Since Hilbert posed the problem of systematically counting and locating lhe limit cycle of polynomial systems on the plane in 1900, much ef Tort has been expended in its investigation. A large body of literature chiefly by Chinese and Soviet authors has addressed this question in the context of differential equations whose field is specified by quadratic polynomials, In this paper we consider t...

In this paper we propose a method for flow control of parts in a manufacturing system with machines that require setups. The setup scheduling problem is investigated in the context of a multilevel hierarchy of discrete events with distinct frequencies. The higher level of the hierarchy calculates a target trajectory in the surplus/backlog space of the part types which must be tracked at the lev...

Relay feedback has a large variety of applications in control engineering. Several interesting phenomena occur in simple relay systems. In this paper, scalar linear systems with relay feedback are analyzed. It is shown that a limit cycle where part of the limit cycle consists of fast relay switchings can occur. This chattering is analyzed in detail and conditions for approximating it by a slidi...

A switched sliding mode control strategy for a class of nonlinear uncertain systems is presented in this paper. It is characterized by an event– driven gain reduction mechanism which relies on a decomposition of the system state into regions. By enforcing sliding mode behaviors on a suitable set of sliding manifolds, while avoiding the generation of limit cycles, the proposed strategy proves to...

Considerable safety benefits are achieved by robustly decoupling the lateral and yaw motions of a car with active steering. Robust unilateral decoupling requires an actuator to generate an additional front wheel steering angle. However, introducing actuators to closed loop systems may cause limit cycles due to actuator saturation and rate limits. Such limit cycles are intolerable w.r.t. safety ...

The robust control problem for nonlinear systems is discussed from the standpoint of the amplitude sensitivity of the nonlinear plant and nal control system. Failure to recognize and accommodate this factor may give rise to nonlinear control systems that behave diierently for small versus large input excitation, or perhaps exhibit limit cycles or instability. Sinusoidal-input describing functio...

This paper investigates the problem of analysis of a Takagi-Sugeno (T-S) fuzzy control system in the frequency domain. First, a linear plant with a T-S fuzzy controller is considered, and the complex dynamic behaviors of the system generated by the nonlinearity in the controller are analyzed. The global stability, instability and existence of limit cycles of the system are predicted with the ai...

The robust control problem for nonlinear systems is discussed from the standpoint of the amplitude sensitivity of the nonlinear plant and final control system. Failure to recognize and accommodate this factor may give rise to nonlinear control systems that behave differently for small versus large input excitation, or perhaps exhibit limit cycles or instability. Sinusoidal-input describing func...

In this paper we analyze the quantum control of squeezed states of harmonic oscillators as well as spin squeezing and its relationship to quadrature squeezed states of other bosonic fields. Squeezing provides a method for reducing noise below the quantum limit and provides an example of the control of under-actuated control systems in the stochastic and quantum context. We consider also the int...

In this paper, an observer-based adaptive feedback controller is developed for a class of chaotic systems. This controller does not need the availability of state variables. It can be used for tracking a smooth orbit that can be a limit cycle or a chaotic orbit of another system. This adaptive feedback controller is constructed with the aid of its H∞ control technique to achieve the H∞ tracking...