P.V. Kokotovic

Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations

Given a parameterized (by sampling period T) family of approximate discrete-time models of a sampled nonlinear plant and given a family of controllers stabilizing the family of plant models for all T sufficiently small, we present conditions which guarantee that the same family of controllers semi-globally practically stabilizes the exact discrete-time model of the plant for sufficiently small sampling periods. When the family of controllers is locally bounded, uniformly in the sampling period, the inter-sample behavior can also be uniformly bounded so that the (time-varying) sampled-data model of the plant is uniformly semi-globally practically stabilized. The result justifies controller design for sampled-data nonlinear systems based on the approximate discrete-time model of the system when sampling is sufficiently fast and the conditions we propose are satisfied. Our analysis is applicable to a wide range of time-discretization schemes and general plant models.

Adaptive control of plants with unknown dead-zones

Model reference adaptive controllers are designed for plants with unknown dead-zones. Several control strategies are investigated in which two sets of adjustable parameters, one belonging to a dead-zone inverse and the other to a linear controller, are either kept fixed or adaptively updated. The developed adaptive control schemes ensure boundedness of all closed-loop signals and reduce the tracking error. >

Inverse Optimality in Robust Stabilization

The concept of a robust control Lyapunov function ({\Bf rclf}) is introduced, and it is shown that the existence of an {\Bf rclf} for a control-affine system is equivalent to robust stabilizability via continuous state feedback. This extends Artsteins theorem on nonlinear stabilizability to systems with disturbances. It is then shown that every {\Bf rclf} satisfies the steady-state Hamilton--Jacobi--Isaacs (HJI) equation associated with a meaningful game and that every member of a class of pointwise min-norm control laws is optimal for such a game. These control laws have desirable properties of optimality and can be computed directly from the {\Bf rclf} without solving the HJI equation for the upper value function.

Adaptive output-feedback control of a class of nonlinear systems

For a class of single-input-single-output nonlinear systems with unknown constant parameters, the authors construct a novel systematic procedure for adaptive nonlinear control design, which requires only output, rather than full-state, measurement and which yields global boundedness and tracking properties without imposing any type of growth constraints on the nonlinearities. The proposed procedure is applicable to nonlinear systems which can be expressed in the output-feedback canonical form. The authors give a coordinate-free characterization of this class of systems, and show that a single-link robotic manipulator with an elastically coupled DC-motor actuator belongs to this class, and can thus be adaptively controlled via the design procedure using only position measurement.<<ETX>>

A note on input-to-state stability of sampled-data nonlinear systems

It is shown for nonlinear systems that sampling sufficiently fast an input-to-state stabilizing (ISS) continuous time control law results in an ISS sampled-data control law. Two main features of our approach are: we show how the nonlinear sampled-data system can be modeled by a functional differential equation (FDE); and we exploit a Razumikhin type theorem for ISS of FDE that was proved by Teel (1998) to analyze the sampled-data system.

Useful nonlinearities and global stabilization of bifurcations in a model of jet engine surge and stall

Compressor stall and surge are complex nonlinear instabilities that reduce the performance and can cause failure of aircraft engines. We design a feedback controller that globally stabilizes a broad range of possible equilibria in a nonlinear compressor model. With a novel backstepping design we retain the systems useful nonlinearities which would be cancelled in a feedback linearizing design. The design control law is simple and, moreover, it is optimal with respect to a meaningful nonquadratic cost functional. As in a previous bifurcation-theoretic design, we change the character of the bifurcation at the stall inception point from subcritical to supercritical. However, since we approach the bifurcation control using Lyapunov tools, our controller achieves not only local but also global stability. The controller requires minimal modeling information and simpler sensing (rotating stall is stabilized without measuring its amplitude).

Adaptive nonlinear output-feedback schemes with Marino-Tomei controller

Three new adaptive nonlinear output-feedback schemes are presented. The first scheme employs the tuning functions design. The other two employ a novel estimation-based design consisting of a strengthened controller-observer pair and observer-based and swapping-based identifiers. They remove restrictive growth and matching conditions present in the previous output-feedback nonlinear estimation-based designs and allow a systematic improvement of transient performance.

Backstepping designs for jet engine stall and surge control

A new systematic method for nonlinear control design-backstepping-is applied to low-order compression system models. Backstepping achieves global asymptotic stability of both stall and surge in the presence of large uncertainties in the compressor model. Throughout our presentation, we explore the control design implications of the nonlinear equilibrium properties of compressors.

Robustness of Adaptive Nonlinear Control to Bounded Uncertainties

Abstract Two robust adaptive control methods are outlined for a class of nonlinear systems. The first method is based on the tuning function design of Krstic et al. (1992), and the second method is based on the modular design of Krstic and Kokotovic (1995). Both methods guarantee robustness with respect to bounded uncertainties and exogenous disturbances, and L ∞ / L 2 estimates are given on the effects of these uncertainties/disturbances on the tracking error.

Global robustness of nonlinear systems to state measurement disturbances

We consider nonlinear control systems for which an estimate x/spl circ/ of the system state x is available for feedback. We assume x/spl circ/=x+d/sub m/, where d/sub m/(t) is an unknown locally bounded state measurement disturbance. We present conditions under which we can design a smooth feedback law u=/spl mu/(x/spl circ/) which renders the mapping from d/sub m/ to x globally input/output stable. For any initial condition, such a feedback law will guarantee that no finite escape times occur, that bounded disturbances d/sub m/ produce bounded signals, and that x/spl rarr/0 when d/sub m//spl rarr/0. We show that the class of systems for which such feedback laws exist include systems in strict feedback form. One important application is in the output feedback stabilization problem, where the disturbance d/sub m/ comes from a separately designed observer.<<ETX>>