Control of Microparticle Assembly

A colloidal system is a large collection of micrometer-sized particles suspended in a liquid, and the state of the system can be measured in real time, using imaging techniques and image processing. The assembly of the particles is driven by interactions between the particles and the surrounding liquid, as well as by external fields, including electromagnetic, flow, and gravitational fields. The dynamics of the many-body system are high-dimensional, nonlinear, and stochastic. However, low-order models are derived in some cases, often using physics-based order parameters, to facilitate studying the system dynamics. With an understanding of the system dynamics, and by manipulating the aforementioned interactions, one can control the assembly process in real time using open-loop and closed-loop feedback control. Theoretical studies and experimental demonstrations of colloidal self-assembly control have been reported, with methods ranging from heuristic rules to model-based optimal feedback control. Expected final online publication date for the Annual Review of Control, Robotics, and Autonomous Systems, Volume 5 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Balanced Energy/Time Optimal Defibrillation

The synthesis of a cardiac defibrillating pulse is cast as a standard optimal feedback control problem that minimizes a weighted measure of consumed energy and elapsed time to reach a nominal defibrillated state. The solution is developed for a general first-order system that includes the widely used parallel resistor/capacitor circuit and energy source as a special case. The novel optimal pulse comprises an exponentially ascending and a rectangular component; it is agile and energy conscious; and it therefore outperforms the waveforms developed thus far that minimize energy or time expenditures alone. Explicit time-domain expressions are derived which may be used for comparing against other commonly studied defibrillating functions. The analytic formulas and computer simulations may be useful to implement performance improvements in defibrillating devices.

Fuzzy optimization of feedback control at induction heating

The problem of multi-criteria fuzzy-optimal feedback control of an induction heater as an object of technological thermophysics with distributed parameters is considered. A general formulation of the fuzzy optimization problem is given, including requirements for the final and intermediate states and taking into account the fuzziness of competing quality criteria. When solving the problem, interconnected electromagnetic and thermal models of the induction heating process were used. The secondary source method was used to simulate electromagnetic processes, and the differential-difference method was used to simulate thermal conductivity. The numerical method for solving the problem is based on the presentation of the control algorithm in the form of an a priori non-fixed and variable system of rules determined during the heating process. The obtained results of numerical modeling confirm the effectiveness of the proposed fuzzy-optimal method for determining the positional control of objects with distributed parameters.

Harmonic Passive Motion Paradigm

Humans can robustly interact with external dynamics that are not yet fully understood. This work presents a hierarchical architecture of semi-autonomous controllers that can control the redundant kinematics of the limbs during dynamic interaction, even with delays comparable to the nervous system. The postural optimisation is performed via a non-linear mapping of the system kineto-static properties, and it allows independent control of the end-effector trajectories and the arms stiffness. The proposed architecture is tested in a physical simulator in the absence of gravity, presence of gravity, and with gravity plus a viscous force field. The data indicates that the architecture can generalise the motor strategies to different environmental conditions. The experiments also verify the existence of a deterministic solution to the task-separation principle. The architecture is also compatible with Optimal Feedback Control and the Passive Motion Paradigm. The existence of a deterministic mapping implies that this task could be encoded in neural networks capable of generalisation of motion strategies to affine tasks.

Policy iteration for Hamilton–Jacobi–Bellman equations with control constraints

Policy iteration is a widely used technique to solve the Hamilton Jacobi Bellman (HJB) equation, which arises from nonlinear optimal feedback control theory. Its convergence analysis has attracted much attention in the unconstrained case. Here we analyze the case with control constraints both for the HJB equations which arise in deterministic and in stochastic control cases. The linear equations in each iteration step are solved by an implicit upwind scheme. Numerical examples are conducted to solve the HJB equation with control constraints and comparisons are shown with the unconstrained cases.