Numerical Method for Optimization of Semi-Passively Controlled Dynamical Systems

Controlled dynamical systems with different type of actuators (e.g. external powered electromotors, magnetostrictive actuators, internal unpowered (passive) spring-damper-like drives, etc.) are considered. \ua0These systems are termed semi-passively controlled. Mathematical statement of optimization problem has proposed that is suitable both for modeling of optimal motion and for optimization of structure of semi-passively controlled dynamical systems with different degree of actuation. Numerical method for solving the proposed optimization problem is described. The method was successfully used for solving optimal control problems for several semi-passively controlled dynamical systems (industrial robots, human locomotor system with intelligent lower limb prosthesis, bipedal locomotion robots, others). The results obtained have confirmed the efficiency of the proposed numerical method for solving optimization problems for semi-passively controlled dynamical systems. Analysis of the results gives insight into the study of the role of inherent dynamics in controlled motion and how much a dynamical system should be governed by external drives and how much by a system’s inherent dynamics. It has been shown that complex goal-directed and cost-efficient controlled motion of underactuated dynamical system can be design using optimal interaction between external powered drives and internal unpowered spring-damper-like drives. This constitutes the powerful ability of semi-passively controlled dynamical systems

Gradient and Passive Circuit Structure in a Class of Non-linear Dynamics on a Graph

We consider a class of non-linear dynamics on a graph that contains and generalizes various models from network systems and control and study convergence to uniform agreement states using gradient methods. In particular, under the assumption of detailed balance, we provide a method to formulate the governing ODE system in gradient descent form of sum-separable energy functions, which thus represent a class of Lyapunov functions; this class coincides with Csisz\'{a}r's information divergences. Our approach bases on a transformation of the original problem to a mass-preserving transport problem and it reflects a little-noticed general structure result for passive network synthesis obtained by B.D.O. Anderson and P.J. Moylan in 1975. The proposed gradient formulation extends known gradient results in dynamical systems obtained recently by M. Erbar and J. Maas in the context of porous medium equations. Furthermore, we exhibit a novel relationship between inhomogeneous Markov chains and passive non-linear circuits through gradient systems, and show that passivity of resistor elements is equivalent to strict convexity of sum-separable stored energy. Eventually, we discuss our results at the intersection of Markov chains and network systems under sinusoidal coupling

Network Synthesis of Linear Dynamical Quantum Stochastic Systems

The purpose of this paper is to develop a synthesis theory for linear dynamical quantum stochastic systems that are encountered in linear quantum optics and in phenomenological models of linear quantum circuits. In particular, such a theory will enable the systematic realization of coherent/fully quantum linear stochastic controllers for quantum control, amongst other potential applications. We show how general linear dynamical quantum stochastic systems can be constructed by assembling an appropriate interconnection of one degree of freedom open quantum harmonic oscillators and, in the quantum optics setting, discuss how such a network of oscillators can be approximately synthesized or implemented in a systematic way from some linear and non-linear quantum optical elements. An example is also provided to illustrate the theory.Comment: Revised and corrected version, published in SIAM Journal on Control and Optimization, 200

The implications of embodiment for behavior and cognition: animal and robotic case studies

In this paper, we will argue that if we want to understand the function of the brain (or the control in the case of robots), we must understand how the brain is embedded into the physical system, and how the organism interacts with the real world. While embodiment has often been used in its trivial meaning, i.e. 'intelligence requires a body', the concept has deeper and more important implications, concerned with the relation between physical and information (neural, control) processes. A number of case studies are presented to illustrate the concept. These involve animals and robots and are concentrated around locomotion, grasping, and visual perception. A theoretical scheme that can be used to embed the diverse case studies will be presented. Finally, we will establish a link between the low-level sensory-motor processes and cognition. We will present an embodied view on categorization, and propose the concepts of 'body schema' and 'forward models' as a natural extension of the embodied approach toward first representations.Comment: Book chapter in W. Tschacher & C. Bergomi, ed., 'The Implications of Embodiment: Cognition and Communication', Exeter: Imprint Academic, pp. 31-5