Howard M. Schwartz

Complementary results on the stability bounds of singularly perturbed systems

In this note, we will provide a new systematic approach to characterize and compute the stability bound of a singularly perturbed linear system. The approach is based on the feedback system representation of an additional matrix perturbation problem. The idea is to change the stability bound problem to the stability problem of an underlying feedback system. This approach allows multiple choices in formulating the underlying feedback system and thus has the potential of characterizing and computing the stability bound in a number of different ways. By formulating two kinds of different feedback systems, some existing and new results on the stability bounds are derived based on the feedback system approach. The new results complement the existing frequency-domain based stability criteria and make the frequency-domain technique more applicable and useful to the stability bound problem. An example is provided to show the new stability criterion is effective and useful in determining the stability bound.

Brief A directional forgetting algorithm based on the decomposition of the information matrix

A novel algorithm for directional forgetting is proposed based on a matrix decomposition method, which is developed in this paper. This algorithm performs exponential forgetting according to the direction of the data vector, thus preventing the problem known as estimator windup which is a characteristic of the standard exponential forgetting algorithm.

Analysis of the Kalman filter based estimation algorithm: an orthogonal decomposition approach

In this paper we shall provide new analysis on some fundamental properties of the Kalman filter based parameter estimation algorithms using an orthogonal decomposition approach based on the excited subspace. A theoretical analytical framework is established based on the decomposition of the covariance matrix, which appears to be very useful and effective in the analysis of a parameter estimation algorithm with the existence of an unexcited subspace. The sufficient and necessary condition for the boundedness of the covariance matrix in the Kalman filter is established. The idea of directional tracking is proposed to develop a new class of algorithms to overcome the windup problem. Based on the orthogonal decomposition approach two kinds of directional tracking algorithms are proposed. These algorithms utilize a time-varying covariance matrix and can keep stable even in the case of unsufficient and/or unbounded excitation.

Issues in Robot Adaptive Control

This paper compares several adaptive control algorithms which have been proposed for robotic manipulators. The methods which are investigated are the indirect method of adaptive control, and two versions of direct adaptive control. The direct adaptive control methods which are investigated are those proposed by Craig, Hsu and Sastry [3] and Slotine and Li [16]. The paper derives the adaptation laws and highlights the differences in the derivations. Each method has been simulated on the same trajectories and the performance is evaluated based on the tracking accuracy, the trajectory error dynamics and on the parameter estimation. Both persistently and non-persistently exciting trajectories are examined. In the case of indirect adaptive control, a regression vector reduction algorithm is proposed to guarantee identifiability of the parameters.

A Reinforcement Learning Adaptive Fuzzy Controller for Differential Games

In this paper we develop a reinforcement fuzzy learning scheme for robots playing a differential game. Differential games are games played in continuous time, with continuous states and actions. Fuzzy controllers are used to approximate the calculation of future reinforcements of the game due to actions taken at a specific time. If an immediate reinforcement reward function is defined, we may use a fuzzy system to tell what is the predicted reinforcement in a specified time ahead. This reinforcement is then used to adapt a fuzzy controller that stores the experience accumulated by the player. Simulations of a modified two car game are provided in order to show the potentiality of the technique. Experiments are performed in order to validate the method. Finally, it should be noted that although the game used as an example involves only two players, the technique may also be used in a multi-game environment.

Optimal control of a robot manipulator using a weighted time-energy cost function

An investigation of optimal control and path planning for a robot manipulator is conducted. A cost function which weights both the energy consumption of the manipulator and the time to go from one specified point to another is used. A nonlinear shooting algorithm is used to solve the minimization problem. The weighting on the manipulator energy consumption is set so that the joint actuators do not switch from positive to negative saturation and high-frequency unmodeled dynamics are not excited. Simulations of a two-degree-of-freedom arm are used to demonstrate the method.<<ETX>>

Genetic based fuzzy logic controller for a wall-following mobile robot

This paper addresses the problem of tuning fuzzy logic controllers. In this paper we presents a new technique called a genetic based fuzzy logic controller (GBFLC). The proposed technique is used to iteratively tune the set of fuzzy logic controller parameters such as membership functions and scaling factors. The proposed technique is also used to reduce the number of fuzzy rules. Computer simulations are performed on a wall-following mobile robot and the results show the usefulness of the proposed technique.

Oscillation, Instability and Control of Stepper Motors

A novel approach to analyzing instability in permanent-magnet stepper motors is presented. It is shown that there are two kinds of unstable phenomena in this kind of motor: mid-frequency oscillation and high-frequency instability. Nonlinear bifurcation theory is used to illustrate the relationship between local instability and mid-frequency oscillatory motion. A novel analysis is presented to analyze the loss of synchronism phenomenon, which is identified as high-frequency instability. The concepts of separatrices and attractors in phase-space are used to derive a quantity to evaluate the high-frequency instability. By using this quantity one can easily estimate the stability for high supply frequencies. Furthermore, a stabilization method is presented. A generalized approach to analyze the stabilization problem based on feedback theory is given. It is shown that the mid-frequency stability and the high-frequency stability can be improved by state feedback.

Self-learning fuzzy logic controllers for pursuit-evasion differential games

This paper addresses the problem of tuning the input and the output parameters of a fuzzy logic controller. The system learns autonomously without supervision or a priori training data. Two novel techniques are proposed. The first technique combines Q(@l)-learning with function approximation (fuzzy inference system) to tune the parameters of a fuzzy logic controller operating in continuous state and action spaces. The second technique combines Q(@l)-learning with genetic algorithms to tune the parameters of a fuzzy logic controller in the discrete state and action spaces. The proposed techniques are applied to different pursuit-evasion differential games. The proposed techniques are compared with the classical control strategy, Q(@l)-learning only, reward-based genetic algorithms learning, and with the technique proposed by Dai et al. (2005) [19] in which a neural network is used as a function approximation for Q-learning. Computer simulations show the usefulness of the proposed techniques.

Adaptive correction method for an OCXO and investigation of analytical cumulative time error upper bound

Traditional oscillators used in timing modules of CDMA and WiMAX base stations are large and expensive. Applying cheaper and smaller, albeit more inaccurate, oscillators in timing modules is an interesting research challenge. An adaptive control algorithm is presented to enhance the oscillators to meet the requirements of base stations during holdover mode. An oscillator frequency stability model is developed for the adaptive control algorithm. This model takes into account the control loop which creates the correction signal when the timing module is in locked mode. A recursive prediction error method is used to identify the system model parameters. Simulation results show that an oscillator enhanced by our adaptive control algorithm improves the oscillator performance significantly, compared with uncorrected oscillators. Our results also show the benefit of explicitly modeling the control loop. Finally, the cumulative time error upper bound of such enhanced oscillators is investigated analytically and comparison results between the analytical and simulated upper bound are provided. The results show that the analytical upper bound can serve as a practical guide for system designers.