Abstract: A novel robust adaptive controller for multi-input multi-output (MIMO) feedback linearizable nonlinear systems possessing unknown nonlinearities, capable of guaranteeing a prescribed performance, is developed in this paper. By prescribed performance we mean that the tracking error should converge to an arbitrarily small residual set, with convergence rate no less than a prespecified value, exhibiting a maximum overshoot less than a sufficiently small prespecified constant. Visualizing the prescribed performance characteristics as tracking error constraints, the key idea is to transform the ldquoconstrainedrdquo system into an equivalent ldquounconstrainedrdquo one, via an appropriately defined output error transformation. It is shown that stabilization of the ldquounconstrainedrdquo system is sufficient to solve the stated problem. Besides guaranteeing a uniform ultimate boundedness property for the transformed output error and the uniform boundedness for all other signals in the closed loop, the proposed robust adaptive controller is smooth with easily selected parameter values and successfully bypasses the loss of controllability issue. Simulation results on a two-link robot, clarify and verify the approach.

Abstract: Conventions and Notation xv Preface xxi Chapter 1. Introduction 1 Chapter 2. Dynamical Systems and Differential Equations 9 Chapter 3. Stability Theory for Nonlinear Dynamical Systems 135 Chapter 4. Advanced Stability Theory 207 Chapter 5. Dissipativity Theory for Nonlinear Dynamical Systems 325 Chapter 6. Stability and Optimality of Feedback Dynamical Systems 411 Chapter 7. Input-Output Stability and Dissipativity 471 Chapter 8. Optimal Nonlinear Feedback Control 511 Chapter 9. Inverse Optimal Control and Integrator Backstepping 557 Chapter 10. Disturbance Rejection Control for Nonlinear Dynamical Systems 603 Chapter 11. Robust Control for Nonlinear Uncertain Systems 649 Chapter 12. Structured Parametric Uncertainty and Parameter-Dependent Lyapunov Functions 719 Chapter 13. Stability and Dissipativity Theory for Discrete-Time Nonlinear Dynamical Systems 763 Chapter 14. Discrete-Time Optimal Nonlinear Feedback Control 845 Bibliography 901 Index 939

Abstract: "Nonlinear and Adaptive Control with Applications" provides a detailed treatment of the design of robust adaptive controllers for nonlinear systems with uncertainties. The authors employ a new tool based on the ideas of system immersion and manifold invariance. Departing, in part, from the Lyapunov-function approach of classical control, new algorithms are delivered for the construction of robust asymptotically-stabilising and adaptive control laws for nonlinear systems. The methods proposed lead to modular schemes. These algorithms cater for nonlinear systems with both parametric and dynamic uncertainties. This innovative strategy is illustrated with several examples and case studies from real applications. Power converters, electrical machines, mechanical systems, autonomous aircraft and computer vision are among the practical systems dealt with. Researchers working on adaptive and nonlinear control theory or on control applications will find this monograph of conspicuous interest while graduate students in control systems and control engineers working with electrical, mechanical or electromechanical systems can also gain much insight and assistance from the methods and algorithms detailed.

Abstract: We consider a tracking problem for a partially feedback linearizable nonlinear system with stable zero dynamics. The system is uncertain and only the output is measured. We use an extended high-gain observer of dimension n+1, where n is the relative degree. The observer estimates n derivatives of the tracking error, of which the first (n-1) derivatives are states of the plant in the normal form and the nth derivative estimates the perturbation due to model uncertainty and disturbance. The controller cancels the perturbation estimate and implements a feedback control law, designed for the nominal linear model that would have been obtained by feedback linearization had all the nonlinearities been known and the signals been available. We prove that the closed-loop system under the observer-based controller recovers the performance of the nominal linear model as the observer gain becomes sufficiently high. Moreover, we prove that the controller has an integral action property in that it ensures regulation of the tracking error to zero in the presence of constant nonvanishing perturbation.

Abstract: An image-based visual servo control is presented for an unmanned aerial vehicle (UAV) capable of stationary or quasi-stationary flight with the camera mounted onboard the vehicle. The target considered consists of a finite set of stationary and disjoint points lying in a plane. Control of the position and orientation dynamics is decoupled using a visual error based on spherical centroid data, along with estimations of the linear velocity and the gravitational inertial direction extracted from image features and an embedded inertial measurement unit. The visual error used compensates for poor conditioning of the image Jacobian matrix by introducing a nonhomogeneous gain term adapted to the visual sensitivity of the error measurements. A nonlinear controller, that ensures exponential convergence of the system considered, is derived for the full dynamics of the system using control Lyapunov function design techniques. Experimental results on a quadrotor UAV, developed by the French Atomic Energy Commission, demonstrate the robustness and performance of the proposed control strategy.

Abstract: This paper considers two cooperative control problems for nonholonomic mobile agents. In the first problem, we discuss the design of cooperative control laws such that a group of nonholonomic mobile agents cooperatively converges to some stationary point under various communication scenarios. Dynamic control laws for each agent are proposed with the aid of sigma-processes and results from graph theory. In the second problem, we discuss the design of cooperative control laws such that a group of mobile agents converges to and tracks a target point which moves along a desired trajectory under various communication scenarios. By introducing suitable variable transformations, cooperative control laws are proposed. Since communication delay is inevitable in cooperative control, in each of the above cooperative control problems, we analyze the effect of delayed communication on the proposed controllers. As applications of the proposed results, formation control of wheeled mobile robots is discussed. It is shown that our results can be successfully used to solve formation control problem. To show effectiveness of the proposed approach, simulation results are included.

Abstract: The dynamics of many physical processes can be suitably described by Port-Hamiltonian (PH) models, where the importance of the energy function, the interconnection pattern and the dissipation of the system is underscored. To regulate the behavior of PH systems it is natural to adopt a Passivity-Based Control (PBC) perspective, where the control objectives are achieved shaping the energy function and adding dissipation. In this paper we consider the PBC techniques of Control by Interconnection (CbI) and Standard PBC. In CbI the controller is another PH system connected to the plant (through a power-preserving interconnection) to add up their energy functions, while in Standard PBC energy shaping is achieved via static state feedback. In spite of the conceptual appeal of formulating the control problem as the interaction of dynamical systems, the current version of CbI imposes a severe restriction on the plant dissipation structure that stymies its practical application. On the other hand, Standard PBC, which is usually derived from a uninspiring and non-intuitive ldquopassive output generationrdquo viewpoint, is one of the most successful controller design techniques. The main objectives of this paper are: (1) To extend the CbI method to make it more widely applicable-in particular, to overcome the aforementioned dissipation obstacle. (2) To show that various popular variants of Standard PBC can be derived proceeding from a unified perspective. (3) To establish the connections between CbI and Standard PBC proving that the latter is obtained restricting the former to a suitable subset-providing a nice geometric interpretation to Standard PBC-and comparing the size of the set of PH plants for which they are applicable.

Abstract: We consider the class of nonlinear optimal control problems (OCPs) with polynomial data, i.e., the differential equation, state and control constraints, and cost are all described by polynomials, and more generally for OCPs with smooth data. In addition, state constraints as well as state and/or action constraints are allowed. We provide a simple hierarchy of LMI- (linear matrix inequality)-relaxations whose optimal values form a nondecreasing sequence of lower bounds on the optimal value. Under some convexity assumptions, the sequence converges to the optimal value of the OCP. Preliminary results show that good approximations are obtained with few moments.

Abstract: In this paper, a feedback linearization-based controller with a high-order sliding mode observer running parallel is applied to a quadrotor unmanned aerial vehicle. The high-order sliding mode observer works as an observer and estimator of the effect of the external disturbances such as wind and noise. The whole observer–estimator–control law constitutes an original approach to the vehicle regulation with minimal number of sensors. Performance issues of the controller–observer are illustrated in a simulation study that takes into account parameter uncertainties and external disturbances. Copyright © 2007 John Wiley & Sons, Ltd.

Abstract: This article presents a unified synchronization framework with application to precision formation flying spacecraft. Central to the proposed innovation, in applying synchronization to both translational and rotational dynamics in the Lagrangian form, is the use of the distributed stability and performance analysis tool, called contraction analysis that yields exact nonlinear stability proofs. The proposed decentralized tracking control law synchronizes the attitude of an arbitrary number of spacecraft into a common time-varying trajectory with global exponential convergence. Moreover, a decentralized translational tracking control law based on phase synchronization is presented, thus enabling coupled translational and rotational maneuvers. While the translational dynamics can be adequately controlled by linear control laws, the proposed method permits highly nonlinear systems with nonlinearly coupled inertia matrices such as the attitude dynamics of spacecraft whose large and rapid slew maneuvers justify the nonlinear control approach. The proposed method integrates both the trajectory tracking and synchronization problems in a single control framework.

Abstract: Two well known approaches to nonlinear control involve the use of control Lyapunov functions (CLFs) and receding horizon control (RHC), also known as model predictive control (MPC). The on-line Euler-Lagrange computation of receding horizon control is naturally viewed in terms of optimal control, whereas researchers in CLF methods have emphasized such notions as inverse optimality. We focus on a CLF variation of Sontag's formula, which also results from a special choice of parameters in the so-called pointwise min- norm formulation. Viewed this way, CLF methods have direct connections with the Hamilton-Jacobi-Bellman formulation of optimal control. A single example is used to illustrate the various limitations of each approach. Finally, we contrast the CLF and receding horizon points of view, arguing that their strengths are complementary and suggestive of new ideas and opportunities for control design. The presentation is tutorial, emphasizing concepts and connec- tions over details and technicalities.

Abstract: The use of a neural network (NN) as a feedforward control element to compensate for nonlinear system uncertainties has been investigated for over a decade. Typical NN-based controllers yield uniformly ultimately bounded (UUB) stability results due to residual functional reconstruction inaccuracies and an inability to compensate for some system disturbances. Several researchers have proposed discontinuous feedback controllers (e.g., variable structure or sliding mode controllers) to reject the residual errors and yield asymptotic results. The research in this paper describes how a recently developed continuous robust integral of the sign of the error (RISE) feedback term can be incorporated with a NN-based feedforward term to achieve semi-global asymptotic tracking. To achieve this result, the typical stability analysis for the RISE method is modified to enable the incorporation of the NN-based feedforward terms, and a projection algorithm is developed to guarantee bounded NN weight estimates.

Abstract: Low gain feedback has found several applications in constrained control systems, robust control and nonlinear control. Low gain feedback refers to a family of stabilizing state feedback gains that are parameterized in a scalar and go to zero as the scalar decreases to zero. Such feedback gains can be constructed either by an eigenstructure assignment algorithm or through the solution of a parametric algebraic Riccati equation (ARE). The eigenstructure assignment approach leads to feedback gains in the form of a matrix polynomial in the parameter, while the ARE approach requires the solution of an ARE for each value of the parameter. This note proposes an alternative approach to low gain feedback design based on the solution of a parametric Lyapunov equation. Such an approach possesses the advantages of both the eigenstructure assignment approach and the ARE-based approach. It also avoids the possible numerical stiffness in solving a parametric ARE and the structural decomposition of the open loop system that is required by the eigenstructure assignment approach.

Abstract: The steady-state regulation error in power converters that use the conventional hysteresis-modulation-based sliding mode controller can be suppressed through the incorporation of an additional integral term of the state variables into the controller. However, it is found that with the indirect type of sliding mode controller (derived based on the equivalent control approach), the same approach of integral sliding mode control is ineffective in alleviating the converter's steady-state error. Moreover, the error increases as the converter's switching frequency decreases. This paper presents an in-depth study of the phenomenon and offers a solution to the problem. Specifically, it is proposed that an additional double-integral term of the controlled variables to be adopted for constructing the sliding surface of indirect sliding mode controllers. Simulation and experimental results are provided for verification.