G. Leitmann

Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems

We consider a dynamic system containing uncertain elements. Only the set of possible values of these uncertainties is known. Based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state. These feedback controls are continuous functions of the state.

Robustness of uncertain systems in the absence of matching assumptions

Abstract We consider a class of uncertain dynamical systems containing uncertain elements. These may be due to model-parameter uncertainty, input disturbance and measurement noise. We require no a priori information on the uncertain elements except that their restraint sets are assumed to be known and compact. This paper describes a general approach for designing controls to assure practical stability in the absence of matching assumptions (which most previous results have needed). The result is applicable to non-linear systems. A specialization to linear systems is then given and a comparison is made with previous work.

Adaptive control of systems containing uncertain functions and unknown functions with uncertain bounds

We consider dynamical systems containing uncertain elements due to imperfect knowledge about the model and the input. Since these uncertainties may result in unstable behavior, we seek controllers which guarantee that all possible responses of the system are uniformly bounded and approach a desired response. Toward that end, we present a class of adaptive controllers.

Robust control of base-isolated structures under earthquake excitation

We propose the use of robust control in conjunction with base isolation in order to assure arbitrarily small motion of a seismically excited structure. The proposed method requires control force application only at the base (first) floor. The efficacy of the scheme is illustrated by extensive simulations for a prototype six-story building.

Compromise Solutions, Domination Structures, and Salukvadze’s Solution

We outline the concepts of compromise solutions and domination structures in such a way that the underlying assumptions and their implications concerning the solution concept suggested by Salukvadze may be clearer. An example is solved to illustrate our discussion.

Robust control design for interconnected systems with time-varying uncertainties

Abstract We consider a design of decentralized control for a class of interconnected non-linear dynamical systems having uncertainty. This uncertainty is (possibly fast) time-varying, and it may appear in each system as uncertain parameter and input disturbance. It also may appear in the interconnections. No statistical information about the uncertainty is imposed; only its possible bound is assumed to be known. The two control schemes proposed here, namely the linear and the non-linear, take the bounds of the interconnections into account. The use of the non-linear control requires more assumptions than the use of linear control. In applications where these assumptions are met, the designers have both controls at their disposal, and depending on the particular application, one may be preferable to the other.

On generalized Stackelberg strategies

The concept of Stackelberg strategy for a nonzero-sum two-person game is extended to allow for a nonunique “rational” response of the follower. This leads to the notion of a generalized Stackelberg strategy for the leader, which guarantees him a cost value that cannot be exceeded, no matter what the “rational” response of the follower. Then, a generalized Stackelberg strategy pair is defined. A simple example is given. The idea of a generalized Stackelberg strategy and strategy pair is then applied to the situation of one leader and many “rational” followers.

Semiactive Control for Vibration Attenuation

With the advent of materials, such as electrorheological fluids, whose material prop erties can be altered rapidly by means of external stimuli, employing such materials as actuators for the controlled attenuation of undesirable vibrations is now possible. Such control schemes are dubbed semiactive in that they attenuate vibrations whether applied actively or passively. We in vestigate various such control schemes, allowing for both separate and joint control of the stiffness and damping characteristics of the material.

Optimal Control of a Prey-Predator System*

Abstract The purpose of this contribution is to illustrate the use of optimal control theory to obtain optimal strategies for the control of a prey-predator system. Two types of control variables are used. One control variable is the rate of release of predators or preys which are bred in laboratories. The other type of control variable is the rate of application of an insecticide. An interesting and unexpected result is that it is feasible to control a pest by means of an insecticide that destroys only the predators but leaves the pests unharmed. This is because the prey-predator system is a dynamical system. The level of the control variable and the timing of its application can be manipulated to produce desired responses from the dynamical system. Another interesting result is that the system can be controlled by releasing pests which have been bred in laboratories. These results may be useful in formulating an integrated control scheme for the management of a pest.

On One Approach to the Control of Uncertain Systems

This paper is a personal history of one area of research with which I have been concerned over the past twenty years and which continues to attract my albeit waning attention, the control of dynamical systems based on uncertain models. Thus, it is a subjective account of various factors which I believe to have steered me to approach the problem via a constructive use of Lyapunov stability theory