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GLOBAL INTERNAL STABILIZABILITY DOES NOT IMPLY GLOBAL EXTERNAL STABILIZABILITY FOR SMALL SENSOR DISTURBANCES

IEEE TRANSACTIONS ON AUTOMATIC control 1995年第12期40卷 2119-2122页

作者： FREEMAN, R Center for Control Engineering and Computation Department of Electrical and Computer Engineering University of California Santa Barbara CA USA

It was shown in [1] that for control-affine nonlinear systems, global asymptotic stabilizability via continuous state feedback implies global input-to-state stabilizability with respect to actuator disturbances. We show that the analogous result for sensor disturbances does not hold: we construct a second-order system which admits a continuous memoryless globally asymptotically stabilizing state feedback controller but for which no such controller can prevent finite escape times from every initial condition in the presence of small sensor disturbances.

关键词： Asymptotic stability Actuators Sensor systems control systems Nonlinear systems Nonlinear control systems State feedback Robust stability control theory Working environment noise

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ADAPTIVE-control OF A CLASS OF NONLINEAR DISCRETE-TIME-SYSTEMS

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INTERNATIONAL JOURNAL OF control 1995年第2期62卷 303-324页

作者： YEH, PC KOKOTOVIC, PV Center for Control Engineering and Computation University of California Santa Barbara CA 93106 U.S.A.

We consider adaptive control via state feedback for a class of feedback linearizable discrete-time systems. To parallel the development in adaptive nonlinear continuous-time control, we employ a systematic procedure to design the controllers and the update laws for the so-called parametric-strict-feedback form and the parametric-pure-feedback form. The geometric conditions that characterize this class of systems are given. Depending on the growth conditions of the nonlinearities, global boundedness and convergence are achieved with various update laws. We also develop adaptive indirect schemes with an observer-based identifier for the parametric-strict-feedback form. As a result, the drawback of overparametrization in direct schemes can be removed.

关键词： Adaptive control systems

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Backstepping Design with Nonsmooth Nonlinearities *

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IFAC Proceedings Volumes 1995年第14期28卷 435-440页

作者： R.A. Freeman P.V. Kokotović Center for Control Engineering and Computation Dept. of Electrical and Computer Engineering University of California Santa Barbara CA 93106 Telephone: (805) 893-4691

We develop tools for backstepping with Lyapunov functions and control laws which are locally Lipschitz but not differentiable. We use Clarke’s generalized gradient and its associated calculus to show that the locally Lipschitz backstepping construction is essentially the same as the differentiable one. Our recursive method is constructive and yields an explicit expression for the control law.

关键词： Backstepping nonsmooth Lyapunov functions generalized gradient

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Tracking controllers for Systems Linear in the Unmeasured States *

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IFAC Proceedings Volumes 1995年第14期28卷 577-582页

For nonlinear systems in extended strict feedback form, where unmeasured states enter linearly, we construct dynamic partial state feedback controllers that achieve the global asymptotic tracking of given reference tr... 详细信息

关键词： Nonlinear systems global tracking dynamic partial state feedback

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Nonlinear control system design via dynamic order reduction

Nonlinear control system design via dynamic order reduction

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IEEE Conference on Decision and control

作者： R. Ghanadan Center for Control Engineering and Computation Department of Electrical and Computer Engineering University of California Santa Barbara CA USA

In this paper we present a design scheme for output tracking of nonlinear systems that are subject to regular perturbations. We show that applications of singular perturbation theory to the input-output feedback linearization technique provides a systematic method to identify the slow "dominant" states and fast "negligible" states. Similar to the backstepping design technique, a suitable state variable is converted into a "control like" variable which in the steady state is forced to approach the desired tracking control law for the reduced order system. We show that this design achieves stable approximate tracking of reasonable reference trajectories for nonlinear systems that are "dominantly" minimum phase. The order of approximation can be arbitrarily improved by addition of correction terms in the control law. The main advantage of this approach is that the design is often performed for a much simpler model which is linear in the new control variable and describes the dominant part of the original system by ignoring some of the fast states that are forced to have little effect on the steady state performance.< >

关键词： Nonlinear control systems Nonlinear dynamical systems Nonlinear systems Steady-state Force control State feedback Linearization techniques Backstepping control systems Reduced order systems

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Tools and procedures for robust control of nonlinear systems

Tools and procedures for robust control of nonlinear systems

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IEEE Conference on Decision and control

作者： R.A. Freeman P.V. Kokotovic Center for Control Engineering and Computation Department of Electrical and Computer Engineering University of California Santa Barbara CA USA

We review some of the existing results on the Lyapunov design of robustly stabilizing feedback laws for uncertain nonlinear systems. Using the concept of a robust control Lyapunov function, we present robust backstepp... 详细信息

关键词： Robust control Nonlinear systems Lyapunov method Feedback control systems Force control Asymptotic stability Nonlinear control systems control engineering control engineering computing

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Robust control Lyapunov functions: the measurement feedback case

Robust control Lyapunov functions: the measurement feedback ...

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IEEE Conference on Decision and control

作者： R.A. Freeman P.V. Kokotovic Center for Control Engineering and Computation Department of Electrical and Computer Engineering University of California Santa Barbara CA USA

We extend the concept of a robust control Lyapunov function (RCLF) for nonlinear systems to the case of measurement feedback. We explore conditions under which the existence of an RCLF is sufficient and/or necessary f... 详细信息

关键词： Robust control Computer aided software engineering State feedback Lyapunov method Robustness control systems Uncertain systems control engineering control engineering computing Nonlinear systems

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A different look at output tracking: control of a VTOL aircraft

A different look at output tracking: control of a VTOL aircr...

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IEEE Conference on Decision and control

作者： P. Martin S. Devasia B. Paden Center for Control Engineering and Computation ECE Department University of California Santa Barbara CA USA Mechanical Engineering Department University of California Santa Barbara CA USA

An important control problem is output tracking. One approach, for slightly nonminimum phase systems is to approximate the system by a minimum phase one. Another approach is to track signals generated by an exosystem. These methods concentrate on properties of the IO system without any attempt to investigate and use structural properties of the IS system. In this paper the authors propose an alternative point of view based on the following simple remark: if one had a state tracker (i.e. a controller able to track any reference state trajectory), the output tracking would reduce to the generation of a good state reference, which is only an open-loop problem, and hence (hopefully) simpler. The idea is simply to split the output tracking problem into two steps.< >

关键词： Aerospace control Trajectory control systems Open loop systems Aircraft propulsion control engineering control engineering computing Mechanical engineering State feedback Signal generators

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An introduction to perspective observability and recursive identification problems in machine vision

An introduction to perspective observability and recursive i...

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IEEE Conference on Decision and control

作者： B.K. Ghosh E.P. Loucks M. Jankovic Department of Systems Science and Mathematics Washington University Saint Louis MO USA Center for Control Engineering and Computation University of California Santa Barbara CA USA

The class of problems considered in the paper arises in machine vision wherein a moving object is observed with the aid of a CCD camera. Under the assumption of perspective projection, a CCD camera observes every point on the object up to a line. The authors pose the problem in the framework of linear system theory and consider a dynamical system.< >

关键词： Observability Machine vision Charge coupled devices Charge-coupled image sensors Equations control systems Computer vision Linear systems US Department of Energy Symmetric matrices

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Global robustness of nonlinear systems to state measurement disturbances

Global robustness of nonlinear systems to state measurement ...

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IEEE Conference on Decision and control

作者： R.A. Freeman P.V. Kokotovic Center for Control Engineering and Computation Department of Electrical and Computer Engineering University of California Santa Barbara CA USA University of California Santa Barbara Santa Barbara CA US Dept. of Electr. & Comput. Eng. California Univ. Santa Barbara CA USA

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.< >

关键词： Nonlinear systems control systems Output feedback State feedback Radio control Stability control engineering control engineering computing Noise robustness Robust control

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