Abstract: A method based on conceptual tools of predictive control is described for solving set-point tracking problems wherein pointwise-in-time input and/or state inequality constraints are present. It consists of adding to a primal compensated system a nonlinear device, called command governor (CG), whose action is based on the current state, set-point, and prescribed constraints. The CG selects at any time a virtual sequence among a family of linearly parameterized command sequences, by solving a convex constrained quadratic optimization problem, and feeds the primal system according to a receding horizon control philosophy. The overall system is proved to fulfill the constraints, be asymptotically stable, and exhibit an offset-free tracking behavior, provided that an admissibility condition on the initial state is satisfied. Though the CG can be tailored for the application at hand by appropriately choosing the available design knobs, the required online computational load for the usual case of affine constraints is well tempered by the related relatively simple convex quadratic programming problem.

Abstract: A new terminal sliding mode control of MIMO linear systems is proposed in this paper. It is shown that, by inserting a nonlinear term of the system state in the MIMO linear sliding mode, a new terminal sliding mode is developed for MIMO linear systems. A terminal sliding mode controller can then be designed to drive the system state variables to reach and retain in the terminal sliding mode. By suitably designing the parameter matrices of the terminal sliding mode, the system state variables reach the system origin in finite time and the closed loop system is infinite stable in the terminal sliding mode.

Abstract: This paper focuses on the problem of exponential stabilization of controllable, driftless systems using time-varying, homogeneous feedback. The analysis is performed with respect to a homogeneous norm in a nonstandard dilation that is compatible with the algebraic structure of the control Lie algebra. It can be shown that any continuous, time-varying controller that achieves exponential stability relative to the Euclidean norm is necessarily non-Lipschitz. Despite these restrictions, we provide a set of constructive, sufficient conditions for extending smooth, asymptotic stabilizers to homogeneous, exponential stabilizers. The modified feedbacks are everywhere continuous, smooth away from the origin, and can be extended to a large class of systems with torque inputs. The feedback laws are applied to an experimental mobile robot and show significant improvement in convergence rate over smooth stabilizers.

Abstract: From the Publisher: Control problems offer an industrially important application and a guide to understanding control systems for those working in Neural Networks. Neural Systems for Control represents the most up-to-date developments in the rapidly growing aplication area of neural networks and focuses on research in natural and artifical neural systems directly applicable to control or making use of modern control theory. The book covers such important new developments in control systems such as intelligent sensors in semiconductor wafer manufacturing; the relation between muscles and cerebral neurons in speech recognition; online compensation of reconfigurable control for spacecraft aircraft and other systems; applications to rolling mills, robotics and process control; the usage of past output data to identify nonlinear systems by neural networks; neural approximate optimal control; model-free nonlinear control; and neural control based on a regulation of physiological investigation/blood pressure control. All researchers and students dealing with control systems will find the fascinating Neural Systems for Control of immense interest and assistance. Key Features: Focuses on research in natural and artifical neural systems directly applicable to contol or making use of modern control theory Represents the most up-to-date developments in this rapidly growing application area of neural networks Takes a new and novel approach to system identification and synthesis

Abstract: In many applications, magnetic suspension systems are required to operate over large variations in air gap. As a result, the nonlinearities inherent in most types of suspensions have a significant impact on performance. Specifically, it may be difficult to design a linear controller which gives satisfactory performance, stability, and disturbance rejection over a wide range of operating points. One way to address this problem is through the use of nonlinear control techniques such as feedback linearization. For most common designs of magnetic suspensions the governing equations are in the so-called companion form, lending themselves to feedback linearization. A single degree of freedom magnetic suspension has been designed and constructed in order to compare the performance of linear and nonlinear digital control schemes in a well-controlled experimental environment. We demonstrate the superiority of nonlinear controllers over conventional controllers for systems with large variations in operating point via experiments on our system.

Abstract: Sensorless current mode (SCM) control is an observer method that provides the operating benefits of current mode control without current sensing. SCM has significant advantages over both conventional peak and average current-mode control techniques in noise susceptibility and dynamic range. The method supports both line and bulk load regulation, and reduces control complexity to a single loop. The static and dynamic performance of SCM are analyzed and verified experimentally for DC-DC converters. Performance in continuous and discontinuous modes compares favorably to conventional techniques when noise is not a factor, but is significantly better when noise and wide load ranges are a concern. The SCM method encompasses one-cycle control as a special case; the general SCM method is introduced here as a public domain control technique.

Abstract: This paper presents an approach to robustness analysis for nonlinear feedback systems. We pursue a notion of model uncertainty based on the closeness of input-output trajectories which is not tied to a particular uncertainty representation, such as additive, parametric, structured, etc. The basic viewpoint is to regard systems as operators on signal spaces. We present two versions of a global theory where stability is captured by induced norms or by gain functions. We also develop local approaches (over bounded signal sets) and give a treatment for systems with potential for finite-time escape. We compute the relevant stability margin for several examples and demonstrate robustness of stability for some specific perturbations, e.g., small-time delays. We also present examples of nonlinear control systems which have zero robustness margin and are destabilized by arbitrarily small gap perturbations. The paper considers the case where uncertainty is present in the controller as well as the plant and the generalization of the approach to the case where uncertainty occurs in several subsystems in an arbitrary interconnection.

Abstract: With the increase in popularity of active materials for control actuation, renewed interest is evident in the derivation of control methodologies for aeroelastic systems. It has been known for some time that prototypical aeroelastic wing sections can exhibit a broad class of pathological response regimes when the system includes certaintypesofnonlinearities.Weinvestigatenonlinearcontrollawsforaeroelasticsystemsthatincludepolynomial structural nonlinearities and study the closed-loop stability of the system. It is shown that locally asymptotically stable(nonlinear)feedbackcontrollerscanbederivedfortheaeroelasticsystemusingpartialfeedbacklinearization techniques. In this case, the stability results are necessarily local in nature and are derived by considering stability of theassociated zero dynamics subsystem. Itis also demonstrated that globally stable (nonlinear)adaptivecontrol methods can be derived for a class of aeroelastic systems under consideration. Numerical simulations are used to provide empirical validation of some of the results.

Abstract: This paper introduces a methodology for the synthesis of nonlinear finite-dimensional output feedback controllers for systems of quasi-linear parabolic partial differential equations (PDE), for which the eigenspectrum of the spatial differential operator can be partitioned into a finite-dimensional slow one and an infinite-dimensional stable fast one. Combination of Galerkin's method with a novel procedure for the construction of approximate inertial manifolds for the PDE system is employed for the derivation of ordinary differential equation (ODE) systems (whose dimension is equal to the number of slow modes) that yield solutions which are close, up to a desired accuracy, to the ones of the PDE system, for almost all times. These ODE systems are used as the basis for the synthesis of nonlinear output feedback controllers that guarantee stability and enforce the output of the closed-loop system to follow up to a desired accuracy, a prespecified response for almost all times.

Abstract: A systems theory framework is presented for the linear stabilization of two-dimensional laminar plane Poiseuille flow. The governing linearized Navier{Stokes equations are converted to control-theoretic models using a numerical discretization scheme. Fluid system poles, which are closely related to Orr{Sommerfeld eigenvalues, and fluid system zeros are computed using the control-theoretic models. It is shown that the location of system zeros, in addition to the well-studied system eigenvalues, are important in linear stability control. The location of system zeros determines the eect of feedback control on both stable and unstable eigenvalues. In addition, system zeros can be used to determine sensor locations that lead to simple feedback control schemes. Feedback controllers are designed that make a new fluid{actuator{sensor{ controller system linearly stable. Feedback control is shown to be robust to a wide range of Reynolds numbers. The systems theory concepts of modal controllability and observability are used to show that feedback control can lead to short periods of highamplitude transients that are unseen at the output. These transients may invalidate the linear model, stimulate nonlinear eects, and/or form a path of ‘bypass’ transition in a controlled system. Numerical simulations are presented to validate the stabilization of both single-wavenumber and multiple-wavenumber instabilities. Finally, it is shown that a controller designed upon linear theory also has a strong stabilizing eect on two-dimensional nite-amplitude disturbances. As a result, secondary instabilities due to innitesimal three-dimensional disturbances in the presence of a nite-amplitude two-dimensional disturbance cease to exist.

Abstract: From the Publisher: Nonlinear and Optimal Control Systems offers a self-contained introduction to analysis techniques used in the design of nonlinear and optimal feedback control systems, with a solid emphasis on the fundamental topics of stability, controllability, optimality, and the corresponding geometry. The book develops and presents these key subjects in a unified fashion. An integrated approach is used to develop stability theory, function minimizing feedback controls, optimal controls, and differential game theory. Starting with a background on differential equations, this accessible text examines nonlinear dynamical systems and nonlinear control systems, including basic results in nonlinear parameter optimization and parametric two-player games. Lyapunov stability theory and control system design are discussed in detail, followed by in-depth coverage of the controllability minimum principle and other important controllability concepts. The optimal control (Pontryagin's) minimum principle is developed and then applied to optimal control problems and the design of optimal controllers. Nonlinear and Optimal Control Systems features examples and exercises taken from a wide range of disciplines and contexts - from engineering control designs to biological, economic, and other systems. Numerical algorithms are provided for solving problems in optimization and control, as well as simulation of systems using nonlinear differential equations. Readers may choose to develop their own code from these algorithms or solve problems with the help of commercial software programs. Providing readers with a sturdy foundation in nonlinear and optimal control system design and application, this new resource is a valuable asset to advanced students and professional engineers in many different fields.

Abstract: This paper presents the dynamic equation, nonlinear control and dynamic parameters identification of the Hexaglide, a new 6-DOF parallel manipulator intended to be used as a high speed milling machine. Using a method based on the virtual work principle, the dynamic equation is found in a compact linear form and then used in a nonlinear adaptive control algorithm based on the minimization of the tracking error. The dynamic parameters are learned during motion and introduced in an inverse dynamic model used as a feedforward compensator. Specific trajectories, exciting the parameters separately, enable a fast stepwise learning of the 12 parameters. A simulation demonstrates the validity of the approach.

Abstract: This paper describes a nonlinear control structure known as a local controller network. The structure consists of a weighted combination of a number of individual controllers, each of which is valid locally in the state space of the plant. Local controller designs are based upon local models valid in operating regimes which do not necessarily contain any physical equilibria. Consequently, the transient performance can be improved. Some 'scheduling' variables determine the current operating regime, and a validity function is assigned to each local controller. A 'feedforward' component may be used in each local controller in order to compensate directly for the operating-point-dependent model offsets. The application of the local controller network approach to a nonlinear control problem, that of longitudinal vehicle dynamics control, is described. A stability analysis for the discrete-time local controller network is given in this paper and the results are compared with known theoretical guidelines for rel...

Abstract: This work introduces a new robust motion control algorithm using partial state feedback for a class of nonlinear systems in the presence of modelling uncertainties and external disturbances. The effects of these uncertainties are combined into a single quantity called perturbation. The major contribution of this work comes as the development and design of a robust observer for the state and the perturbation which is integrated into a Variable Structure Controller (VSC) structure. The proposed observer combines the procedures of Sliding Observers (Slotine et al, 1987) with the idea of Perturbation Estimation (Elmali and Olgac, 1992). The result is what is called Sliding Perturbation Observer (SPO). The VSC follows the philosophy of Sliding Mode Control (SMC) (Slotine and Sastry, 1983). This combination of controller/observer gives rise to the new routine called Sliding Mode Control with Sliding Perturbation Observer (SMCSPO). The stability analysis shows how the algorithm parameters are scheduled in order to assure the sliding modes of both controller and observer. A simplified form of the general design procedure is also presented in order to ease the practical applications of SMCSPO. Simulations are presented for a two-link manipulator to verify the proposed approach. Experimental validation of the methodology is also performed on a PUMA 560 robot. A superior control performance is obtained over some full state feedback techniques such as SMC and Computed Torque Method.

Abstract: This paper introduces a sensorless nonlinear control scheme for controlling the speed of a permanent magnet synchronous motor (PMSM) driving an unknown load torque. The states of the motor and disturbance torque are estimated via an extended nonlinear observer avoiding the use of mechanical sensors. The control strategy is an exact feedback linearization law, with trajectory tracking evaluated on estimated values of the PMSM states and the disturbance torque. The system performance is evaluated by simulations.

Abstract: A nonlinear vectorial backstepping control law for commercial ships is derived by using the concept of vectorial backstepping. Vectorial backstepping is done in 3 steps corresponding to the state vectors of the ship dynamics, kinematics and actuator dynamics. Emphasis is placed on compensation of the actuator dynamics since the bandwidth of the propellers, thrusters and rudders often is close to the bandwidth of the ship dynamics. Global exponential tracking is proven by applying Lyapunov stability analysis. The case study is simultaneously global exponential tracking of the surge and sway positions (x,y) and the yaw angle /spl psi/ of a surface ship. This can only be done by applying nonlinear control theory due to the nonlinear structure of the kinematic equations, Coriolis and centripetal forces, and hydrodynamic damping forces.

Abstract: In this paper, we propose a method of robust nonlinear H master-slave synchronization for chaotic Lur'e systems with applications to secure communication. The scheme makes use of vector field modulation and either full static state or linear dynamic output error feedback control. The master-slave systems are assumed to be nonidentical and channel noise is taken into account. Binary valued continuous time message signals are recovered by minimizing the -gain from the exogenous input to the tracking error for the standard plant representation of the scheme. The exogenous input takes into account the message signal, channel noise and parameter mismatch. Matrix inequality conditions for dissipativity with finite -gain of the standard plant form are derived based on a quadratic storage function. The controllers are designed by solving a nonlinear optimization problem which takes into account both channel noise and parameter mismatch. The method is illustrated on Chua's circuit.

Abstract: As has been realized, the flexible-link manipulators have attracted more and more attention from robot control theorists and/or robot users because of its various potential advantages But since the control degree-of-freedom is much less than that of the system, many control strategies which succeed in the conventional rigid robot control cannot be directly used in the flexible robot control problems In this paper, a nonlinear control scheme has been proposed as a solution to these control problems In particular, to cope with the existing model uncertainty, an adaptive version of this nonlinear control law has been proposed Stability proof of the overall closed-loop system is then given via Lyapunov analysis In addition, extensive experimental results are also provided to demonstrate the effectiveness of the proposed controller

Abstract: In this paper we provide the first proof of stability of an extremum seeking feedback scheme by employing the tools of averaging and singular perturbation analysis. Our scheme is much more general that the existing extremum control results which represent the plant as a static nonlinear map possibly cascaded with a linear dynamic block-we allow the plant to be a general nonlinear dynamic system (possibly non-affine in control and open-loop unstable) whose reference-to-output equilibrium map has a maximum, and whose equilibria are locally exponentially stabilizable.

Abstract: In this paper, we examine the global stability and instability problems for a class of discrete-time adaptive nonlinear stochastic control. The systems to be controlled may exhibit chaotic behavior and are assumed to be linear in unknown parameters but nonlinear in output dynamics, which are characterized by a nonlinear function (say, f(x)). It is found and proved that in the scalar parameter case there is a critical stability phenomenon for least squares (LS)-based adaptive control systems. To be specific, let the growth rate of f(x) be f(x)=O(/spl par/x/spl par//sup 6/) with b/spl ges/0, then it is found that b=4 is a critical value for global stability, i.e., the closed-loop adaptive system is globally stable if b<4 and is unstable in general if b/spl ges/4. As a consequence, we find an interesting phenomenon that the linear case does not have: for some LS-based certainty equivalence adaptive controls, even if the LS parameter estimates are strongly consistent, the closed-loop systems may still be unstable. This paper also indicates that adaptive nonlinear stochastic control that is designed based on, e.g., Taylor expansion (or Weierstrass approximation) for nonlinear models, may not be feasible in general.