Adaptive dynamic programming

Unlike the many soft computing applications where it suffices to achieve a "good approximation most of the time," a control system must be stable all of the time. As such, if one desires to learn a control law in real-time, a fusion of soft computing techniques to learn the appropriate control law with hard computing techniques to maintain the stability constraint and guarantee convergence is required. The objective of the paper is to describe an adaptive dynamic programming algorithm (ADPA) which fuses soft computing techniques to learn the optimal cost (or return) functional for a stabilizable nonlinear system with unknown dynamics and hard computing techniques to verify the stability and convergence of the algorithm. Specifically, the algorithm is initialized with a (stabilizing) cost functional and the system is run with the corresponding control law (defined by the Hamilton-Jacobi-Bellman equation), with the resultant state trajectories used to update the cost functional in a soft computing mode. Hard computing techniques are then used to show that this process is globally convergent with stepwise stability to the optimal cost functional/control law pair for an (unknown) input affine system with an input quadratic performance measure (modulo the appropriate technical conditions). Three specific implementations of the ADPA are developed for 1) the linear case, 2) for the nonlinear case using a locally quadratic approximation to the cost functional, and 3) the nonlinear case using a radial basis function approximation of the cost functional; illustrated by applications to flight control.     

On the implementation of an analog ATPG: the nonlinear case

In order to reduce the complexity of the fault diagnosis equations and still retain computational simplicity, a self-testing algorithm has been proposed and implemented on a VMS VAX 11/780 for linear circuits. A prototype implementation of such an algorithm for nonlinear circuits and systems is presented. The proposed analog automatic test program generator (AATPG) for nonlinear circuits and systems is divided into offline and online processes. Unlike the simulation of the pseudocircuits in the linear case, which can be achieved by a matrix/vector multiplication, the circuit simulator SPICE is used to simulate the nonlinear pseudocircuits. The automatic SPICE code generator required for this simulation is presented. The proposed AATPG for nonlinear circuits has been implemented on a VMS VAX 11/780. The actual test can be run in either a fully automatic mode or interactively     

A new performance measure for stochastic optimization in Hilbert space

A stochastic optimization theory predicated on the minimization of the memoryless part of an error covariance operator is formulated. The existence of an appropriate memoryless part transformator is verified and its properties delineated. The resultant memoryless part of the error covariance operator is then used as a performance measure in a stochastic filtering problem which is minimized in the partial ordering of the positive hermitian operators. This results in an explicit solution to the filtering problem which formally replicates the classical solution obtained via a mean squared error criterion but which bypasses the restrictive hypotheses required to guarantee the existence of a mean squared error.The results presented in this paper were obtained while the author was visiting at the Department of Electrical Engineering, Texas Tech University.This research supported in part by NSF Grant ENG-79-11315.     

On the design of feedback controllers to achieve prescribed initial value constraints

The problem of designing a stabilizing compensator for a control system to achieve prescribed initial value constraints ⁽ⁱ⁾(0⁺)=y_i is considered. Indeed, modulo certain technical conditions, such a compensator exists if and only if y_i=0;i= 0,1,...,rp +rt –2; whererp is the relative degree of the plant andrt is the relative degree of the system input. This theorem is derived and a complete parameterization of the set of compensators that achieve the prescribed design constraints is formulated.This research was supported in part by NSF Grant No. 921106.     

Linear Hopfield networks and constrained optimization

It is shown that a Hopfield neural network (with linear transfer functions) augmented by an additional feedforward layer can be used to compute the Moore-Penrose generalized inverse of a matrix. The resultant augmented linear Hopfield network can be used to solve an arbitrary set of linear equations or, alternatively, to solve a constrained least squares optimization problem. Applications in signal processing and robotics are considered. In the former case the augmented linear Hopfield network is used to estimate the "structured noise" component of a signal and adjust the parameters of an appropriate filter on-line, whereas in the latter case it is used to implement an on-line solution to the inverse kinematics problem.     

Development and application of a Lyapunov synthesis based neural adaptive controller

The focus of this paper is to describe a neural adaptive control (NAC) technology derived using a Lyapunov synthesis technique. The NAC is a nonlinear adaptive controller which requires minimal plant information. It adapts its gains in real time to maintain the desired performance and to automatically compensate for changes in plant dynamics caused by system failures, environmental changes, or component damage. As such, the NAC control technology has the potential to enhance system performance by automatically optimizing its control laws for each operating regime. It can also increase reliability by automatically compensating for plant damage and system failures.     

Time-discrete networks

In this letter, the authors pose an interesting area of study which, it is felt, will lead to a clarification of the relationship between network theory and system theory. Specifically, it is proposed that a formal study be made of networks of RLC components characterised by difference relations rather than differential relations. The main contribution is a set of definitions which preserve stability, passivity and other energy relations in the discrete-time case and which pass to the continuous time relations as the step size becomes small. The formalism introduced shows promise of providing a foundation for digital-computer network simulators.     

Feedback system design: The single-variate case — Part I

A recently developed algebraic approach to the feedback system design problem is reviewed via the derivation of the theory in the single-variate case. This allows the simple algebraic nature of the theory to be brought to the fore while simultaneously minimizing the complexities of the presentation. Rather than simply giving a single solution to the prescribed design problem we endeavor to give a complete parameterization of the set of compensators which meet specifications. Although this might at first seem to complicate our theory it, in fact, opens the way for a sequential approach to the design problem in which one parameterizes the subset of those compensators which meet the second specification...etc. Specific problems investigated include feedback system stabilization, the tracking and disturbance rejection problem, robust design, transfer function design, pole placement, simultaneous stabilization, and stable stabilization.This research was supported by the Joint Services Electronics Program at Texas Tech University under ONR Contract 76-C-1136.