Showing papers by "Petar V. Kokotovic published in 1991"

Systematic design of adaptive controllers for feedback linearizable systems

Abstract: A systematic procedure for the design of adaptive regulation and tracking schemes for a class of feedback linearizable nonlinear systems is developed. The coordinate-free geometric conditions, which characterize this class of systems, do not constrain the growth of the nonlinearities. Instead, they require that the nonlinear system be transformable into the so-called parametric-pure feedback form. When this form is strict, the proposed scheme guarantees global regulation and tracking properties, and substantially enlarges the class of nonlinear systems with unknown parameters for which global stabilization can be achieved. The main results use simple analytical tools, familiar to most control engineers. >

Systematic Design of Adaptive Controllers for Feedback Linearizable Systems

Abstract: A systematic procedure is developed for the design of new adaptive regulation and trackdng schemes for a class of feedback linearizable nonlinear systems. The coordinate-free geometric conditions, which characterize this class of systems, neither restrict the location of the unknown parameters, nor constrain the growth of the nonlinearities. Instead, they require that the nonlinear system be transformable into the so-called pure-feedback form. When this form is "strict", the proposed scheme guarantees global regulation and tracking properties, and substantially enlarges the class of nonlinear systems with unknown parameters for which global stabilization can be achieved. The main results of this paper use simple analytical tools, familiar to most control engineers.

The peaking phenomenon and the global stabilization of nonlinear systems

Abstract: The problem of global stabilization is considered for a class of cascade systems. The first part of the cascade is a linear controllable system and the second part is a nonlinear system receiving the inputs from the states of the first part. With zero input, the equilibrium of the nonlinear part is globally asymptotically stable. In linear systems, a peaking phenomenon occurs when high-gain feedback is used to produce eigenvalues with very negative real parts. It is established that the destabilizing effects of peaking can be reduced if the nonlinearities have sufficiently slow growth. A detailed analysis of the peaking phenomenon is provided. The tradeoffs between linear peaking and nonlinear growth conditions are examined. >

Adaptive nonlinear control of systems containing a deadzone

Abstract: The authors present an adaptive nonlinear controller for a plant containing a nonsmooth nonlinearity with unknown parameters in the span of the control (specifically, a deadzone). They develop a Lyapunov-based adaptation scheme which updates the parameters of the specific region of the deadzone in which the system is operating. They then employ some switching logic to turn on and off the adaptation as the state of the system proceeds from one region of the deadzone to another. A significant feature of the adaptive controller is the presence of set uncertainty. Thus, conceptually, adaptation is not only for unknown parameters, but also for the regions of the piecewise smooth nonlinearity. >

Adaptive output-feedback control of a class of nonlinear systems

Abstract: 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. >

Adaptive feedback linearization of nonlinear systems

Abstract: After an examination of the restrictive assumptions that limit the applicability of existing adaptive nonlinear control schemes, new adaptive regulation and tracking schemes are developed for a class of feedback linearizable nonlinear systems. The coordinate-free geometric conditions, which characterize this class of systems, neither restrict the location of the unknown parameters, nor constrain the growth of the nonlinearities. Instead, they require that the nonlinear system be transformable into the so-called pure-feedback form. When this form is “strict”, the proposed scheme guarantees global regulation and tracking properties, and substantially enlarges the class of nonlinear systems with unknown parameters for which global stabilization can be achieved. The new design procedure is systematic and its stability proofs use simple analytical tools, familiar to most control engineers.

On stability properties of nonlinear systems with slowly varying inputs

Abstract: Systems with slowly varying inputs are discussed as a special class of two-time-scale systems, and singular perturbation results are seen as convenient tools to analyze their properties. A lemma by F.C. Hoppensteadt (Trans. Amer. Math. Soc., vol.123, p.521-35, 1966) for a parameterized family of systems is restated and applied to the analysis of systems with slowly varying inputs. >

Adaptive Control of an Arc Welding Process

Abstract: This paper reports on the successful application of a pseudogradient adaptive algorithm for self-tuning a PI puddle width controller for consumable-electrode gas metal arc welding. The gradient of the output with respect to the controller parameters is approximated and used to form a steepest descent algorithm to minimize the squared output error. Experimental data confirming the algorithm performance is presented.

Adaptive output-feedback control of systems with output nonlinearities

Abstract: For a class of single-input single-output nonlinear systems with unknown constant parameters, one presents a direct model-reference adaptive control scheme, which requires only output, rather than full-state, measurement. The nonlinearities are not required to satisfy any growth conditions. The assumptions on the linear part of the nonlinear system are the same as in the standard adaptive control problem for linear systems, which now appears as a special case of the nonlinear problem solved in this paper

Boundedness Properties of Simple Indirect Adaptive Control Systems

Abstract: Examining adaptive controllers for a first order, linear, continuous time plant, with different estimators, and control laws, we obtain explicit solutions completely describing the nonliner behavior of the resultant adaptive systems. Some of these adaptive systems exhibit either finite time escapes, or other forms of unbounded behavior, due to a loss of stabilizability of the estimated model. Some fixes for the loss of stabilizability are analyzed. Implications of these results for the general indirect adaptive control case are discussed.

Approximate Decoupling of Regularly Perturbed Nonlinear Systems

Abstract: Conditions for static state feedback decoupling with internal stability may not hold for a regularly perturbed system even though they hold for the unperturbed system. We show for the case where the objective for the decoupled controller is asymptotic trackimg, that with small iterative corrections on the decoupling controller for the unperturbed system, we can achieve decoupled tracking within 0( E k) error where k is the order of the iteration, even when the regular perturbation makes the system nonminimum phase.

On the Stability and Robustness of an Adaptive Nonlinear Control Scheme

Abstract: We study the stability and robustness properties of an adaptive nonlinear regulation scheme. For the case where the equilibrium of the nonlinear system depends on the unknown parameters, we prove the robustness of the adaptive scheme to unmodeled dynamics using converse Lyapunov arguments. We also show that under some additional conditions, the closed-loop adaptive system has an exponentially stable parameter-dependent equilibrium, and is robust not only to small bounded disturbances and unmodeled dynamics, but also to slow time variations of the unknown parameters. *This work was supported in part by the National Science Foundation under Grant ECS-87-15811 and in part by the Air Force Office of Scientific Research under Grant AFOSR 90-0011.