Feedback control of unsupported standing in paraplegia. Part I: optimal control approach

This is the first of a pair of papers which describe an investigation into the feasibility of providing artificial balance to paraplegics using electrical stimulation of the paralyzed muscles. By bracing the body above the shanks, only stimulation of the plantarflexors is necessary. This arrangement prevents any influence from the intact neuromuscular system above the spinal cord lesion. Here, the authors extend the design of the controllers to a nested-loop LQG (linear quadratic Gaussian) stimulation controller which has ankle moment feedback (inner loops) and inverted pendulum angle feedback (outer loop). Each control loop is tuned by two parameters, the control weighting and an observer rise-time, which together determine the behavior. The nested structure was chosen because it is robust, despite changes in the muscle properties (fatigue) and interference from spasticity

In-Silico Proportional-Integral Moment Control of Stochastic Gene Expression

The problem of controlling the mean and the variance of a species of interest in a simple gene expression is addressed. It is shown that the protein mean level can be globally and robustly tracked to any desired value using a simple PI controller that satisfies certain sufficient conditions. Controlling both the mean and variance however requires an additional control input, e.g. the mRNA degradation rate, and local robust tracking of mean and variance is proved to be achievable using multivariable PI control, provided that the reference point satisfies necessary conditions imposed by the system. Even more importantly, it is shown that there exist PI controllers that locally, robustly and simultaneously stabilize all the equilibrium points inside the admissible region. The results are then extended to the mean control of a gene expression with protein dimerization. It is shown that the moment closure problem can be circumvented without invoking any moment closure technique. Local stabilization and convergence of the average dimer population to any desired reference value is ensured using a pure integral control law. Explicit bounds on the controller gain are provided and shown to be valid for any reference value. As a byproduct, an explicit upper-bound of the variance of the monomer species, acting on the system as unknown input due to the moment openness, is obtained. The results are illustrated by simulation.Comment: 28 pages; 9 Figures. arXiv admin note: substantial text overlap with arXiv:1207.4766, arXiv:1307.644

Robust H2/H∞-state estimation for discrete-time systems with error variance constraints

Copyright [1997] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper studies the problem of an H∞-norm and variance-constrained state estimator design for uncertain linear discrete-time systems. The system under consideration is subjected to time-invariant norm-bounded parameter uncertainties in both the state and measurement matrices. The problem addressed is the design of a gain-scheduled linear state estimator such that, for all admissible measurable uncertainties, the variance of the estimation error of each state is not more than the individual prespecified value, and the transfer function from disturbances to error state outputs satisfies the prespecified H∞-norm upper bound constraint, simultaneously. The conditions for the existence of desired estimators are obtained in terms of matrix inequalities, and the explicit expression of these estimators is also derived. A numerical example is provided to demonstrate various aspects of theoretical results

Multivariable predictive controller for a test stand of air conditionning

In this paper a Multivariable Predictive Controller has been proposed in a stochastic framework for a M-input N-output system. It has been investigated using a simulation study based on an experimental model of an industrial test stand of air conditioning. Comparisons with the existing PID regulation show a great improvement : both step response and coupling effect limitation have been improved. With a 32 ms calculation time on a PC with 486DX processor (or 8 ms with a Pentium 100 processor), this regulator is able to answer the problems raised by this industrial test stand. Compatible with the industrial regulation hardware, this control algorithm will be soon set up and tested to lead the future air conditioning tests

Time Complexity of Decentralized Fixed-Mode Verification

Given an interconnected system, this note is concerned with the time complexity of verifying whether an unrepeated mode of the system is a decentralized fixed mode (DFM). It is shown that checking the decentralized fixedness of any distinct mode is tantamount to testing the strong connectivity of a digraph formed based on the system. It is subsequently proved that the time complexity of this decision problem using the proposed approach is the same as the complexity of matrix multiplication. This work concludes that the identification of distinct DFMs (by means of a deterministic algorithm, rather than a randomized one) is computationally very easy, although the existing algorithms for solving this problem would wrongly imply that it is cumbersome. This note provides not only a complexity analysis, but also an efficient algorithm for tackling the underlying problem