Algorithm For Nonlinear Systems Research Articles

Direct neural network-based self-tuning control for a class of nonlinear systems

Most self-tuning control algorithms for nonlinear systems become invalid when the controlled systems have nonminimum phase property. In this article, a direct neural network-based self-tuning control strategy is developed to deal with this problem under the certainty equivalence principle. Based on an equivalent linearized model from the local linearization, the controller structure is designed using a modified Clarke index with the guaranteed closed-loop stability and without the traditional requirement of the globally boundedness. For the system with unknown parameters, the controller is self-tuned by an on line RBF neural network identifier. Satisfactory simulations illustrate the effectiveness and adaptability of the proposed strategy even under system parameter variations.

Monotonic Newton method based ILC with parameter optimization for non-linear systems

Despite the significant progress on iterative learning control (ILC) in the past decade, ILC algorithms for non-linear systems are still under development. Monotonic convergence is one of the desirable properties of non-linear ILC. In this paper, by introducing a relaxation index, a Newton method based ILC is shown to converge monotonically. Simulations verify the effectiveness of the new algorithm. Potential improvements are discussed for future work.

Error Propagation in Implicit Pseudodynamic Testing of Nonlinear Systems

Error propagation analysis of an implicit pseudodynamic algorithm has been developed for linear elastic systems. However, these error propagation results might not be applicable to nonlinear systems. Since the pseudodynamic testing method aims at investigating the nonlinear behavior of a seismically loaded structure it is important to perform the error propagation analysis of the implicit pseudodynamic algorithm for nonlinear systems. A technique to conduct the nonlinear error propagation analysis of an implicit pseudodynamic algorithm is constructed and is illustrated by analyzing the constant average acceleration method. Theoretical results reveal that the numerical and error propagation properties for nonlinear systems are generally inherited from those of linear elastic systems although some properties are affected by the step degree of nonlinearity. It is verified that the most important property of unconditional stability is preserved for nonlinear systems for a complete pseudodynamic test procedure even if the convergence error is present. It is concluded that error propagation for the improved implementation is superior to that of the direct implementation and is consistent with that developed for linear elastic systems.

A reference governor-based controller for a cable robot under input constraints

Cable-suspended robots are structurally similar to parallel actuated robots but with the fundamental difference that cables can only pull the end-effector but not push it. From a scientific point of view, this feature makes feedback control of cable-suspended robots lot more challenging than their counter- part parallel actuated robots. In this brief, we look into the control design for a nonredundant cable-suspended robot under positive input constraints. The design is based on feedback linearization controllers augmented with a reference governor (RG). This RG operates in accordance with the receding horizon strategy, by generating admissible reference signals, that do not violate the input constraints. An important issue in implementing such an algorithm for nonlinear systems is to predict the system behavior in a computationally efficient way. We show that feedback lin- earization controllers with the RG can offer an efficient way to predict the system's future states, using the error dynamics of inner feedback loop. Finally, the effectiveness of the proposed method is illustrated by numerical simulation and laboratory experiments on a 6-degree-of-freedom cable suspended robot.

On the solution of the tracking problem for non-linear systems with MPC

This paper presents a Model Predictive Control (MPC) algorithm for non-linear systems which solves the tracking problem for asymptotically constant references. Closed-loop stability of the equilibrium and asymptotic zero-error regulation are guaranteed. The performance of the method is discussed with the classical Continuous Stirred Tank Reactor (CSTR) control application.

TRACKING OF NON-SQUARE NONLINEAR SYSTEMS WITH MODEL PREDICTIVE CONTROL

This paper presents a Model Predictive Control (MPC) algorithm for nonlinear systems. It allows the tracking of reference signals constant after a certain time by imposing integral action on the error variables, rather than on the control moves as in standard MPC methods. The plant under control, the state and control constraints and the performance index to be minimized are described in continuous time, while the manipulated variables are allowed to change at fixed and uniformly distributed sampling times. A simulation example is reported and discussed in detail.

Model Predictive Control of Continuous-Time Nonlinear Systems With Piecewise Constant Control

A new model predictive control (MPC) algorithm for nonlinear systems is presented. The plant under control, the state and control constraints, and the performance index to be minimized are described in continuous time, while the manipulated variables are allowed to change at fixed and uniformly distributed sampling times. In so doing, the optimization is performed with respect to sequences, as in discrete-time nonlinear MPC, but the continuous-time evolution of the system is considered as in continuous-time nonlinear MPC.

Convergence Acceleration Scheme for Self-consistent Orthogonal-basis-set Electronic Structure Methods

A new self-consistent convergence acceleration scheme that is a variant of the Newton-Raphson algorithm for non-linear systems of equations is presented. With this scheme, which is designed for use with minimal orthogonal basis set electronic structure methods, the conventional Newton-Raphson scaling with respect to the number of atoms is enhanced from quartic to cubic. The scheme is demonstrated using a self-consistent environment-dependent tight binding model for hydrocarbons that allows an efficient and reasonably precise simulation of charge density distortions due to external electric fields, finite system sizes, and surface effects. In the case of a metallic system, self-consistency convergence starts at a high fictitious temperature, typically 1500 K. As the electron density approaches the self-consistent configuration the temperature is decreased. Typically, seven to nine iterations are required to achieve self-consistency in metallic systems to a final temperature of 300 K. For systems with a finite band gap the convergence may start at the target temperature so that temperature reduction is unnecessary, and typically two iterations are needed to achieve self-consistency. The convergence algorithm can handle extremely high applied fields and is very robust with respect to initial electron densities.

Tracking of Nonlinear Systems via Model Based Predictive Control

Abstract This paper presents a new Model Predictive Control ( MPC ) algorithm for nonlinear systems which solves the output tracking problem for asymptotically constant references. Closed-loop stability of the equilibrium and asymptotic zero-error regulation are guaranteed. The method is based on the solution of a finite-horizon optimization problem where the future error and control deviation norms are minimized. In the optimization it is assumed that a stabilizing linear dynamic regulator is used at the end of the control horizon, although it is never applied in practice. State and control constraints can be included in the problem and preprogrammed reference signals can be considered. The performances of the method are discussed on the classical Continuous Stirred Tank Reactor ( CSTR ) control application.

Truncated difference ABS type algorithm for nonlinear systems*

A truncated form of the difference ABS-type algorithm is proposed and its local convergence property is investigated.

A partitioned adaptive approach to nonlinear channel equalization

The problem of identifying digital transmitted symbols over nonlinear communication channels is addressed. The equalization scenario is considered from the decision point of view, and constitutes a joint identification and estimation situation due to incomplete knowledge of the system model. A new class of multilinearization algorithms for nonlinear systems is derived according to partitioning theory concepts. The procedure targets on adaptively selecting the best reference points for linearization from an ensemble of generated trajectories that span the whole state space of the desired signal. In the various simulations examined, the partitioned-based equalizer is found superior to the classical extended Kalman filter.

Production planning with simulation techniques

Conley (1985) presented a multi-stage simulation algorithm for non-linear systems of equations that could be enhanced by the use of more sophisticated combination transformations in conjunction with his basic simulation sampling scheme. This allows the solution of larger non-linear systems and makes practical the modelling of processes with more variables and constraints. A production scheduling problem with 25 variables and constraints is presented in this paper.

A two-level costate prediction algorithm for non-linear systems

A two level costate prediction algorithm is developed for the optimisation of non-linear discrete dynamical systems. The algorithm is proved to converge under fairly mild conditions. The algorithm appears to require substantially smaller computation time and storage than previous two level algorithms. The method is illustrated on a practical problem of optimisation of turbogenerator transient performance.