Adaptive regulation of MIMO linear systems against unknown sinusoidal exogenous inputs

This paper deals with the adaptive regulation problem in linear multi‐input multi‐output systems subject to unknown sinusoidal exogenous inputs, where the frequencies, amplitudes, and phases of the sinusoids are unknown and where the number of sinusoids is assumed to be known. The design of an adaptive regulator for the system under consideration is performed within a set of Q‐parameterized stabilizing controllers. To facilitate the design of the adaptive regulator, triangular decoupling is introduced in part of the closed‐loop system dynamics. This is achieved through the proper selection of the controller state feedback gain and the structure of the Q parameter. Regulation conditions are then presented for the case where the sinusoidal exogenous input properties are known. For the case where the sinusoidal exogenous input properties are unknown, an adaptation algorithm is proposed to tune the Q parameter in the expression of the parameterized controller. The online tuning of the Q parameter allows the controller to converge to the desired regulator. Convergence results of the adaptation algorithm are presented. A simulation example involving a retinal imaging adaptive optics system is used to illustrate the performance of the proposed adaptive system. Copyright © 2008 John Wiley & Sons, Ltd.     

MIMO multi‐periodic repetitive control system: universal adaptive control schemes

This paper presents a simple adaptive multi‐periodic repetitive control scheme when the MIMO LTI plant is not necessarily positive real (PR), however it is strictly minimum‐phase, the spectrum of high‐frequency gain matrix CB is symmetric and lies in the open right/left half complex plane(sign/spectrum definite). The non‐identifier‐based direct adaptive control technique, which does not need plant parameter information, is used to construct adaptive schemes and the system stability is analysed by Lyapunov second method. The extension to plant under certain non‐linear perturbations and an exponential stability scheme are also discussed. Finally, an adaptive proportional plus multi‐periodic repetitive control scheme is proposed. The theoretical findings are supported with simulations. Copyright © 2006 John Wiley & Sons, Ltd.     

Passivity‐based control for stabilization,regulation and tracking purposes of a class of nonlinear systems

In this paper, a new passivity‐based control (PBC) scheme based on state feedback is proposed in order to solve tracking, regulation and stabilization problems for a class of multi‐input multi‐output (MIMO) nonlinear systems expressed in the normal form, with time‐invariant parameters and locally bounded reference weakly minimum phase. For the proposed control scheme two new different state feedbacks, one non‐adaptive for the case when the system parameters are assumed to be known and the other adaptive for the case of unknown parameters, are developed. For the adaptive case it is assumed that the unknown parameters appear linearly in the equations. Analysis of the transient behaviour of the proposed control schemes is presented through the simulation of two examples. Copyright © 2006 John Wiley & Sons, Ltd.     

Adaptive inverse control of unmodeled stable SISO and MIMO linear systems

Adaptive‐signal‐processing techniques have been employed with great success in such applications as: system identification, channel equalization, statistical prediction and noise/echo cancellation. From a mathematical point of view, there is little difference between these applications and the types of operations required by control systems to control a dynamical system. This paper presents an approach to control systems called adaptive inverse control in which adaptive‐signal‐processing techniques are used throughout. Adaptive inverse control comprises three simultaneous processes. The plant is automatically modeled using adaptive system identification techniques. The dynamic response of the system is adaptively controlled using the resulting model and methods related to channel equalization. Adaptive disturbance canceling is performed using methods similar to noise canceling. The method applies directly to stable single‐input single‐output (SISO) and multi‐input multi‐output (MIMO) plants, and does not require an a priori model of the system. If the plant is unstable, it must first be stabilized using conventional feedback. This implies that at least a rudimentary model need be made if the plant is unstable. Once the plant is stabilized, adaptive inverse control may be applied to the stabilized system. Copyright © 2002 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.     

Intelligent control using multiple models and neural networks

Most adaptive control algorithms for nonlinear discrete time systems become invalid when the controlled systems have non‐minimum phase properties and large uncertainties. In this paper, an intelligent control method using multiple models and neural networks (NN) is developed to deal with those problems. The proposed control method includes a set of fixed controllers, a re‐initialized neural network (NN) adaptive controller and a free‐running NN adaptive controller. The bounded‐input‐bounded‐output (BIBO) stability and performance convergence of the system are guaranteed by the free‐running adaptive controller, while the multiple fixed controllers and the re‐initialized adaptive controller are used to improve the transient response. Simulation results are presented to demonstrate the effectiveness of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.     

Passification‐based adaptive control of linear systems: Robustness issues

Passivity is a widely used concept in control theory having led to many significant results. This paper concentrates on one characteristic of passivity, namely passification‐based adaptive control. This concept applies to multi‐input multi‐output systems for which exists a combination of outputs that renders the open‐loop system hyper‐minimum phase. Under such assumptions, the system may be passified by both high‐gain static output feedback and by a particular adaptive control algorithm. This last control law is modified here to guarantee its coefficients to be bounded. The contribution of this paper is to investigate its robustness with respect to parametric uncertainty. Time response characteristics are illustrated on examples including realistic situations with noisy output and saturated input. Theoretical results are formulated as linear matrix inequalities and can hence be readily solved with semi‐definite programming solvers. Copyright © 2007 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.     

An indirect adaptive pole‐placement control for MIMO discrete‐time stochastic systems

In this paper, an indirect adaptive pole‐placement control scheme for multi‐input multi‐output (MIMO) discrete‐time stochastic systems is developed. This control scheme combines a recursive least squares (RLS) estimation algorithm with pole‐placement control design to produce a control law with self‐tuning capability. A parametric model with a priori prediction outputs is adopted for modelling the controlled system. Then, a RLS estimation algorithm which applies the a posteriori prediction errors is employed to identify the parameters of the model. It is shown that the implementation of the estimation algorithm including a time‐varying inverse logarithm step size mechanism has an almost sure convergence. Further, an equivalent stochastic closed‐loop system is used here for constructing near supermartingales, allowing that the proposed control scheme facilitates the establishment of the adaptive pole‐placement control and prevents the closed‐loop control system from occurring unstable pole‐zero cancellation. An analysis is provided that this control scheme guarantees parameter estimation convergence and system stability in the mean squares sense almost surely. Simulation studies are also presented to validate the theoretical findings. Copyright © 2005 John Wiley & Sons, Ltd.     

Sliding mode disturbance observer‐based adaptive control for uncertain MIMO nonlinear systems with dead‐zone

In this paper, an adaptive integral sliding mode control (ISMC) scheme is developed for a class of uncertain multi‐input and multi‐output nonlinear systems with unknown external disturbance, system uncertainty, and dead‐zone. The research is motivated by the fact that the ISMC scheme against unknown external disturbance and system uncertainty is very important for multi‐input and multi‐output nonlinear systems. The system uncertainty, the unknown external disturbance, and the effect of dead‐zone are integrated as a compounded disturbance, which is well estimated using a sliding mode disturbance observer (SMDO). Then, the adaptive ISMC based on the designed SMDO is presented to guarantee the satisfactory tracking performance in the presence of system uncertainty, external disturbance, and dead‐zone. Finally, the designed adaptive ISMC strategy based on SMDO is applied to the attitude control of the near space vehicle, and simulation results are presented to illustrate the effectiveness of the proposed adaptive ISMC scheme using the SMDO. Copyright © 2016 John Wiley & Sons, Ltd.     

A small‐gain approach for adaptive output‐feedback NN control of switched pure‐feedback nonlinear systems

This paper investigates the problem of adaptive output‐feedback neural network (NN) control for a class of switched pure‐feedback uncertain nonlinear systems. A switched observer is first constructed to estimate the unmeasurable states. Next, with the help of an NN to approximate the unknown nonlinear terms, a switched small‐gain technique‐based adaptive output‐feedback NN control scheme is developed by exploiting the backstepping recursive design scheme, input‐to‐state stability analysis, the common Lyapunov function method, and the average dwell time (ADT) method. In the recursive design, the difficulty of constructing an overall Lyapunov function for the switched closed‐loop system is dealt with by decomposing the switched closed‐loop system into two interconnected switched systems and constructing two Lyapunov functions for two interconnected switched systems, respectively. The proposed controllers for individual subsystems guarantee that all signals in the closed‐loop system are semiglobally, uniformly, and ultimately bounded under a class of switching signals with ADT, and finally, two examples illustrate the effectiveness of theoretical results, which include a switched RLC circuit system.     

A study of decoupling with skeleton matrix in two‐degree‐of‐freedom generalized minimum variance control

There are many multi‐input multi‐output (MIMO) systems in chemical plants, and they have multiple time delays of different length in each input and output pair. This paper explains a two‐degree‐of‐freedom (2DOF) control system based on generalized minimum variance control (GMVC) for MIMO systems. It can improve the tracking performance with respect to the reference signals and the response properties for the disturbance. The states between the sampling period can be expressed by using the modified z transform to take account of multiple time delays. Additionally, a tracking controller is designed to decouple the plant. © 2011 Wiley Periodicals, Inc. Electr Eng Jpn, 176(1): 28–36, 2011; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/eej.21046     

Linear-like properties arise naturally in the adaptive control setting

Classical discrete-time adaptive controllers typically provide asymptotic stabilization and tracking; usually the affect of the noise is at best bounded-input bounded-output. Recently we have shown that if you design a discrete-time adaptive controller in just the right way, then in a variety of situations you not only obtain exponential stability, but also a bounded gain on the noise in every p−norm, as well as a never-before-seen linear-like convolution bound on the input–output behavior. Quite surprisingly, the approach is very natural, and relies on the use of the unmodified, original projection algorithm to carry out parameter estimation; if the set of plant uncertainty is not convex, then a multi-estimator and switching are used. The goal of this paper is to provide an overview of the approach, discuss the results-to-date, and list some of the open problems.     

Stabilizing switching control for nonlinear system based on quasi‐ARX RBFN model

In this paper, a fuzzy switching adaptive control approach is presented for nonlinear systems. The proposed fuzzy switching adaptive control law is composed of a quasi‐ARX radial basis function network (RBFN) prediction model and a fuzzy switching mechanism. The quasi‐ARX RBFN prediction model consists of two parts: a linear part used for a linear controller to ensure boundedness of the input and output signals; and an RBFN nonlinear part used to improve control accuracy. By using the fuzzy switching scheme between the linear and nonlinear controllers to replace the 0/1 switching, it can realize a better balance between stability and accuracy. Theoretical analysis and simulation results show the effectiveness of the proposed control method on the stability, accuracy, and robustness. © 2012 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Adaptive neural dynamic surface control of MIMO nonlinear time delay systems with time‐varying actuator failures

In this paper, an adaptive dynamic surface control approach is developed for a class of multi‐input multi‐output nonlinear systems with unknown nonlinearities, bounded time‐varying state delays, and in the presence of time‐varying actuator failures. The type of the considered actuator failure is that some unknown inputs may be stuck at some time‐varying values where the values, times, and patterns of the failures are unknown. The considered actuator failure can cover most failures that may occur in actuators of the systems. With the help of neural networks to approximate the unknown nonlinear functions and combining the dynamic surface control approach with the backstepping design method, a novel control approach is constructed. The proposed design method does not require a priori knowledge of the bounds of the unknown time delays and actuator failures. The boundedness of all the closed‐loop signals is guaranteed, and the tracking errors are proved to converge to a small neighborhood of the origin. The proposed approach is employed for a double inverted pendulums benchmark as well as a chemical reactor system. The simulation results show the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

On constructing complex grid multi‐wing hyperchaotic system: Theoretical design and circuit implementation

This paper further investigates some novel methods for generating complex grid multi‐wing hyperchaotic attractors from four‐dimensional (4D) quadratic hyperchaotic systems, based on our previous works. First, a modified double‐wing hyperchaotic Lü system by using non‐uniform variable scaling transformation is obtained, and n‐wing hyperchaotic system equipped with a duality‐symmetric multi‐segment quadratic function is also constructed. Then, by switching control in the z direction, mirror symmetry conversion and rotation transformation, three classes of n × m‐wing hyperchaotic systems are respectively realized. Finally, two types of improved module‐based circuits are designed for generating various grid multi‐wing hyperchaotic attractors. One characteristic of the proposed approaches lies in their generality, which is also suitable for constructing 4D grid multi‐wing hyperchaotic Lorenz and Chen systems. Both numerical simulation and circuit implementation have demonstrated the feasibility and effectiveness of the proposed approaches. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive controller design and disturbance attenuation for SISO linear systems with zero relative degree under noisy output measurements

In this paper, we present robust adaptive controller design for SISO linear systems with zero relative degree under noisy output measurements. We formulate the robust adaptive control problem as a nonlinear H^∞‐optimal control problem under imperfect state measurements, and then solve it using game theory. By using the a priori knowledge of the parameter vector, we apply a soft projection algorithm, which guarantees the robustness property of the closed‐loop system without any persistency of excitation assumption of the reference signal. Owing to our formulation in state space, we allow the true system to be uncontrollable, as long as the uncontrollable part is stable in the sense of Lyapunov, and the uncontrollable modes on the jω‐axis are uncontrollable from the exogenous disturbance input. This assumption allows the adaptive controller to asymptotically cancel out, at the output, the effect of exogenous sinusoidal disturbance inputs with unknown magnitude, phase, and frequency. These strong robustness properties are illustrated by a numerical example. Copyright © 2009 John Wiley & Sons, Ltd.     

An adaptive control scheme using multiple reference models

This paper develops an extended model reference adaptive control scheme to expand the capacity of state feedback state tracking adaptive control to handle the plant‐model matching uncertainties for single‐input LTI systems. The extended scheme is developed, using multiple reference model systems (only one of which is required to be able to match the controlled plant), and multiple controllers (which are updated from adaptive laws generated from multiple reference model systems based estimation errors), as two key features of such design to relax a plant‐model matching condition. A switching mechanism is constructed using those multiple estimation errors, capable of selecting the suitable control input from the multiple control signals, to achieve the desired system performance. An aircraft flight control example is presented to show the capacity of such design in relaxing a practical design condition. Copyright © 2013 John Wiley & Sons, Ltd.     

Optimal control of multi‐hop control networks based on the MLD framework

A multi‐hop control network (MHCN) is a control system in which plants and controllers are connected through a multi‐hop wireless network modeled by a directed graph. In this paper, based on the MLD (mixed logical dynamical) framework, which is one of the powerful methods in hybrid systems control, we propose a modeling method and an optimal control method of MHCNs. First, a directed graph in MHCNs and a switch of the control input are modeled by a pair of a linear state equation and a linear inequality with binary variables. Thus, the MLD model expressing a given MHCN is derived. Next, using the MLD model, the optimal control problem is transformed into a mixed integer quadratic programming problem. Finally, numerical examples are presented. The proposed method provides us a basic result for control of MHCNs. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Nonlinear reference tracking control of a gas turbine with load torque estimation

Input–output linearization‐based adaptive reference tracking control of a low‐power gas turbine model is presented in this paper. The gas turbine is described by a third‐order nonlinear input‐affine state‐space model, where the manipulable input is the fuel mass flowrate and the controlled output is the rotational speed. The stability of the one‐dimensional zero dynamics of the controlled plant is investigated via phase diagrams. The input–output linearizing feedback is extended with a load torque estimator algorithm resulting in an adaptive feedback scheme. The tuning of controller parameters is performed considering three main design goals: appropriate settling time, robustness against environmental disturbances and model parameter uncertainties, and avoiding the saturation of the actuator. Simulations show that the closed‐loop system is robust with respect to the variations in uncertain model and environ‐mental parameters and its performance satisfies the defined requirements. Copyright © 2007 John Wiley & Sons, Ltd.