulators is important in improving productivity and quality. However, robotic manipulators are multivariable nonlinear dynamic systems. Designing a model-based controller for robotic system control is difficult because its mathematical model is hard to accurately establish. This study proposed a self-organizing fuzzy controller (SOFC) to control a robotic system and evaluate its control performance. The SOFC continually updates the learning strategy in the form of fuzzy rules during the control process. The learning rate and the weighting distribution value of the controller are hard to regulate, so its fuzzy control rules may be modified to such an extent that the system response generally causes oscillatory phenomena. Two fuzzy logic controllers were designed according to the system output error and the error change, and introduced to the SOFC to determine the appropriate parameters of the learning rate and the weighting distribution, in order to eliminate this oscillation. This new modifying self-organizing fuzzy controller (NMSOFC) can effectively improve the control performance of the system, reduce the time consumed to establish a suitable fuzzy rule table, and support practical and convenient fuzzy controller applications. To confirm the applicability of the proposed intelligent controllers, this work retrofitted an old robot for a control system to evaluate the feasibility of motion control. Experiment results indicate the NMSOFC has better control performance in reducing the tracking errors of the joint-space trajectories and the positions, and requires less computational time than does the traditional fuzzy controller.

Fault accommodation of a class of multivariable nonlinear dynamical systems using a learning approach

Presents a learning approach for accommodating faults occurring in a class of nonlinear multi-input-multi-output (MIMO) dynamical systems. Changes in the system dynamics due to a fault are modeled as unknown nonlinear functions of the measurable state variables. The closed-loop stability of the robust fault accommodation scheme is established using Lyapunov redesign methods. A simulation example, based on a model of a jet engine compression system, is used to illustrate the fault accommodation design procedure.

Nonlinear System Identification Using Lyapunov Based Fully Tuned Dynamic RBF Networks

This paper presents a stable, on-line identification scheme for multivariable nonlinear dynamic system. Growing Gaussian Radial Basis Function (GRBF) network with all its parameters being adaptable is used to approximate an unknown nonlinear system. Based on a continuous-time framework, the parameter adjustment law is derived using Lyapunov synthesis approach, which guarantees the stability of the overall system. In addition, to ensure the convergence of the approximation error, a growing strategy for the network is selected and a dead zone is incorporated in the tuning law. Simulation studies on identifying a time-varying nonlinear missile dynamics illustrate the superior performance of the proposed scheme. The studies also indicate that stability and reduction in approximation error can be extended to a network with pruning strategy, thereby resulting in a Growing and Pruning (GAP) RBF network, which can implement a more compact network structure.

Multiple Hyperball CMAC Structure for Large Dimension Mapping

The cerebellar model articulation controller (CMAC) is often used in neural computation and neurocontrol systems as output predictors or models of dynamic systems through static mapping from input space to output space. Hyperball CMAC (HCMAC) is presented in the paper. As a fast learning network, its performance is very easy to be analyzed. The simulation results, from the application of three kinds of CMAC, demonstrate that the HCMAC has a better learning performance than CMAC with general basis functions (Chiang; Lin, 1996) and general Albus CMAC (Albus, 1975). For mapping with large-dimensional input, the conventional CMACs need large weight memory space, while the need usually is not met. In order to overcome the issue, a new CMAC structure containing several HCMACs is proposed, the input space of each HCMAC is a subset of input space to be mapped. The CMAC structure is called SHCMAC. Simulations for the SHCMAC used in a multivariable nonlinear dynamic system modelling are performed to demonstrate its powerful associative memory performance and the accuracy in modeling

A hybrid fuzzy logic and neural network algorithm for robot motion control

Robotic manipulators are multivariable nonlinear coupling dynamic systems. Industrial robots were controlled by using a traditional controller, the control performance of which may change with respect to operating conditions. Since the robotic manipulators have complicated nonlinear mathematical models, control systems based on the system model are difficult to design. In this paper, a model-free hybrid fuzzy logic and neural network algorithm was proposed to control this multi-input/multi-output (MIMO) robotic system. First, a fuzzy logic controller was designed to control individual joints of this 4-degree-of-freedom (DOF) robot. Secondly, a coupling neural network controller was introduced to take care of the coupling effect among joints and refine the control performance of this robotic system. The experimental results showed that the application of this control strategy effectively improved the trajectory tracking precision.

Adaptive fuzzy modeling of nonlinear dynamical systems

Fuzzy modeling of multivariable discrete-time nonlinear dynamical systems is approached analytically in this paper. We start by developing a proper framework based on the key notions of fuzzy quantization and function approximation. With the suitable formulation, an on-line scheme is developed that adaptively forms the fuzzy model from samples of a dynamical system by generating and modifying a set of fuzzy rules and membership functions. The convergence analysis of the scheme is carried out rigorously, based on the Lyapunov theory, and the major convergence result is established. The scheme is also applied to a real-world modeling problem to demonstrate its feasibility and effectiveness.

State estimation scheme for nonlinear dynamical systems based on the stochastic approximation

An algorithm for the state estimation of multivariable nonlinear dynamic systems with noisy nonlinear observation systems is investigated on the basis of stochastic approximation procedure. Using an extended version of Dvoretzky's theorem, we derive a sufficient condition that estimation error converges to zero, both in the mean square and with probability one for noise-free multivariable dynamical systems. We then show that our estimation procedure makes the estimation error bounded in the mean square norm for noisy dynamical systems. Some numerical examples are presented for the illustration of the approach mentioned above.