Online identification and nonlinear control of the electrically stimulated quadriceps muscle

A new approach for estimating nonlinear models of the electrically stimulated quadriceps muscle group under nonisometric conditions is investigated. The model can be used for designing controlled neuro-prostheses. In order to identify the muscle dynamics (stimulation pulsewidth-active knee moment relation) from discrete-time angle measurements only, a hybrid model structure is postulated for the shank-quadriceps dynamics. The model consists of a relatively well known time-invariant passive component and an uncertain time-variant active component. Rigid body dynamics, described by the Equation of Motion (EoM), and passive joint properties form the time-invariant part. The actuator, i.e. the electrically stimulated muscle group, represents the uncertain time-varying section. A recursive algorithm is outlined for identifying online the stimulated quadriceps muscle group. The algorithm requires EoM and passive joint characteristics to be known a priori. The muscle dynamics represent the product of a continuous-time nonlinear activation dynamics and a nonlinear static contraction function described by a Normalised Radial Basis Function (NRBF) network which has knee-joint angle and angular velocity as input arguments. An Extended Kalman Filter (EKF) approach is chosen to estimate muscle dynamics parameters and to obtain full state estimates of the shank-quadriceps dynamics simultaneously. The latter is important for implementing state feedback controllers. A nonlinear state feedback controller using the backstepping method is explicitly designed whereas the model was identified a priori using the developed identification procedure

Towards Scalable Synthesis of Stochastic Control Systems

Formal control synthesis approaches over stochastic systems have received significant attention in the past few years, in view of their ability to provide provably correct controllers for complex logical specifications in an automated fashion. Examples of complex specifications of interest include properties expressed as formulae in linear temporal logic (LTL) or as automata on infinite strings. A general methodology to synthesize controllers for such properties resorts to symbolic abstractions of the given stochastic systems. Symbolic models are discrete abstractions of the given concrete systems with the property that a controller designed on the abstraction can be refined (or implemented) into a controller on the original system. Although the recent development of techniques for the construction of symbolic models has been quite encouraging, the general goal of formal synthesis over stochastic control systems is by no means solved. A fundamental issue with the existing techniques is the known "curse of dimensionality," which is due to the need to discretize state and input sets and that results in an exponential complexity over the number of state and input variables in the concrete system. In this work we propose a novel abstraction technique for incrementally stable stochastic control systems, which does not require state-space discretization but only input set discretization, and that can be potentially more efficient (and thus scalable) than existing approaches. We elucidate the effectiveness of the proposed approach by synthesizing a schedule for the coordination of two traffic lights under some safety and fairness requirements for a road traffic model. Further we argue that this 5-dimensional linear stochastic control system cannot be studied with existing approaches based on state-space discretization due to the very large number of generated discrete states.Comment: 22 pages, 3 figures. arXiv admin note: text overlap with arXiv:1407.273

CMOS design of chaotic oscillators using state variables: a monolithic Chua's circuit

This paper presents design considerations for monolithic implementation of piecewise-linear (PWL) dynamic systems in CMOS technology. Starting from a review of available CMOS circuit primitives and their respective merits and drawbacks, the paper proposes a synthesis approach for PWL dynamic systems, based on state-variable methods, and identifies the associated analog operators. The GmC approach, combining quasi-linear VCCS's, PWL VCCS's, and capacitors is then explored regarding the implementation of these operators. CMOS basic building blocks for the realization of the quasi-linear VCCS's and PWL VCCS's are presented and applied to design a Chua's circuit IC. The influence of GmC parasitics on the performance of dynamic PWL systems is illustrated through this example. Measured chaotic attractors from a Chua's circuit prototype are given. The prototype has been fabricated in a 2.4- mu m double-poly n-well CMOS technology, and occupies 0.35 mm/sup 2/, with a power consumption of 1.6 mW for a +or-2.5-V symmetric supply. Measurements show bifurcation toward a double-scroll Chua's attractor by changing a bias current