Robust Control Of Nonlinear Systems Research Articles

Robust control of nonlinear systems in the presence of unknown exogenous dynamics

A robust control is designed for a class of uncertain systems, the proposed control is distinct and novel in that it does not require any information of a bounding function on nonlinear uncertainties in the system. Instead, the uncertainties to be compensated for are generated by an exogenous system whose dynamics are either completely unknown or partially unknown. The only requirements on the exogenous system are that its unknown dynamics are bounded by a known function and that its output is bounded. The proposed robust control is based on a nonlinear observer that estimates the uncertainties. It is shown that, under different sets of conditions, local, semiglobal, or global stability of uniform ultimate boundedness or asymptotic stability can be achieved.

Robust control of nonlinear systems with parametric uncertainty

Probabilistic robustness analysis and synthesis for nonlinear systems with uncertain parameters are presented. Monte Carlo simulation is used to estimate the likelihood of system instability and violation of performance requirements subject to variations of the probabilistic system parameters. Stochastic robust control synthesis searches the controller design parameter space to minimize a cost that is a function of the probabilities that design criteria will not be satisfied. The robust control design approach is illustrated by a simple nonlinear example. A modified feedback linearization control is chosen as controller structure, and the design parameters are searched by a genetic algorithm to achieve the tradeoff between stability and performance robustness.

Robust control of nonlinear systems by estimating time variant uncertainties

In this paper, robust control design is considered for nonlinear systems with time-variant uncertainties. Instead of assuming that the bounding function on uncertainties is either known or parameterizable in terms of unknown constants, uncertainties or their bounding functions are estimated. It is shown that bounded uncertainties from a known or partially known exo-system can be estimated as a part of a globally stabilizing robust control. The proposed method extends the existing results of adaptive robust control, and it makes robust control more applicable by requiring less information on uncertainties.

Neural network adaptive robust control of nonlinear systems in semi-strict feedback form

In this paper, the recently proposed neural network adaptive robust control (NNARC) design is generalized to synthesize performance oriented control laws for a class of nonlinear systems transformable to the semi-strict feedback forms through the incorporation of backstepping design techniques. Both repeatable (or state dependent) unknown nonlinearities and nonrepeatable unknown nonlinearities such as external disturbances are considered. In addition, unknown nonlinearities can exist in the virtual control input channel of each intermediate step as well. All unknown but repeatable nonlinear functions are approximated by outputs of multi-layer neural networks to achieve a better model compensation for an improved performance. All NN weights are tuned on-line with no prior training needed. In order to avoid the possible divergence of the on-line tuning of neural networks, discontinuous projections with fictitious bounds are used in the NN weight adjusting law to make sure that all NN weights are tuned within a prescribed range. By doing so, even in the presence of approximation error and nonrepeatable nonlinearities such as disturbances, a controlled learning is achieved and the possible destabilizing effect of on-line tuning of NN weights could be avoided. Certain robust control terms can then be constructed to attenuate various model uncertainties effectively for a guaranteed output tracking transient performance and a guaranteed final tracking accuracy in general. The precision motion control of a linear motor drive system with slow electrical dynamics is used as a case study to illustrate the proposed NNARC methodology. Experimental results with a simulated slow electrical dynamics are presented.

Principle of minimum entropy production in applied soft computing for advanced intelligent robotics and mechatronics

A new approach to design of smart intelligent control systems for advanced robotics and mechatronics is developed. The principle of minimum entropy production in a control object motion and a control system as a fitness function for genetic algorithm is used. Simulation results of a smart robust control of non-linear systems described as coupled oscillators are presented.

Uncertainty modelling and robust output feedback control of nonlinear discrete systems: a mathematical programming approach

We present a mathematical programming approach to robust control of nonlinear systems with uncertain, possibly time-varying, parameters. The uncertain system is given by different local affine parameter-dependent models in different parts of the state space. It is shown how this representation can be obtained from a nonlinear uncertain system by solving a set of continuous linear semi-infinite programming problems, and how each of these problems can be solved as a (finite) series of ordinary linear programs. Additionally, the system representation includes control and state constraints. The controller design method is derived from Lyapunov stability arguments and utilizes an affine parameter-dependent quadratic Lyapunov function. The controller has a piecewise affine output feedback structure, and the design amounts to finding a feasible solution to a set of linear matrix inequalities combined with one spectral radius constraint on the product of two positive definite matrices. A local solution approach to this non-convex feasibility problem is proposed. Complexity of the design method and some special cases such as state feedback are discussed. Finally, an application of the results is given by proposing an on-line computationally feasible algorithm for constrained nonlinear state-feedback model predictive control with robust stability. Copyright © 2000 John Wiley & Sons, Ltd.

Robust Control of Nonlinear Systems Using Model-Error Control Synthesis

A new approach for the robust control of nonlinear systems is presented. This approach employs an optimal real-time nonlinear estimator to determine model error corrections to the control input using a one time-step ahead technique. Control compensation is achieved by using the estimated model error as a signal synthesis adaptive correction to the nominal control input so that maximum performance is achieved in the face of extreme model uncertainty and disturbance inputs. A significant advantage of this approach over other adaptive methods is that model parameters need not be updated online. Instead, the effects of these errors are used to update the actual control signal, which leads to a simple design strategy. The model-error control synthesis approach is used in conjunction with a variable structure controller to suppress the wing-rock motion of a slender delta wing. Simulation results indicate that the model-error control synthesis approach is extremely effective in providing closed-loop robustness in the face of significant model uncertainties and disturbance inputs. 1 Assistant Professor, Texas A&M University, Department of Aerospace Engineering, College Station, TX 77843-3141. Senior Member AIAA.

I/O linearization based μ synthesis for nonlinear robust control systems

This paper deals with μ synthesis for nonlinear robust control systems based on I/O linearization. By nonlinear state feedback, nonlinear systems can be linearized as controllable linear systems, such that uncertain nonlinear systems can be expressed as linear fractional transformations (LFTs) on the generalized linearized plants and uncertainty By H ∞ optimization based μ synthesis technique, controllers can be obtained for the LFTs. Then the nonlinear robust control laws can be constructed by combining the controllers and the nonlinear state feedback. An example is given to illustrate the design.

A nonlinear sliding mode control design approach based on neural network modelling

A complete nonlinear framework for the modelling and robust control of nonlinear systems is proposed. The use of neural networks for continuous time modelling to obtain a certain nonlinear canonical form is investigated. The model obtained is used with recently proposed dynamic sliding mode controller design methods. The robustness bounds needed for controller design are determined from modelling errors. A modified version of the backpropagation theorem is also introduced. Copyright © 1999 John Wiley & Sons, Ltd.

Design and validation of linear robust controllers for nonlinear plants

SUMMARY This paper describes a robust nonlinear control system design procedure inspired by the nonlinear control ideas of Horowitz’s Quantitative Feedback Theory.1 The central concept is the identification of a family of linear time-invariant (LTI) plants that is equivalent to an uncertain nonlinear (and/or time varying) plant in the sense that an LTI controller feasible for this linear plant family is also feasible for the original nonlinear plant. We identify two conditions for evaluating an equivalent linear family (the equivalence condition and the continuity condition) and show that when these two conditions are satisfied an LTI controller that provides satisfactory robust control of an equivalent linear plant family also provides satisfactory robust control for the related uncertain nonlinear plant, independent of the robust design technique used. We then use these two conditions to analyse the validity of the nonlinear QFT design technique published earlier. Our results suggest that nonlinear QFT can be an attractive approach to nonlinear robust control but its validity (in the sense that the linear design solves the nonlinear control problem) can be demonstrated only if additional conditions and contraints not previously reported are satisfied. ( 1998 John Wiley & Sons, Ltd.

μ Analysis and μ synthesis for nonlinear robust control systems

A μ analysis and μ synthesis method for nonlinear robust control systems was presented. The nonlinear robust control problem using μ method was described. By means of the nonlinear state feedback and state coordinates transformation, many uncertain nonlinear systems can be transformed as a linear fractional transformation (LFT) on the generalized plant and the uncertainty. Based on the LFT, a linear robust controller can be obtained by the D-K iteration and then a corresponding nonlinear robust control law is constructed. An example was given in the paper.

“Loop-at-a-Time” Design of Dynamic Surface Controllers for Nonlinear Systems

The use of multiple surface sliding controllers for robust control of nonlinear systems with mismatched uncertainties has produced a number of impressive applications, but also raised a few theoretical questions. Among the latter are the use of numerical differencing to obtain derivatives of desired trajectories, robustness to uncertainties in the gain terms and the common practice of filtering desired trajectories for implementation. This paper seeks to address these issues through the concept of a Dynamic Surface Controller, in which filters form an integral part of the structure. This filtering removes the need for numerical differencing and guarantees a certain smoothness, enabling other assumptions of smoothness to be relaxed. In this paper, the Dynamic Surface Controller is coupled with a sequential design procedure that carves a system workspace out of the state space. Within this bounded region, bounded tracking performance can be rigorously guaranteed in the presence of uncertainties and constraints such as rate limits and saturation can be systematically avoided. The design of a Dynamic Surface Controller and the advantages of the workspace concept are demonstrated in the context of engine speed control.

モデル化誤差を考慮した非線形系の適応ロバスト補償器の一構成法

モデル化誤差を考慮した非線形系の適応ロバスト補償器の一構成法

Adaptive Robust Control for Nonlinear Systems with Mismatched Uncertainties.

In this paper, the adaptive robust output tracking problem for a class of nonlinear systems which have both mismatched uncertainties and matched uncertainties has been addressed. The nominal system is input-output linearizable. Based on the input-output linearization technique and Lyapunov approach, an adaptive control law is developed to track the bounds on the plant uncertainties so that no prior knowledge of the bounds is required. it is shown that the output of the closed-loop systems ultimately track the desired output with a bounded tracking error despite the system uncertainties. An example is performed to illustrate the effectiveness of the proposed control scheme.

Robust control of nonlinear systems: An application to science policy

Robust control of nonlinear systems: An application to science policy

Min-Max Characterization of a Small Noise Limit on Risk-Sensitive Control

Stochastic control problems on a finite horizon with exponential cost criteria are considered. By taking a kind of singular limit a Hamilton--Jacobi--Isaacs equation is obtained. Its solution is characterized as the lower value function of a deterministic differential game related to robust control of nonlinear systems.

Adaptive Robust Control of Non linear Systems: Effective Use of Information

Abstract This paper considers the adaptive robust control of nonlinear systems in the presence of parametric uncertainties and uncertain nonlinearities. The assumption on the allowable uncertain nonlinearities is relaxed to the extent that uncertain nonlinearities are required to be bounded by some known functions multiplied by unknown but bounded time-varying disturbances only. The approach uses robust feedback to attenuate the effect of uncertainties to achieve a prescribed transient performance and final tracking accuracy. The approach also uses parameter adaptation to reduce model uncertainties to achieve asymptotic tracking in the presence of parametric uncertainties without using switching or infinite-gain feedback. Different design methods are examined and compared.

Robust Nonlinear Feedback Design via Quantifier Elimination Theory

In this paper symbolic-computation methods are used to design simple fixed-structure robust controller for nonlinear systems. Design specifications are reduced to logically quantified polynomial inequalities. The quantifier-elimination (QE) software package QEPCAD is used to eliminate quantifiers on state and plant parameters, to obtain regions of admissible controller parameters, that guarantee robust stability and performance.

Recent developments in nonlinear H∞ control

The last few years have seen a number of exciting developments in the area known as nonlinear H ∞ control. The aim of work in this area is to design robust controllers for nonlinear systems using generalizations of the highly successful H ∞ methods used in linear systems theory. In this paper we give an overview of the problems and methods of nonlinear H ∞ control, including the H ∞ norm ( L 2 gain), stability, information state methods, and factorization. The development of this area has involved important contributions from a number of researchers using a variety of techniques. In addition, H ∞ control has spurred renewed interest in some traditional areas such as differential games, dissipative systems, and stochastic (risk-sensitive) control.

Sensorless Positioning Control of Single-Link Robot Arm by Means of Sliding Mode Observer-Controller.

The advantages of applying sensorless control to mechanical systems are cost reduction, prevention of instability of the control system by collocation, noise reduction, decrease of breakdown frequency, increase of reliability and space saving. In this study, we deal with a sensorless positioning control problem of a single-link robot arm with nonlinear friction torque at the drive system. The state of the system is estimated by means of an observer from the angular velocity obtained indirectly from the coil current of the motor to drive the arm, and controlled by a controller. In order to realize such a control system, robust performances are required in the state estimation in addition to the control law. We combined a sliding mode observer and a sliding mode controller to construct a nonlinear robust control system. Then, we applied it to the motion control system of the robot arm. Finally, we investigated the performance with regard to positioning control of the arm.