Abstract: We consider the application of a formulation of passivity-based control (PBC), known as interconnection and damping assignment (IDA) to the problem of stabilization of underactuated mechanical systems, which requires the modification of both the potential and the kinetic energies. Our main contribution is the characterization of a class of systems for which IDA-PBC yields a smooth asymptotically stabilizing controller with a guaranteed domain of attraction. The class is given in terms of solvability of certain partial differential equations. One important feature of IDA-PBC, stemming from its Hamiltonian formulation, is that it provides new degrees of freedom for the solution of these equations. Using this additional freedom, we are able to show that the method of "controlled Lagrangians"-in its original formulation-may be viewed as a special case of our approach. As illustrations we design asymptotically stabilizing IDA-PBCs for the classical ball and beam system and a novel inertia wheel pendulum.

Abstract: A fast terminal dynamics is proposed and used in the design of the sliding-mode control for single-input single-output nonlinear dynamical systems. The inherent dynamic properties of the fast terminal sliding modes are explored and conditions to ensure its applicability for control designs are obtained.

Abstract: In this paper, direct adaptive neural-network (NN) control is presented for a class of affine nonlinear systems in the strict-feedback form with unknown nonlinearities. By utilizing a special property of the affine term, the developed scheme,avoids the controller singularity problem completely. All the signals in the closed loop are guaranteed to be semiglobally uniformly ultimately bounded and the output of the system is proven to converge to a small neighborhood of the desired trajectory. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters. Simulation results are presented to show the effectiveness of the approach.

Abstract: In this paper, we introduce a new method of model reduction for nonlinear control systems. Our approach is to construct an approximately balanced realization. The method requires only standard matrix computations, and we show that when it is applied to linear systems it results in the usual balanced truncation. For nonlinear systems, the method makes use of data from either simulation or experiment to identify the dynamics relevant to the input}output map of the system. An important feature of this approach is that the resulting reduced-order model is nonlinear, and has inputs and outputs suitable for control. We perform an example reduction for a nonlinear mechanical system.

Abstract: We propose a modular reinforcement learning architecture for nonlinear, nonstationary control tasks, which we call multiple model-based reinforcement learning (MMRL). The basic idea is to decompose a complex task into multiple domains in space and time based on the predictability of the environmental dynamics. The system is composed of multiple modules, each of which consists of a state prediction model and a reinforcement learning controller. The "responsibility signal," which is given by the softmax function of the prediction errors, is used to weight the outputs of multiple modules, as well as to gate the learning of the prediction models and the reinforcement learning controllers. We formulate MMRL for both discrete-time, finite-state case and continuous-time, continuous-state case. The performance of MMRL was demonstrated for discrete case in a nonstationary hunting task in a grid world and for continuous case in a nonlinear, nonstationary control task of swinging up a pendulum with variable physical parameters.

Abstract: Considers the problem of global stabilization by output feedback, for a family of nonlinear systems that are dominated by a triangular system satisfying a linear growth condition. The problem has remained unsolved due to the violation of the commonly assumed conditions in the literature. Using a feedback domination design method which is not based on the separation principle, we explicitly construct a linear output compensator making the closed-loop system globally exponentially stable.

Abstract: We consider adaptive output feedback control of uncertain nonlinear systems, in which both the dynamics and the dimension of the regulated system may be unknown. However, the relative degree of the regulated output is assumed to be known. Given a smooth reference trajectory, the problem is to design a controller that forces the system measurement to track it with bounded errors. The classical approach requires a state observer. Finding a good observer for an uncertain nonlinear system is not an obvious task. We argue that it is sufficient to build an observer for the output tracking error. Ultimate boundedness of the error signals is shown through Lyapunov's direct method. The theoretical results are illustrated in the design of a controller for a fourth-order nonlinear system of relative degree two and a high-bandwidth attitude command system for a model R-50 helicopter.

Abstract: A new image-based control strategy for visual servoing of a class of under-actuated rigid body systems is presented. The proposed control design applies to "eye-in-hand" systems where the camera is fixed to a rigid body with actuated dynamics. The control design is motivated by a theoretical analysis of the dynamic equations of motion of a rigid body and exploits passivity-like properties of these dynamics to derive a Lyapunov control algorithm using robust backstepping techniques. The proposed control is novel in considering the full dynamic system incorporating all degrees of freedom (albeit for a restricted class of dynamics) and in not requiring measurement of the relative depths of the observed image points. A motivating application is the stabilization of a scale model autonomous helicopter over a marked landing pad.

Abstract: A controller is developed for underactuated surface ships with only surge force and yaw moment available to globally asymptotically track a reference trajectory generated by a suitable virtual ship in a frame attached to the ship body. The reference trajectory is allowed too be a curve including a straight line. The control development is based on Lyapunov's direct method and backstepping technique, and utilizes several properties of ship dynamics and their interconnected structure. Numerical simulations are provided to validate the effectiveness of the proposed controller.

Abstract: The paper focuses on the problem of having the output of nonlinear systems track a prescribed C/sup 1/ reference signal. It is proved that, under mild assumptions, global practical output tracking is achievable by smooth state feedback, although asymptotic output tracking is usually not possible (even locally) because the linearized system has uncontrollable modes whose eigenvalues are on the right half plane. Smooth feedback controllers which solve the problem of global practical output tracking are explicitly constructed, based on a modified 'adding a power integrator' approach. This feedback design method also leads to solutions to challenging benchmark control problems, including practical output tracking of an underactuated unstable two degrees of freedom mechanical system.

Abstract: In this paper, advantages and disadvantages of classical PID are investigated from its basic principles. A new type controller Active Disturbances Rejection Controller(ADRC) with excellent characters is constructed via some links with especial functions,such as Tracking Differentiator(TD),Extended States Observer(ESO)and Nonlinear PID(NPID),which are based on the nonlinear control mechanisms. Furthermore, the new active disturbances rejection control technique is formed. The new controller possesses the following characteristics:the algorithm is simple; the adjustment of the parameters is easier.

Abstract: This paper describes the study results of developing an attitude control system for agile spacecraft which require rapid retargeting and fast transient settling. In particular, a nonlinear feedback control logic is developed for large-angle, rapid multi-target retargeting maneuvers subject to various physical constraints, including the actuator saturation, slew rate limit, control bandwidth limit, etc. Simulation results for an agile spacecraft equipped with control moment gyros demonstrate the effectiveness and robust performance of the proposed nonlinear feedback control system.

Abstract: This paper presents a nonlinear robust control algorithm for accurate positioning of a single degree of freedom rotary manipulator actuated by Shape Memory Alloy (SMA) A model for an SMA actuated manipulator is presented The model includes nonlinear dynamics of the manipulator, a constitutive model of Shape Memory Alloy, and electrical and heat transfer behavior of SMA wire This model is used for open and closed loop motion simulations of the manipulator Experiments are presented that show results similar to both closed and open loop simulation results Due to modeling uncertainty and nonlinear behavior of the system, classic control methods such as Proportional-Integral-Derivative control are not able to present fast and accurate performance Hence a nonlinear, robust control algorithm is presented based on Variable Structure Control This algorithm is a control gain switching technique based on the weighted average of position and velocity feedbacks This method has been designed through simulation and tested experimentally Results show fast, accurate, and robust performance of the control system Computer simulation and experimental results for different stabilization and tracking situations are also presented

Abstract: From the Publisher: Nonlinear Control of Engineering Systems is a research monograph on Lyapunov-based control design and analysis techinques for nonlinear systems. The basic idea is to illustrate how recent Lyapunov-based techniques can be utilized to develop control designs for nonlinear systems including: mechanical systems, electrical systems, robotic systems, aerospace systems, and underactuated systems. The introduction presents: (i) motivation for the Lyapunov-based design and analysis techniques, (ii) an overview of the book, (iii) some simple examples as an aid to the less experienced reader. The book presents a complete and detailed theoretical treatment of the stated control objective, and contains a detailed description of the experimental testbed and the results obtained by implementing the developed control algorithms. The experimental results will serve to complement the theoretical content of the book by: (i) demonstrating the feasibility of implementing "complex" nonlinear control algorithms with current computational hardware, (ii) guiding the reader towards adapting these techniques to his/her own needs or for further research, and (iii) bridging the gap between theoretical design and analysis and real-time implementation.

Abstract: Controls for an optical scanner, such as a single fiber scanning endoscope (SFSE) that includes a resonating optical fiber and a single photodetector to produce large field of view, high-resolution images. A nonlinear control scheme with feedback linearization is employed in one type of control to accurately produce a desired scan. Open loop and closed loops controllers are applied to the nonlinear optical scanner of the SFSE. A closed loop control (no model) uses either phase locked loop and PID controllers, or a dual-phase lock-in amplifier and two PIDs for each axis controlled. Other forms of the control that employ a model use a frequency space tracking control, an error space tracking control, feedback linearizing controls, an adaptive control, and a sliding mode control.

Abstract: In the automotive industry, suspension systems are designed to provide desirable vehicle ride and handling properties. This paper presents the development of a robust intelligent nonlinear controller for active suspension systems based on a comprehensive and realistic nonlinear model. The inherent complex nonlinear system model's structure, and the presence of parameter uncertainties, have increased the difficulties of applying conventional linear and nonlinear control techniques. Recently, the combination of sliding mode, fuzzy logic, and neural network methodologies has emerged as a promising technique for dealing with complex uncertain systems. In this paper, a sliding mode neural network inference fuzzy logic controller is designed for automotive suspension systems in order to enhance the ride and comfort. Extensive simulations are performed on a quarter-car model, and the results show that the proposed controller outperforms existing conventional controllers with regard to body acceleration, suspension deflection, and tire deflection.

Abstract: State-dependent Riccati equation (SDRE) techniques are general design methods which provide a systematic and effective means of designing nonlinear controllers, observers, and filters. The paper provides an overview of the capabilities of SDRE control and goes into detail concerning the art of carrying out effective SDRE designs for both systems that conform and do not conform to the basic structure and conditions required by the method. The paper is centered around the SDRE nonlinear regulator. The following situations which prevent a straightforward application of the SDRE method to the control problem at hand are addressed: the existence of state-independent terms, the existence of state-dependent terms which do not go to zero as the state vector goes to zero, the existence of nonlinearity in the controls, and the existence of uncontrollable and unstable but bounded state dynamics.

Abstract: In this thesis, new system identication methods are presented for three particular types of nonlinear systems: linear parameter-varying state-space systems, bilinear state-space systems, and local linear state-space systems. Although most work on nonlinear system identication deals with nonlinear input-output descriptions, this thesis focuses on state-space descriptions. State-space systems are considered, because they are especially suitable for dealing with multiple inputs and outputs, and they usually require less parameters to describe a system than input-output descriptions do. Equally important, the starting point of many nonlinear control methods is a state-space model of the system to be controlled.

Abstract: In this paper, we study the H/sub /spl infin// control problem for nonlinear descriptor systems governed by a set of differential-algebraic equations (DAEs) of the form Ex/spl dot/ = F(x, w, u), z = Z(x, w, u), y = Y(x, w, u), where E is, in general, a singular matrix. Necessary and sufficient conditions are derived for the existence of a controller solving the problem. We first give various sufficient conditions for the solvability of H/sub /spl infin// control problem for DAEs. Both state-feedback and output-feedback cases are considered. Then, necessary conditions for the output feedback control problem to be solvable are obtained in terms of two Hamilton-Jacobi inequalities plus a weak coupling condition. Moreover, a parameterization of a family of output feedback controllers solving the problem is also provided.

Abstract: This paper proposes a new control scheme for regulating the instantaneous power for PWM AC/DC type rectifiers under generalized unbalanced operating conditions. By nullifying the oscillating components of instantaneous power at the poles of the converter instead of the front-end through solving a set of nonlinear control equations in real time, the harmonics in the output DC voltage can be eliminated more effectively under generalized unbalanced operating conditions on the AC input side. The control scheme allows the PWM rectifier to generate a DC output without substantial even-order harmonics and to maintain nearly unity power factor under generalized unbalanced operating conditions, which makes it possible to reduce the size of the DC-link capacitor and AC inductors leading to the possibility of reduced total cost. Simulation results along with experimental results under the two examples of the unbalanced operating conditions confirm the feasibility of the new control method.

Abstract: With the rapid advance of digital control hardware, it is time to take the simple but effective proportional-integral-derivative (PID) control technology to the next level of performance and robustness. For this purpose, a nonlinear PID and active disturbance rejection framework are introduced in this paper. It complements the existing theory in that (1) it actively and systematically explores the use of nonlinear control mechanisms for better performance, even for linear plants; (2) it represents a control strategy that is rather independent of mathematical models of the plants, thus achieving inherent robustness and reducing design complexity. Stability analysis, as well as software/hardware test results, are presented. It is evident that the proposed framework lends itself well in seeking innovative solutions to practical problems while maintaining the simplicity and the intuitiveness of the existing technology.

Abstract: A contouring controller for biaxial systems that integrates the effects of feedback, feedforward, and cross-coupled control is proposed in this study. Conventional approaches to contouring control suffer from the complicated contour-error model and from lack of a systematic way for controller design. The integrated controller is based on polar coordinates under which a relatively simple contour-error model can be obtained. Taking the simple contour error as a state variable, the contouring-control problem is transformed into a stabilization problem. The feedback-linearization technique incorporated with linear feedback or robust control (such as sliding-mode control) can then yield the integrated controller. The proposed method is verified both numerically and experimentally and is compared with the conventional approach. It is found that the proposed controller is better for high speed and/or noncircular contouring. In addition, it can be applied to either linear plants or nonlinear plants (like linear motors).

Abstract: We develop an adaptive output feedback control methodology for nonaffine in control of uncertain systems having full relative degree. Given a smooth reference trajectory, the objective is to design a controller that forces the system measurement to track it with bounded errors. A neural network with linear parameters is introduced as an adaptive signal. A simple linear observer is proposed to generate an error signal for the adaptive laws. Ultimate boundedness is shown through Lyapunov's direct method. Simulations of a nonlinear second-order system illustrate the theoretical results.