Petar V. Kokotovic

Systematic design of adaptive controllers for feedback linearizable systems

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. >

Singular perturbations and order reduction in control theory - An overview

Recent results on singular perturbations are surveyed as a tool for model order reduction and separation of time scales in control system design. Conceptual and computational simplifications of design procedures are examined by a discussion of their basic assumptions. Over 100 references are organized into several problem areas. The content of main theorems is presented in a tutorial form aimed at a broad audience of engineers and applied mathematicians interested in control, estimation and optimization of dynamic systems.

Singular perturbations and time-scale methods in control theory: Survey 1976-1983

Recent progress in the use of singular perturbation and two-time-scale methods of modeling and design for control systems is reviewed. Over 350 references are organized into major problem areas. Representative issues and results are discussed with a view to outlining research directions and indicating potential areas of application. The survey is aimed at engineers and applied mathematicians interested in model-order reduction, separation of time scales and allied simplified methods of control system analysis and design. The exposition does not assume prior knowledge of singular perturbation methods.

An integral manifold approach to the feedback control of flexible joint robots

The control problem for robot manipulators with flexible joints is considered. The results are based on a recently developed singular perturbation formulation of the manipulator equations of motion where the singular perturbation parameter µ is the inverse of the joint stiffness. For this class of systems it is known that the reduced-order model corresponding to the mechanical system under the assumption of perfect rigidity is globally linearizable via nonlinear static-state feedback, but that the full-order flexible system is not, in general, linearizable in this manner. The concept of integral manifold is utilized to represent the dynamics of the slow subsystem. The slow subsystem reduces to the rigid model as the perturbation parameter µ tends to zero. It is shown that linearizability of the rigid model implies linearizability of the flexible system restricted to the integral manifold. Based on a power series expansion of the integral manifold around µ = 0, it is shown how to approximate the feedback linearizing control to any order in µ. The result is then an approximate feedback linearization which, assuming stability of the fast variables, linearizes the system for all practical purposes.

Adaptive regulation of nonlinear systems with unmodeled dynamics

Conditions are given for global stability of an adaptive control law designed for the reduced order model of a class of higher order nonlinear plants. In the presence of unmodeled dynamics. which account for the difference between the model and the plant, the regulation property is preserved in a stability region. The size of the region is estimated via a set of bounds that not only proves robustness, but also allows a comparison between adaptive and nonadaptive nonlinear controls.

A positive real condition for global stabilization of nonlinear systems

Abstract We study the possibility of globally stabilizing, by means of a smooth state feedback, systems obtained by cascading a linear controllable system and a general nonlinear system. Our main result is that global stabilization can be achieved if the output of the linear system can be chosen to be ‘feedback positive real’ (FPR). Some recent stabilization conditions appear as special cases of the new FPR condition. Examples of systems with the FPR property are given.

An extended direct scheme for robust adaptive nonlinear control

Abstract The proposed adaptive scheme achieves regulation for a class of nonlinear systems with unknown constant parameters and unmodeled dynamics. The scheme does not employ overparametrization and does not restrict the class of nonlinearities by any growth conditions. Instead, the dependence on the unknown parameters is restricted by an extended matching condition, which, however, is satisfied in many systems of practical importance, such as most types of electric motors.

Singular perturbation of linear regulators: Basic theorems

The behavior of the solution of the Riccati equation for the linear regulator problem with a parameter whose perturbation changes the order of the system is analyzed. Sufficient conditions are given under which the solution of the original problem tends to the solution of a low-order problem. This result can be used for the decomposition of a high-order problem into two low-order problems.

A Riccati equation for block-diagonalization of ill-conditioned systems

A simple transformation, originally introduced for singularly perturbed systems, is now applicable to a larger class of time-invariant systems.

Singular perturbation and iterative separation of time scales

This tutorial paper presents an iterative method for the separation of slow and fast modes, which removes the inconsistencies of the classical quasi-steady-state approach and systematically improves the accuracy of the lower order models. It also serves as a self-contained introduction to singular perturbations. State variable reformulation and time scale identification are discussed and illustrated with power system examples. A correction procedure for nonlinear systems is also presented.