Nonlinear control of feedforward systems with bounded signals

Published versio

Feedback Stabilization Methods for the Numerical Solution of Systems of Ordinary Differential Equations

In this work we study the problem of step size selection for numerical schemes, which guarantees that the numerical solution presents the same qualitative behavior as the original system of ordinary differential equations, by means of tools from nonlinear control theory. Lyapunov-based and Small-Gain feedback stabilization methods are exploited and numerous illustrating applications are presented for systems with a globally asymptotically stable equilibrium point. The obtained results can be used for the control of the global discretization error as well.Comment: 33 pages, 9 figures. Submitted for possible publication to BIT Numerical Mathematic

Normal forms for underactuated mechanical systems with symmetry

We introduce cascade normal forms for underactuated mechanical systems that are convenient for control design. These normal forms include three classes of cascade systems, namely, nonlinear systems in strict feedback form, feedforward form, and nontriangular quadratic form (to be defined). In each case, the transformation to cascade systems is provided in closed-form. We apply our results to the Acrobot, the rotating pendulum, and the cart-pole system

Uniform semiglobal practical asymptotic stability for non-autonomous cascaded systems and applications

It is due to the modularity of the analysis that results for cascaded systems have proved their utility in numerous control applications as well as in the development of general control techniques based on ``adding integrators''. Nevertheless, the standing assumptions in most of the present literature on cascaded systems is that, when decoupled, the subsystems constituting the cascade are uniformly globally asymptotically stable (UGAS). Hence existing results fail in the more general case when the subsystems are uniformly semiglobally practically asymptotically stable (USPAS). This situation is often encountered in control practice, e.g., in control of physical systems with external perturbations, measurement noise, unmodelled dynamics, etc. This paper generalizes previous results for cascades by establishing that, under a uniform boundedness condition, the cascade of two USPAS systems remains USPAS. An analogous result can be derived for USAS systems in cascade. Furthermore, we show the utility of our results in the PID control of mechanical systems considering the dynamics of the DC motors.Comment: 16 pages. Modifications 1st Feb. 2006: additional requirement that links the parameter-dependency of the lower and upper bounds on the Lyapunov function, stronger condition of uniform boundedness of solutions, modification and simplification of the proofs accordingl

Monotone Control Systems

Monotone systems constitute one of the most important classes of dynamical systems used in mathematical biology modeling. The objective of this paper is to extend the notion of monotonicity to systems with inputs and outputs, a necessary first step in trying to understand interconnections, especially including feedback loops, built up out of monotone components. Basic definitions and theorems are provided, as well as an application to the study of a model of one of the cell's most important subsystems.Comment: See http://www.math.rutgers.edu/~sontag/ for related wor

Robust Asymptotic Stabilization of Nonlinear Systems with Non-Hyperbolic Zero Dynamics

In this paper we present a general tool to handle the presence of zero dynamics which are asymptotically but not locally exponentially stable in problems of robust nonlinear stabilization by output feedback. We show how it is possible to design locally Lipschitz stabilizers under conditions which only rely upon a partial detectability assumption on the controlled plant, by obtaining a robust stabilizing paradigm which is not based on design of observers and separation principles. The main design idea comes from recent achievements in the field of output regulation and specifically in the design of nonlinear internal models.Comment: 30 pages. Preliminary versions accepted at the 47th IEEE Conference on Decision and Control, 200