Paper: Model reference adaptive control algorithms for industrial robots

In this paper, Chin's (1987 b) integral method of deriving Lyapunov functions for the investigation of nonlinear system stability is extended. Whereas in Chin's method, each weighting function includes only one state variable, in the extended integral method the weighting functions can be any continuous functions of time, some or all state variables and their time derivatives. As a result of the less restrictive weighting functions, the sensitivity of the method to the form of the state-space model is reduced, which gives the user more freedom in deriving the Lyapunov functions. The method also extends the integral method in the sense that it can be applied to both autonomous and non-autonomous systems. Furthermore, the intrinsic method of Chin (1988) is shown to be a special case of the extended integral method. Many examples from the literature and from engineering applications are provided to show that the extended method is surprisingly easy to apply, and results in Lyapunov functions for more general...

An extended integral method to derive Lyapunov functions for nonlinear systems

A nonlinear adaptive excitation control is designed for a synchronous generator modeled by a standard third order model on the basis of the physically available measurements of relative angular speed, active electric power and terminal voltage. The power angle, which is a crucial variable for the excitation control, is not assumed to be available for feedback. The feedback control is supposed to achieve transient stabilization and voltage regulation when faults occur to the turbines so that the mechanical power may permanently take any (unknown) value within its physical bounds. Transient stabilization and voltage regulation are achieved by a nonlinear adaptive controller, which generates both converging estimates of the mechanical power and the new equilibrium point compatible with the required terminal voltage.

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Adaptive nonlinear excitation control of synchronous generators with unknown mechanical power

The integral method proposed by Chin (1986) is extended and generalized. The generalized integral method derives suitable Lyapunov functions for a general class of non-linear system expressed in state variables as n first-order non-linear differential equations. Four examples, including those studied by Mukherjee et al. (1972) and Miyagi and Taniguchi (1981), are considered.

Generalized integral method to derive Lyapunov functions for nonlinear systems

The problem of the necessary and sufficient conditions for an exact direct determination of both a Lyapunov function υ and the asymptotic stability domain D of the zero state is solved for time-invariant non-linear continuous-time systems with continuous unique motions. The conditions provide a complete algorithm for their simultaneous determination. They permit arbitrary selection of a positive definite function p for which D +υ = −p has a solution υ in order to generate a system Lyapunov function υ from D +υ = −p as for linear time-invariant systems. This expresses their substantial difference from Lyapunov's original results and their developments so far. The latter are expressed in terms of the existence of a system Lyapunov function but the former are not. The theorems of the paper establish a new insight into, and a methodology for, a study of Lyapunov stability properties and other qualitative features of nonlinear dynamic systems. Simple examples illustrate the theorems and the procedure for their...

Exact determination of a Lyapunov function and the asymptotic stability domain

A flexible and systematic way for the construction of Lyapunov functions which lends itself to the use of nonlinear programming techniques is presented. The class of Lyapunov functions obtained is shown to be energy functions (Hamiltonians) for an equivalent system.

R. Marino

Papers

Hamiltonian-type Lyapunov functions