Adaptive optimization of discrete stochastic systems

The general theory of stochastic optimal control is based on determining a control which minimizes an expected cost. However, the use of minimum expected cost as a design objective is arbitrary. A direct consequence of this choice is the need for extensive statistical information. If the required statistical data is not available or not accurate, the controller is suboptimum. The thesis begins with the investigation of the conventional method of solution and proposes an interpretation of the solution which introduces a different approach. This approach does not use the expected cost as design objective. The suggested new criterion is based on a trade-off between deterministic optimization and a cost penalty for estimation error. In order to have a basis of comparison with the conventional method, the proposed adaptive stochastic controller is compared with the standard stochastic optimal controller for a linear discrete system associated with linear measurements, additive noise and quadratic cost. The basic feature of the proposed method is the introduction of an adaptive filter gain which enters the proposed cost index algebraically and couples the controller with the estimator. Unlike the conventional Kalman-Bucy filter gain, the proposed gain is a scalar independent of the second and higher order moments of noise distributions. Simulation is carried out on second and fifth order linear systems with gaussian and non gaussian noises distributions. There is a moderate cost increase of 1% to 12%. The method is then extended to nonlinear systems. A general solution of the nonlinear problem is formulated and a complete investigation of the properties of the solution is given for different cases. Stability of the expected tracking error of the filter is guaranteed by introducing bounds on the filter gain. Problems arising from the use of suboptimum structures for the control are examined and discussed. It is shown that for a class of systems the proposed method has a particularly attractive form. As in the linear case, the required statistical information is limited to the expected values of the noises, and the expected value of the initial state of the system. Simulation executed on second order systems indicates a cost decrease of 1% to 20% when compared with the method using an extended Kalman-Bucy filter.Applied Science, Faculty ofElectrical and Computer Engineering, Department ofGraduat

A simple iterative method for sub-optimal control of linear time delay systems with quadratic cost

The usual approach for obtaining the optimal control For a linear time-delay system with a quadratic cost consists of first deriving a set of necessary conditions for optimality and then using conventional iterative numerical methods to find a control satisfying those conditions. The burden of computation in this approach is enormous. The iterative scheme proposed in this paper does not proceed along these lines. Instead, the delay term is treated liko an extra perturbing input. A linear non-delay system is optimized at each stage, and the resulting sequence of control functions converges rapidly to the sub-optimal control for the original problem, as illustrated by two numerical examples

Suboptimal control of neutral systems

The usual approach for obtaining the optimal control for a neutral system with quadratic cost consists of first deriving a set of necessary conditions for optimality and then using conventional iterative numerical methods to find a control satisfying those conditions. The burden of computation in this approach is enormous. The suboptimum iterative scheme proposed in this paper does not proceed along those lines. Instead, the neutral system is first converted into a non-linear time-delay system. The non-linear delay term is then treated like an extra perturbing input. A linear non-delay system is optimized at each stage and the resulting sequence of control functions converges rapidly to a suboptimal control for the original problem. One numerical example illustrates the technique

The biomechanics of the thoracolumbar fascia

The back muscles alone are unable to provide the extensor moment required to lift large weights, and must be aided by another source of anti-flexion moments. It has been postulated that contraction of the abdominal muscles can provide an extension moment by developing tension in the thoracolumbar fascia (TLF). Anatomical studies and a biomechanical analysis, however, reveal that the anti-flexion moment generated in this way is only very small. Too little of the abdominal musculature attaches to the TLF to generate a significant tension in it. Previous calculations of the forces in the TLF have overestimated the tension developed in it because of erroneous assumptions and interpretations of the relevant anatomy. Whatever the role played by the TLF in lifting it must be essentially independent of abdominal mechanisms