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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...
We study the solution properties of a family of inverted pendulum systems driven by odd periodic forcing. Using the Schauder fixed point theorem, we show that the inverted pendulum with an odd periodic driving acceleration at the pivot always possesses an odd periodic solution. Fundamental to the production of good estimates is the development of a Green's function for an unstable harmonic oscillator...
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 considers an ldquohomotopy methodrdquo for solving the exact tracking problem for nonlinear affine nonminimum phase systems. The method is presented in a general setting and is applied to the special case of the spherical pendulum. This approach allows finding sufficient conditions for exact tracking for T-periodic curves and bounds on the internal dynamics.
Stabilization for a collection of feedback linearizable systems with uncertain parameter is dealt with in this paper. Necessary and sufficient conditions for a quadratic control Lyapunov function to be a common control Lyapunov function for these systems are obtained. A continuous state feedback control is designed based on the common control Lyapunov function. It can simultaneously stabilize these...
Phase space is a useful tool for explanations of complex system. However, in some cases, the basic patterns of behavior which is intended to be explored in phase space may be overwhelmed with details. This paper develops a method to research the qualitative phase space in non-linear time series, which decreases the number of the time serial states and predigests behavior trajectories through abstract,...
We consider a single-input single-output (SISO) nonlinear system which has a well defined normal form with asymptotically stable zero dynamics. We allow the system's equation to depend on bounded uncertain parameters which do not change the relative degree. Our goal is to design an output feedback controller which regulates the output to a constant reference in the presence of constant unkown input...
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