Robust Control Of Nonlinear Systems Research Articles

Comments on “Chattering Free Robust Control for Nonlinear Systems”

The above paper claims that: 1) its sliding mode control does not contain any discontinuous function (or switching function) and 2) hence is chatter-free. In this letter, we present a simple counter-example to claim 1).

Adaptive control of a chaotic permanent magnet synchronous motor

This paper proposes a simple adaptive controller design method for a chaotic permanent magnet synchronous motor (PMSM) based on the sliding mode control theory which has given an effective means to design robust controllers for nonlinear systems with bounded uncertainties. The proposed sliding mode adaptive controller does not require any information on the PMSM parameter and load torque values, thus it is insensitive to model parameter and load torque variations. Simulation results are given to verify that the proposed method can be successfully used to control a chaotic PMSM under model parameter and load torque variations.

Fully Probabilistic Adaptive Control with Arbitrary Density Functions of Forward Models and Inverse Controllers

Robust controllers for nonlinear systems with non Gaussian random inputs and uncertain parameters can be reliably designed using probabilistic methods. In this paper, a design approach based on the combination of robust stochastic adaptive method and mixture density network (MDN) is proposed for general nonlinear ARMAX models with uncertain parameters and with non-Gaussian random inputs. Using MDNs, the probabilistic models of both the forward and inverse dynamics are estimated such that they are dependent on the state and the control input. The optimal control strategy is then derived which minimizes uncertainty of the closed loop system. In simulations, we see that the proposed MDN stochastic adaptive control algorithm outperforms the conventional stochastic adaptive control methods.

Non-linear disturbance observer-based robust control for systems with mismatched disturbances/uncertainties

Robust control of non-linear systems with disturbances and uncertainties is addressed in this study using disturbance observer-based control (DOBC) technique. In this framework, the ‘disturbance’ is a generalised concept, which may include external disturbances, unmodelled dynamics and system parameter perturbations. The existing DOBC methods were only applicable for the case where disturbances and uncertainties satisfy so-called matching condition, that is, they enter the system in the same channel as the control inputs. By appropriately designing a disturbance compensation gain vector in the composite control law, a non-linear disturbance observer-based robust control method is proposed in this study to attenuate the mismatched disturbances and the influence of parameter variations from system output channels. The proposed method is applied to a missile system with non-linear dynamics in the presence of various uncertainties and external disturbances. Simulation shows that, compared with the widely used non-linear dynamic inversion control (NDIC) and NDIC plus integral action methods, the proposed method provides much better disturbance attenuation ability and stronger robustness against various parameter variations.

Tube‐based robust nonlinear model predictive control

AbstractThis paper extends tube‐based model predictive control of linear systems to achieve robust control of nonlinear systems subject to additive disturbances. A central or reference trajectory is determined by solving a nominal optimal control problem. The local linear controller, employed in tube‐based robust control of linear systems, is replaced by an ancillary model predictive controller that forces the trajectories of the disturbed system to lie in a tube whose center is the reference trajectory thereby enabling robust control of uncertain nonlinear systems to be achieved. Copyright © 2011 John Wiley & Sons, Ltd.

Operator-based robust control for nonlinear systems with Prandtl–Ishlinskii hysteresis

This article presents an operator-based robust control method for nonlinear systems with Prandtl–Ishlinskii (PI) hysteresis. On the existence of the hysteresis, the system usually exhibits undesirable oscillations and even instability. While addressing the hysteresis, PI model is adopted to describe it. Especially, the PI model is decomposed into two terms: an invertible part and a disturbance part. In this way, the invertible part could be considered as a part of the nonlinear system. Based on the concept of Lipschitz's operator and the robust right coprime factorisation condition, a robust control design scheme is given to guarantee the bounded input bounded output stability of the obtained system. Further, a tracking operator design method is given to ensure the control system output-tracking performance under the existence of the disturbance part. Numerical simulation results are presented to validate the effectiveness of the proposed method.

Error Dynamics Shaping: a new robust control for nonlinear systems

AbstractThis paper introduces to Error Dynamics Shaping (EDS), an original nonlinear control methodology inspired from energy-based principles, which allows a robust stabilisation of closed-loop systems despite parametric uncertainties and disturbances. This methodology provides explicit state feedback control laws with intuitive tuning parameters. Based on the early idea to try and generate dissipative closed-loops with an adjustable damping degree when controlling physical systems, EDS defines a control procedure devoted to nonlinear systems that needs no energy formulation. It only requires the knowledge of a state space model of the system to be controlled. This approach is first described in a formal way, and then illustrated through an example.

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.

Operator-based robust nonlinear control system design for MIMO nonlinear plants with unknown coupling effects

In this article, operator-based robust nonlinear control system design for multi-input multi-output (MIMO) plants with unknown coupling effects is considered. That is, by using operator-based robust nonlinear control design, coupling effects existing in the MIMO nonlinear plants can be decoupled based on a feedback design and robust right coprime factorisation approach, the coupling effects caused by controllers and plant outputs can be stabilised by using definition of Lipschitz operator and contraction mapping theorem, and output tracking performance can be realised by a tracking design scheme. Finally, a simulation example about temperature control process of 3-input/3-output aluminum plate is given to support the theoretical analysis.

Singular perturbation method for robust control of nonlinear systems

In this paper, we consider robust control of nonlinear systems, via inclusion nonlinear systems solution and H ∞ controller using singular perturbation method. First, using technique for solving inclusion nonlinear systems, we transform the nonlinear system to ordinary nonlinear system. Then using normal form equations, we eliminate the nonlinear part of the system matrix of equations of system and transform it to a linear diagonal form. Separating new equations to slow and fast subsystems, due to the singular perturbation method and with the assumption of norm-boundedness of the fast dynamics, we can treat them as disturbance and design H ∞ controller for a system with a lower order than the original one that stabilizes the overall closed loop system. The proposed method is applied to a nominal system.

Observer-based fuzzy adaptive robust control of nonlinear systems with time delays and unmodeled dynamics

In this paper, an adaptive fuzzy output feedback backstepping control approach is developed for a class of nonlinear time-delay systems with unmeasured states and unmodeled dynamics. Using fuzzy logic systems to approximate unknown nonlinear functions, a fuzzy state observer is designed for estimating the unmeasured states. By combining adaptive backstepping technique with adaptive fuzzy control design and using changing supplying function idea, an observer-based adaptive fuzzy backstepping control approach is developed. It is proved that the proposed adaptive fuzzy control approach is able to guarantee that all the signals in the closed-loop system are semiglobally uniformly ultimately bounded (SUUB) and the output of the controlled system converges to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approach.

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.

Adaptive Sliding-Mode Control for Nonlinear Systems With Uncertain Parameters

This correspondence proposes a systematic adaptive sliding- mode controller design for the robust control of nonlinear systems with uncertain parameters. An adaptation tuning approach without high- frequency switching is developed to deal with unknown but bounded system uncertainties. Tracking performance is guaranteed. System robustness, as well as stability, is proven by using the Lyapunov theory. The upper bounds of uncertainties are not required to be known in advance. Therefore, the proposed method can be effectively implemented. Experimental results demonstrate the effectiveness of the proposed control method.

Adaptive robust control of nonlinear systems with dynamic uncertainties

AbstractIn this paper, the discontinuous projection‐based adaptive robust control (ARC) approach is extended to a class of nonlinear systems subjected to parametric uncertainties as well as all three types of nonlinear uncertainties—uncertainties could be state‐dependent, time‐dependent, and/or dynamic. Departing from the existing robust adaptive control approach, the proposed approach differentiates between dynamic uncertainties with and without known structural information. Specifically, adaptive robust observers are constructed to eliminate the effect of dynamic uncertainties with known structural information for an improved steady‐state output tracking performance—asymptotic output tracking is achieved when the system is subjected to parametric uncertainties and dynamic uncertainties with known structural information only. In addition, dynamic normalization signals are introduced to construct ARC laws to deal with other uncertainties including dynamic uncertainties without known structural information not only for global stability but also for a guaranteed robust performance in general. Copyright © 2008 John Wiley & Sons, Ltd.

Adaptive Sliding-Mode Control for NonlinearSystems With Uncertain Parameters

This correspondence proposes a systematic adaptive sliding-mode controller design for the robust control of nonlinear systems with uncertain parameters. An adaptation tuning approach without high-frequency switching is developed to deal with unknown but bounded system uncertainties. Tracking performance is guaranteed. System robustness, as well as stability, is proven by using the Lyapunov theory. The upper bounds of uncertainties are not required to be known in advance. Therefore, the proposed method can be effectively implemented. Experimental results demonstrate the effectiveness of the proposed control method.

Dynamic surface control approach to adaptive robust control of nonlinear systems in semi-strict feedback form

This article considers the adaptive robust control of a class of single-input-single-output nonlinear systems in semi-strict feedback form using radial basis function (RBF) networks. It is well known that the standard backstepping design may suffer from “explosion of terms”. To overcome this problem, the recently developed dynamic surface control technique which employs a first-order low-pass filter at each step of the backstepping design procedure is generalized to the nonlinear system under study. Our attention is paid to achieve guaranteed transient performance of the adaptive controller. At each step of design, a feedback controller strengthened by nonlinear damping terms to counteract nonlinear uncertainties is designed to guarantee input-to-state practical stability of the corresponding subsystem, and then parameter adaptations are introduced to reduce the ultimate error bound. Furthermore, for the output trajectory tracking problem, it is recommended to adopt the partial adaptation policy to reduce the computational burden due to “curse of dimension” of the RBF networks. Finally, numerical examples are included to verify the results of theoretical analysis.

838 観測器の応答と誤差の評価に基づく知的安全制御系設計

This paper considers the design problem of intelligent safe control system from the viewpoint of control engineering. There are various approaches to guarantee safety for automatic control. In this paper, first, a design of intelligent safe control system based on evaluation of response and error in observer is introduced. This approach is applicable to unexpected situation to some extent. Furthermore, the possibility of designing a nonlinear robust control system applicable to unexpected situation is presented by introducing an architecture of safe control system considering the governing principle of control objects.

A robust Markov game controller for nonlinear systems

This paper proposes a reinforcement learning (RL)-based game-theoretic formulation for designing robust controllers for nonlinear systems affected by bounded external disturbances and parametric uncertainties. Based on the theory of Markov games, we consider a differential game in which a 'disturbing' agent tries to make worst possible disturbance while a 'control' agent tries to make best control input. The problem is formulated as finding a min-max solution of a value function. We propose an online procedure for learning optimal value function and for calculating a robust control policy. Proposed game-theoretic paradigm has been tested on the control task of a highly nonlinear two-link robot system. We compare the performance of proposed Markov game controller with a standard RL-based robust controller, and an H~ theory-based robust game controller. For the robot control task, the proposed controller achieved superior robustness to changes in payload mass and external disturbances, over other control schemes. Results also validate the effectiveness of neural networks in extending the Markov game framework to problems with continuous state-action spaces.

Robust Adaptive Control of a Three-Axis Motion Simulator With State Observers

The development of a nonlinear robust adaptive tracking control system for a three-axis motion simulator is presented in this paper. The motion simulator is used to test and calibrate certain spacecraft instruments within a hardware-in-the-loop environment. Permanent magnet synchronous motor (PMSM) drives are used as simulator actuators. The control system is developed based on Lyapunov stability theory for which only rotor position and stator current signals are required. By using mechanical and electrical state observers, the measurement of acceleration and load torque which is usually required when motor dynamics are considered, is avoided. The control system can be made adaptable to constant unknown motor parameters and load inertia and robust to unknown but bounded fast varying disturbances. Simulation and experimental results are presented to verify the stability and efficacy of the proposed control system.

Decentralized nonlinear robust control of UAVs in close formation

AbstractThis paper treats the design of a decentralized nonlinear robust control system for formation flying of multiple unmanned aerial vehicles (UAVs). In close formation, it is assumed that vortex of any UAV affects the motion of all the UAVs behind it. The forces produced by these vortices are complex functions of relative position co‐ordinates of the UAVs. In this paper, these forces are treated as unknown functions, which cannot be parameterized. Since the system is not invertible in the wind axes system, a simplified co‐ordinate system obtained from the wind axes system for which the velocity roll (bank angle) is zero, is considered for the design of the control system. A nonlinear robust control system for the separation trajectory control of the wing aircraft in the simplified wind coordinate system is derived. Uncertain functions and unmeasured variables are estimated using a high‐gain observer for the synthesis of the control system. Each wing UAV synthesizes its control law using its own state variables and the relative position of the preceding UAV with respect to the wing UAV. Thus the control system is decentralized since each UAV has to communicate (depending on sensors for position measurement) with at most one (preceding) UAV, and no data transmission from the remaining vehicles is required. Simulation results for two UAVs are presented which show precise separation trajectory control of each wing UAV in spite of the presence of unknown and unstructured vortex forces, while the lead aircraft maneuvers. Furthermore, these results confirm that when the wing aircraft is positioned properly in the vortex of the lead aircraft, it experiences reduction in its required flight power. Copyright © 2003 John Wiley & Sons, Ltd.