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In recent years competition in the industrial world has become intense. As a result, the necessity for highly effective control techniques has increased. Furthermore, simple control structure and high robustness are also desirable. To meet these demands, model-driven type control theories type have been proposed. If these controllers are able to describe the model of the process accurately, then perfect...
Existing reachability theory and optimal control theory are applied to a class of nonlinear systems with ellipsoidal initial reachability sets, reflecting information typically provided by industry-standard optimal estimation methods. Analytical expressions for position-and velocity-extrema are developed, yielding necessary conditions for reachability as well as tools for significant reduction in...
This work proposes a robust control framework to address the problem of practical tracking for a class of nonlinear systems described as hybrid automata. The framework reposes both on a suitable definition of the references to be tracked and on input-to-state stability properties of the feedback laws in order to guarantee a desired behavior of the hybrid automata in terms of robust transition between...
This paper proposes a method to estimate the region of attraction of nonlinear polynomial systems. Based on quadratic Lyapunov functions, stability analysis conditions in a ??quasi??-LMI form are stated in a regional (local) context. An LMI-based optimization problem is then derived for computing the Lyapunov matrix maximizing the estimate of the region of attraction of the origin.
We present an algorithm for an event based approach to the global optimal control of nonlinear systems with coarsely quantized state measurement. The quantized measurements induce regions of the state space and the events represent the change of the system's state from one quantization region to another. We investigate the theoretical properties of the approach and illustrate the performance by a...
Time-delay is a widespread phenomenon of control system. Time-delay characteristics have a serious impact on system stability and performance. It is valuable to study iterative learning control of time-delay system. In this paper, we study the effects of multiple time delay on the convergence of nonlinear time-delay systems applying ??-norm and a set of inequalities. It will be shown that time-delay...
A new type of global stability is introduced and its equivalent Lyapunov characterization is presented. The problem of global stability of the compact set composed by all invariant solutions of a nonlinear system (several equilibriums, for instance) is analyzed. Consideration of such set allows us to present global stability properties for multi-stable systems.
In this paper a new approach is proposed to find an approximate solution for nonlinear path planning problem. In this approach, first a new problem is defined in the calculus of variations which is equivalent to the original problem. The new problem can be expressed as an optimal control problem by introducing slack variable. Then a metamorphosis is performed in the space of problem by defining an...
This paper proposes a reactive motion controller for a humanoid robot to maintain balance against a large disturbance, by relatively stepping. A reactive step is performed by the robot, so that it reduces the disturbance force. Several problems are addressed: first the motion is designed to ensure the respect of stepping constraints such as a dynamical stability, motion feasibility of the swing leg...
In this paper, a PD-type sampled-data iterative learning control algorithm is proposed for a class of nonlinear systems with time delays and uncertain disturbances, including random input disturbance and random output measurement noise. By introducing Taloy' s norm, a rigorous proof is given for the convergence at each sampling point. A sufficient condition is derived to ensure that the real output...
The approximation of humanoid robot by an inverted pendulum is one of the most used model to generate a stable motion using a planned Zero Moment Point (ZMP) trajectory. In this paper, we aim at proposing to improve the reliability of this model using system identification techniques. To achieve this goal, we propose an identification method which is the result of the comprehensive application of...
In this paper, the Volterra series decomposition of a class of time invariant system, polynomial in the state and affine in the input, with an exponentially stable linear part is analyzed. A formal recursive expression of Volterra kernels of the input-to-state system is derived and the singular inversion theorem is used to prove the non-local-in-time convergence of the Volterra series to a trajectory...
In some dynamic systems, it is desirable to keep the state trajectory within a predefined (constrained) subset of the state space, referred to as an operating region. However, for certain systems, state trajectories leave the operating region in finite time due to system dynamics. To keep the state trajectory in the operating region as long as possible, a constrained time optimal control problem can...
We consider networks of input-to-state dynamically stable (ISDS) systems and provide a small gain condition under which the entire network is again ISDS. A Lyapunov formulation of the nonlinear small gain theorem for two interconnected ISDS systems is proved. It provides a constructive method to find an ISDS Lyapunov function for such an interconnection.
This paper studies the global robust output regulation problem for a class of output feedback systems subject to an uncertain exosystem by using output feedback control. An adaptive control technique is used to handle the unknown parameter vector in the exosystem. It is shown that this unknown parameter vector can be exactly estimated asymptotically if the controller incorporates a minimal internal...
In this paper, we propose a new iterative learning control (ILC) scheme, which is devoted to dealing with unknown parameters that are both time varying and iteration varying. In particular, we consider iteration-varying parameters that are generated by a second-order internal model. By incorporating the internal model into the parametric learning law, the ILC scheme can handle more generic nonlinear...
This paper develops semistability analysis results for nonlinear switched systems. Semistability is the property whereby the solutions of a dynamical system converge to Lyapunov stable equilibrium points determined by the system initial conditions. The main results of the paper involve sufficient conditions for semistability using multiple Lyapunov functions and integral-type inequalities.
Hula-hoop is not only one of familiar toys but also interesting system as a nonlinear control system. While humans play hula-hoop, hoop does not slide on the body but rotates around it. Though it is controlled only by the motion of the body, humans can realize enduring rotary motion without dropping hoop. The purpose of this paper is modeling and control of hula-hoop system as a nonlinear control...
The presented work addresses the observation problem for a large class of nonlinear systems, including systems which are nonlinear in the unmeasured states. Assuming partial state measurements, the unmeasured states are reconstructed so that a prediction of the measured states converges to a neighborhood of the actual measurements. This prediction-based observer algorithm relies on carefully selected...
Previous inverse optimal adaptive controllers (IOACs) have been developed that can handle structured (i.e., linear in the parameters (LP)) uncertainty for a particular class of nonlinear systems. A full-state feedback IOAC is developed in the companion Part I paper for Euler-Lagrange systems with an uncertain time varying inertia matrix. In this paper, an output feedback IOAC is developed to asymptotically...
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