An evolutionary random search algorithm is proposed for learning of the optimum bid in double auction markets where the agents are either members of the population of sellers or the population of buyers. Sellers and buyers are attempting to learn their optimum bid or offer prices, respectively, that maximize their individual gain in the next round of the game. The performance of the algorithm presented in this paper is compared with the performance of the genetic learning algorithm previously used for the same purpose. Multiple simulations demonstrate that the new algorithm converges faster to a market equilibrium. Learning in the presence of uncertainties is also studied.

A new stabilizing nonlinear controller for the vertical motion of an electrically actuated hopping robot is introduced and analyzed. The approach starts by finding reference limit cycles from the "passive dynamics" of a mass-spring system. The controller then modulates the system dynamics via the leg actuator during the stance phase to force the system trajectory to converge to this reference limit cycle. The controlled system dynamics is a continuous yet nonsmooth vector field. A piecewise-continuous Lyapunov function and the general forms of Lasalle's invariance and domain of attraction theorems are used to prove global asymptotic stability of the desired limit cycles. It is also shown that the derived passive dynamic cycles are indeed the positive limit sets of the controlled system. The rate of convergence can be adjusted but is limited by actuator constraints.

The paper considers a specific class of wheeled mobile robots, namely, mobile wheeled pendulums (MWPs). Robots pertaining to this class are composed of two wheels rotating about a central body. The main feature of MWP pertains to the central body, which can rotate about the wheel axis. As such motion is undesirable, the problem of the stabilization of the central body in an MWP is crucial. The novelty of the work reported here resides in the construction of: 1) the system controllability Lie algebra for the purpose of a rigorous controllability analysis and the computation of the largest feedback-linearizable subsystem; 2) a controller by input-output linearization of the system for achieving the desired steering rate of the robot while stabilizing the central body; 3) a controller based on the internal properties of the system to achieve the desired heading velocity of the robot; and 4) a controller based on the sliding-mode approach for controlling both the position and the orientation of the robot. The entire control structure that permits full control of the robot posture comprises three imbricated loops. Simulations showing good performance of the controlled system are provided. Preliminary tests performed on an experimental platform confirm the validity of the controller.

We introduce a novel control scheme for an anti-tilting mobile robot moving on an inclined plane. The robot pertains to the family of mobile wheeled pendulums. The challenge faced here consists in designing a controller for the robot orientation and its forward velocity, while, concurrently, stabilizing the unstable zero-dynamics, due to the undamped oscillation of the central body. An internal feedback control structure is proposed, composed of two imbricated loops, and based on an intrinsic dynamical property of the system, that would be referred to as the natural behavior of the system. Simulations of the controlled motion, using MATLAB/Simulink, are provided

We present a new approach for vertical motion feedback control of a hopping robot. The task of the feedback control is to stabilize the robotic system to a desired limit cycle under existing constraints on the controls. Unlike most previous methods, the approach presented here does not rely on the construction of the Poincare map, which simplifies the subsequent analysis, but can be difficult or impossible to obtain analytically. The method can also be applied to more complicated, possibly nonlinear models of legged robots, as well as other variable structure systems.

This paper presents a novel, systematic approach to the construction of feedback control for stabilization to a set point of drift free systems. The method relies on the introduction of a set of guiding functions whose sum vanishes only at the reference set point. The guiding functions are not Lyapunov functions, however, a comparison of their values allows one to determine a desired direction of system motion and permits construction of a sequence of controls such that the sum of the guiding functions decreases in an average sense. The method is applied to control a model of a four wheeled platform which can serve as a support for a mobile robot.