Norman P. Coleman

Adaptive feedback linearization control of chaotic systems via recurrent high-order neural networks

In the realm of nonlinear control, feedback linearization via differential geometric techniques has been a concept of paramount importance. However, the applicability of this approach is quite limited, in the sense that a detailed knowledge of the system nonlinearities is required. In practice, most physical chaotic systems have inherent unknown nonlinearities, making real-time control of such chaotic systems still a very challenging area of research. In this paper, we propose using the recurrent high-order neural network for both identifying and controlling unknown chaotic systems, in which the feedback linearization technique is used in an adaptive manner. The global uniform boundedness of parameter estimation errors and the asymptotic stability of tracking errors are proved by the Lyapunov stability theory and the LaSalle-Yoshizawa theorem. In a systematic way, this method enables stabilization of chaotic motion to either a steady state or a desired trajectory. The effectiveness of the proposed adaptive control method is illustrated with computer simulations of a complex chaotic system.

Optimal digital redesign of continuous-time controllers

This paper proposes a new optimal digital redesign technique for finding a dynamic digital control law from the available analog counterpart and simultaneously minimizing a quadratic performance index. The proposed technique can be applied to a system with a more general class of reference inputs, and the developed digital regulator can be implemented using low cost microcomputers.

Block-Diagonalization and Block-Triangularization of a Matrix via the Matrix Sign Function.

Abstract A matrix sign function in conjunction with a geometric approach is utilized to construct a block modal matrix and a (scalar) modal matrix of a system map, so that the system map can be block-diagonalized and block-triangularized, and that the Riccati-type problems can be solved.

Algorithms for solvents and spectral factors of matrix polynomials

A generalized Newton method, based on the contracted gradient of a matrix polynomial, is derived for solving the right (left) solvents and spectral factors of matrix polynomials. Two methods of selecting initial estimates for rapid convergence of the newly developed numerical method are proposed. Also, new algorithms for solving complete sets of the right (left) solvents and spectral factors without directly using the eigenvalues of matrix polynomials are derived. The proposed computer-aided method can be used to determine the spectral factorization of a matrix polynomial for optimal control, filtering and estimation problems.

Observer-type Kalman innovation filter for uncertain linear systems

An observer-type of Kalman innovation filtering algorithm to find a practically implementable best Kalman filter, and such an algorithm based on the evolutionary programming (EP) optima-search technique, are proposed, for linear discrete-time systems with time-invariant unknown-but-hounded plant and noise uncertainties. The worst-case parameter set from the stochastic uncertain system represented by the interval form with respect to the implemented best filter is also found in this work for demonstrating the effectiveness of the proposed filtering scheme. The new EP-based algorithm utilizes the global optima-searching capability of EP to find the optimal Kalman filter and state estimates at every iteration, which include both the best possible worst case Interval and the optimal nominal trajectory of the Kalman filtering estimates of the system state vectors. Simulation results are included to show that the new algorithm yields more accurate estimates and is less conservative as compared with other related robust filtering schemes.

Digital interval modeling and hybrid control of uncertain systems

This paper addresses two issues: (1) converting a continuous-time uncertain system to an equivalent discrete-time interval model; and (2) constructing a robust digital control law from a robust analogue control law for hybrid control of sampled-data uncertain systems. The system matrices characterizing the state-space representation of the original continuous-time uncertain systems are assumed to be interval matrices. The Pade approximation method together with a geometric-series approximation method is employed to obtain the generalized enclosing discrete-time interval models. The generalized enclosing interval models are able to tightly enclose the exact discrete-time uncertain model, and can be utilized for digital simulation and digital design of continuous-time uncertain systems. A new family of digitally redesigned interval controllers is constructed from a continuous-time robust controller for robust digital control of continuous-time uncertain systems. Using the newly digitally redesigned interval controllers, the dynamic states of the digitally controlled sampled-data uncertain systems are able to closely match those of the original analogously controlled continuous-time uncertain systems for a relatively longer sampling period.

Optimization of Weapon–Target Pairings Based on Kill Probabilities

In this paper, we present a novel optimization algorithm for assigning weapons to targets based on desired kill probabilities. For the given weapons, targets, and desired kill probabilities, our optimization algorithm assigns weapons to targets that satisfy the desired kill probabilities and minimize the overkill. The minimization of overkill assures that any proper subset of the weapons assigned to a target results in a kill probability that is less than the desired kill probability on such a target. Computational results for up to 120 weapons and 120 targets indicate that the performance of this algorithm yields an average improvement in quality of solutions of 26.8% over the greedy algorithms, whereas execution times remained on the order of milliseconds.

Control of Weapon Pointing Systems Based on Robotic Formulation

A robotic formulation and control of weapon pointing systems are investigated. Specifically, a complete mathematical model for a helicopter and tank gun-turret system has been developed based on robotic formulation and methodology. The resultant mathematical model will automatically take into account the interaxis dynamics and nonlinear coupling between the azimuth and elevation axes, thereby providing more insight into the physics of the gun-turret characteristics. One of the major advantages of the proposed approah is that modern robotic technology, known for its versatility and ability to meet stringent performance requirements, can be utilized in the design and implementation of a large class of modern weapon pointing and platform systems with superior performance capabilities.

Semi-autonomous formation control of a single-master multi-slave teleoperation system

The primary objective of this paper is to develop an adaptive formation control method for a team of mobile robotic agents, which implements formation control, obstacle avoidance, and operator induced error compensation for unconstrained motions. In this approach, a leader robot is selected and teleoperated by an operator and the follower robots are autonomously coordinated to make a formation to perform a variety of tasks such as searching and/or pursuing targets, reconnaissance, etc. The formation can be reconfigured to avoid collisions with stationary obstacles and among the member robots. The performance of the developed method was investigated through haptic simulations and experiments. In the simulation study, a haptic device was used as the master robot, and three virtual nonholonomic mobile platforms were employed. The developed method was implemented on two differentially driven Pioneer-AT platforms. Both studies demonstrated consistent performance of the semi-autonomous formation control method in the presence of time-varying communication delays, erroneous operator commands, and stationary obstacles.

Stability of a class of multivariable control systems described by nested matrix continued-fractions

This paper deals with the stability of a class of multivariable control systems which can be described by a right (left) matrix fraction description and associated right (left) matrix continued-fraction description in the nested Cauer form. Some simple sufficient conditions and some simple necessary conditions are developed for stability determination of the class of multivariable systems via the Lyapunov stability and instability theorems. By simple testing of the (positive or negative) definiteness of a set of matrix quotients obtained from the matrix Sturm algorithms, the stability of the class of multivariable systems can be determined. The matrix fraction descriptions of interest may be unsymmetric and reducible.