Neural network based terminal iterative learning control for uncertain nonlinear non‐affine systems

In this paper, a novel neural network based terminal iterative learning control method is proposed for a class of uncertain nonlinear non‐affine systems to track run‐varying reference point with initial state variance. In this new control scheme, the non‐affine terminal dynamics are converted affine, and the unrealisable recurrent network is simplified into realisable static network. As a result, the effect of initial state and control signal on terminal output can be estimated by neural network. With this estimation, the proposed control scheme can drive nonlinear non‐affine systems to track run‐varying reference point in the presence of initial state variance. Stability and convergence of this approach are proven, and numerical simulation results are provided to verify its effectiveness.     

Adaptive control of non‐linear systems with unknown virtual control coefficients

This paper deals with state feedback adaptive control of parametric‐strict‐feedback (triangular) non‐linear systems with unknown virtual control coefficients. A priori knowledge of the signs of the virtual coefficients is not required, and control signals and adaptive laws are smooth. Asymptotic tracking of smooth reference signals is achieved while all the variables remain bounded. The proposed algorithms make use of backstepping and tuning functions, and enlarge the class of non‐linear systems with unknown parameters for which asymptotic output tracking can be achieved. Copyright © 2000 John Wiley & Sons, Ltd.     

Multiobjective constrained MPC with simultaneous closed‐loop identification

Model predictive control (MPC) methodologies are commonly used techniques for constrained control problems. In this paper, the principle of prioritized multiobjective optimization is incorporated in an adaptive MPC framework in order to improve the closed‐loop performance in the case of time‐varying systems. Instead of weighting the different control goals, the proposed methodology creates a hierarchy according to the importance of each objective and optimizes each one separately. In each optimization step a constraint is added, so that previous in rank objective functions maintain their optimal values. Adaptive capabilities are introduced in the proposed MPC formulation, by considering the persistent excitation requirement as a top priority objective, which is optimized first. The efficiency of the proposed MPC configuration is evaluated through three dynamic processes and the expected advantages are confirmed. Copyright © 2006 John Wiley & Sons, Ltd.     

Inverse optimal adaptive control for non‐linear uncertain systems with exogenous disturbances

A Lyapunov‐based inverse optimal adaptive control‐system design problem for non‐linear uncertain systems with exogenous ℒ︁₂ disturbances is considered. Specifically, an inverse optimal adaptive non‐linear control framework is developed to explicitly characterize globally stabilizing disturbance rejection adaptive controllers that minimize a nonlinear‐nonquadratic performance functional for non‐linear cascade and block cascade systems with parametric uncertainty. It is shown that the adaptive Lyapunov function guaranteeing closed‐loop stability is a solution to the Hamilton–Jacobi–Isaacs equation for the controlled system and thus guarantees both optimality and robust stability. Additionally, the adaptive Lyapunov function is dissipative with respect to a weighted input–output energy supply rate guaranteeing closed‐loop disturbance rejection. For special integrand structures of the performance functionals considered, the proposed adaptive controllers additionally guarantee robustness to multiplicative input uncertainty. In the case of linear‐quadratic control it is shown that the operations of parameter estimation and controller design are coupled illustrating the breakdown of the certainty equivalence principle for the optimal adaptive control problem. Finally, the proposed framework is used to design adaptive controllers for jet engine compression systems with uncertain system dynamics. Copyright © 2000 John Wiley & Sons, Ltd.     

A convex optimization approach to adaptive stabilization of discrete‐time LTI systems with polytopic uncertainties

This paper suggests a simple convex optimization approach to state‐feedback adaptive stabilization problem for a class of discrete‐time LTI systems subject to polytopic uncertainties. The proposed method relies on estimating the uncertain parameters by solving an online optimization at each time step, such as a linear or quadratic programming, and then, on tuning the control law with that information, which can be conceptually viewed as a kind of gain‐scheduling or indirect adaptive control. Specifically, an admissible domain of stabilizing state‐feedback gain matrices is designed offline by means of linear matrix inequality problems, and based on the online estimation of the uncertain parameters, the state‐feedback gain matrix is calculated over the set of stabilizing feedback gains. The proposed stabilization algorithm guarantees the asymptotic stability of the overall closed‐loop control system. An example is given to show the effectiveness of the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Control of sub‐harmonic oscillation in peak current mode buck converter with dynamic resonant perturbation

In this paper, a dynamic resonant perturbation (DRP) method is proposed to control sub‐harmonic oscillation in a peak current mode controlled buck converter. Different from the traditional non‐feedback resonant parametric perturbation method, the proposed DRP method extracts an approximate sinusoidal control signal from the output voltage. The self‐stabilizing condition for the designed control signal is presented, and its analog circuit implementation is given as well. Furthermore, the system stability boundary is obtained by investigating the system eigenvalues, and the control parameter is effectively determined. The presented simulation and experiment results show that the proposed DRP method eliminates sub‐harmonic oscillation without sacrificing the peak value of the inductor current and features with a self‐stabilizing characteristic for external condition changes. Copyright © 2014 John Wiley & Sons, Ltd.     

Swing‐up and stabilization control of a cart– pendulum system via energy control and controlled Lagrangian methods

This paper addresses a swing‐up and stabilizing problem for a cart– pendulum system, which consists of a pendulum and a motor‐driven cart. Existing methods are based on the strategy of swing‐up of the pendulum by energy control methods, then switching the controllers to balance the pendulum when it approaches the upright position. The switching angle influences significantly control performance, so the pendulum might fall down if the angle is inadequately chosen. This paper proposes a swing‐up and stabilizing control method which makes it possible to determine an appropriate switching angle more arbitrarily. In addition to the energy control method for swing‐up, a stabilizing method based on controlled Lagrangians is adopted instead of a linear controller. The attractive domain of the closed‐loop system with this method can be known in advance and is wider than with linear controllers. In this way, our proposed control strategy overcomes the difficulty in choosing the switching angle of the controllers. An experimental result illustrates the effectiveness of the proposed method. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 160(4): 24– 31, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20534     

Semi‐adaptive control of convexly parametrized systems with application to temperature regulation of chemical reactors

In this paper, we are interested in the problem of adaptive control of non‐linearly parametrized systems. We investigate the viability of defining a stabilizing parameter update law for the case when the plant model is convex on the uncertain parameters. We show that, when the only prior knowledge is convexity, there does not exist an adaptation law—derivable from the standard separable Lyapunov function technique of Parks—applicable for all the state space. Therefore, we propose a semi‐adaptive state feedback controller where adaptation takes place only in the region of the state space where convexity can be used to reduce parameter uncertainty. In the remaining part of the state space we freeze the adaptation and switch to a robust controller. This scheme ensures semi‐global stability for convexly parametrized non‐linear systems with matched uncertainty. The proposed controller is then applied to the problem of temperature regulation of continuous stirred exothermic chemical reactors where reaction heat is convex in the uncertain parameters. Copyright © 2001 John Wiley & Sons, Ltd.     

A design method of a generalized predictive control system based on parametrization of two‐degree‐of‐freedom integral controllers

A new design method for a generalized predictive control (GPC) system based on parametrization of two‐degree‐of‐freedom integral controllers has been proposed. The objective is to guarantee stability of the control system without depending on the design parameters and to achieve low sensitivity against the plant perturbation and the disturbance. The design procedure consists of two steps. First, we design a basic integral controller for a nominal plant using the linear quadratic Gaussian (LQG) method and parametrize a class of two‐degree‐of‐freedom stabilizing controllers. Next, we tune the feedforward controller to incorporate the GPC method into our control structure. A numerical example is presented to show the effectiveness of the proposed method by comparing it with the conventional GPC method. © 1999 Scripta Technica, Electr Eng Jpn, 129(2): 62–70, 1999     

Bilinear models in adaptive control

A key issue, which is addressed in the paper, is the development of an efficient adaptive control algorithm for disturbed, non‐linear objects. A generalized non‐linear model of the controlled plant is proposed. Model of disturbances is assumed to be a bilinear time‐series model. Minimum‐variance control of non‐linear systems with bilinear model of disturbances is considered. For a generalized system model simple, weighed and generalized adaptive control algorithms are proposed. A comparison of different non‐linear adaptive control algorithms is performed. Copyright © 2000 John Wiley & Sons, Ltd.     

Direct adaptive control for non‐linear uncertain systems with exogenous disturbances

A direct adaptive non‐linear control framework for multivariable non‐linear uncertain systems with exogenous bounded disturbances is developed. The adaptive non‐linear controller addresses adaptive stabilization, disturbance rejection and adaptive tracking. The proposed framework is Lyapunov‐based and guarantees partial asymptotic stability of the closed‐loop system; that is, asymptotic stability with respect to part of the closed‐loop system states associated with the plant. In the case of bounded energy L₂ disturbances the proposed approach guarantees a non‐expansivity constraint on the closed‐loop input–output map. Finally, several illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach. Copyright © 2002 John Wiley & Sons, Ltd.     

Non‐invasive chaos control of DC–DC converter and its optimization

The frequency‐domain‐based realization condition related to a novel non‐invasive chaos control is presented in this paper. According to the common piecewise‐linear characteristics of PWM‐controlled DC–DC converter system, a general expression for its Jacobian matrix is derived for optimizing the control parameters of the proposed non‐invasive chaos control. The relevant simulation and experiment results about the application of the chaos control to a voltage‐mode Buck converter are given, which confirm the feasibility of the parameter‐optimization method and the validity of the proposed non‐invasive chaos control. Copyright © 2010 John Wiley & Sons, Ltd.     

LONG-RANGE PREDICTIVE CONTROL WITH STEADY STATE ERROR WEIGHTING

The long-range predictive control strategy is extended to include a terminal matching condition so that the final control law minimizes the squares of prediction errors over a small future prediction horizon and at steady state. The weighting on the terminal condition is a better alternative than a large prediction horizon, which requires a heavy computational load. It also leads to the formulation of an approximate long range predictive controller with knowledge of only a few initial step response coefficients and the steady state gain. Evaluations of steady state error weighting show that the weighting provides similar effects to ordinary control weighting but in addition has the stabilizing effects of a large predictive control horizon. An adaptive version of this control strategy has been successfully applied to the control of mean arterial blood pressure. © 1997 by John Wiley & Sons, Ltd.     

Discrete space vector modulation and optimized switching sequence model predictive control for three-level voltage source inverters

This paper proposes a discrete space vector modulation and optimized switching sequence model predictive controller for three-level neutral-point-clamped inverters in grid-connected applications. The proposed strategy is based on cascaded model predictive control (MPC) for controlling the grid current while maintaining the capacitor voltage balanced without weighting factor. To enhance the closed-loop performance, the external MPC evaluates 19 basic and 138 virtual vectors (VV) of the proposed space vector method. The optimal control voltage is then selected using an extended deadbeat method to reduce the execution time of the proposed control algorithm. By using the discrete space vector modulation principle, the VV are synthesized based on switching sequence (SS) and are divided into negative and positive SSs considering their impact on the neutral point (NP) potential. The inner MPC evaluates both types of SSs and selects the one that keeps the capacitor voltage balanced. Various controllers are evaluated and compared against the proposed control strategy. The results show that the proposed strategy improves performance without weighting factor, while maintaining a total harmonic distortion of current to be less than 2%. Compared to the modulated MPC which provides the same fxed switching frequency, the proposed controller reduces the computational burden by over 50% while also providing better NP voltage balance accuracy     

Non‐linear analog circuit fault diagnosis with large change sensitivity

Large change sensitivity has been proved efficient at, but restricted to, generating a linear circuit fault dictionary. This paper discusses the extension of large change sensitivity to non‐linear analog circuit fault diagnosis. The fault dictionary is divided into d.c. and a.c. sections. In the d.c. domain, non‐linear components are approximated with piecewise linear models. By relating the operating region of each piecewise linear model to the magnitude of a single fault in a procedure termed preconditioning, it is shown that large change sensitivity can efficiently compute the response of a faulty non‐linear circuit. Results presented of an analysis of computational complexity show a significant reduction in the cost of simulating single linear resistor faults in a non‐linear circuit using this method. In addition, after establishing that the resistive portion of the circuit is fault free, a fault dictionary is constructed for dynamic components using large change sensitivity in the small signal a.c. domain. Included with a discussion on the issues of large change sensitivity based simulation‐before‐test, a small non‐linear circuit is used to demonstrate the effectiveness of the proposed fault diagnosis algorithm. Copyright © 2000 John Wiley & Sons, Ltd.     

A new decoupling design of self‐tuning multivariable generalized predictive control

A novel robust decoupling method with multivariable generalized predictive control (MGPC) for a class of nonlinear systems is presented in an adaptive version. The cross‐coupling action and the non‐linear actors of the system are identified on‐line by a neural network. A feedforward compensation based on generalized predictive control, is proposed for decoupling control. A modified recursive least‐squares (RLS) algorithm can be used to estimate the linear parameters for time‐varying systems. Simulations are carried out and the results show the effectiveness of the proposed algorithm. Copyright © 1999 John Wiley & Sons, Ltd.     

A robustification tool for adaptive non‐linear control

This paper presents a conceptually simple robustification approach for the adaptive control of a class of non‐linear systems with static and dynamic uncertainties. This approach generates a new class of robust adaptive non‐linear controllers and is based upon a combined application of the well‐known adaptive backstepping and recent non‐linear small‐gain techniques. The presented method is illustrated via a third‐ order chemical reactor with only temperature information, and under relaxed conditions. An adaptive output‐feedback stabilizer is obtained without resorting to any state observer. Copyright © 1999 John Wiley & Sons, Ltd.     

基于扩张状态观测器的 PMLSM 高阶自适应 非奇异快速终端滑模控制

为改善永磁直线同步电机控制系统的位置跟踪精度和鲁棒性,提出了一种基于扩张状态观测的高阶自适应非奇异快 速终端滑模控制方案。首先,设计了一种高阶非奇异快速终端滑模面,通过引入反馈电流实现对电机位置、速度和电流的整 体控制。其次,设计新型滑模趋近律,使控制系统能快速将误差趋近于零并削弱抖振。同时,引入自适应律估计并实时调整 趋近律系数。最后,设计了扩张状态观测观测外部扰动,从而提高位置跟踪系统的动态和稳态性能。基于 Lyapunov 稳定性 理论,证明了该控制系统的稳定性。通过仿真与实验验证,结果表明,提出的控制方法能有效提高系统的位置跟踪精度,并且 增强了系统的抗干扰能力。     

Discrete‐time periodic adaptive control for parametric systems with non‐sector nonlinearities

In this paper, a periodic adaptive control approach is proposed for a class of discrete‐time parametric systems with non‐sector nonlinearities. The proposed periodic adaptive control law is characterized by either one‐period delayed parametric updating or two‐period delayed parametric updating when input gain contains periodic unknowns. Logarithmic‐type discrete Lyapunov function is employed to handle the difficulties caused by the uncertainties that do not satisfy the linear growth condition. Some extensions to nonlinear systems with multiple unknown parameters and time‐varying input gain, tracking tasks, as well as higher‐order systems in canonical form, are also discussed. Copyright © 2013 John Wiley & Sons, Ltd.     

On parameter estimation for excitation control of synchronous generators

This paper deals with the problem of identification of the network parameters and the desired equilibrium in applications of excitation control for synchronous generators. Our main contribution is the construction of a new non‐linear identifier that provides asymptotically consistent estimates (with guaranteed transient bounds) of the line impedance and the equilibrium for the classical three‐dimensional flux‐decay model of a single generator connected to an infinite bus. This model is non‐linear, and non‐linearly parameterized, and the equilibria depend also non‐linearly on the unknown parameters. The proposed estimator can be used, adopting a certainty equivalent approach, to make adaptive any power system stabilizer that relies on the knowledge of these parameters. The behaviour of the scheme is illustrated in two simulated case studies with the interconnection and damping assignment passivity‐based controller recently proposed by the authors. Copyright © 2004 John Wiley & Sons, Ltd.