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In feedback control of dynamical systems, the choice of a higher loop gain is typically desirable to achieve a faster closed-loop dynamics, smaller tracking error, and more effective disturbance suppression. Yet, an increased loop gain requires a higher control effort, which can extend beyond the actuation capacity of the feedback system and intermittently cause actuator saturation. To benefit from the advantages of a high feedback gain and simultaneously avoid actuator saturation, this paper advocates a dynamic gain adaptation technique in which the loop gain is lowered whenever necessary to prevent actuator saturation, and is raised again whenever possible. This concept is optimized for linear systems based on an optimal control formulation inspired by the notion of linear quadratic regulator (LQR). The quadratic cost functional adopted in LQR is modified into a certain quasi-quadratic form in which the control cost is dynamically emphasized or deemphasized as a function of the system state. The optimal control law resulted from this quasi-quadratic cost functional is essentially nonlinear, but its structure resembles an LQR with an adaptable gain adjusted by the state of system, aimed to prevent actuator saturation. Moreover, under mild assumptions analogous to those of LQR, this optimal control law is stabilizing. As an illustrative example, application of this optimal control law in feedback design for dc servomotors is examined, and its performance is verified by numerical simulations. 

This paper presents the design, implementation, feedback stabilization, and experimental validation of a novel permanent magnet levitation system. Conventionally, magnetic levitation systems utilize electromagnets to levitate magnetic objects against gravity by stabilizing them around equilibrium points at which the applied magnetic force balances the gravity. This magnetic force must be dynamically adjusted by means of a stabilizing feedback loop, which is established by easy control of the electromagnet voltage. Despite the key advantage of easier control, electromagnets often produce much weaker magnetic forces compared to permanent magnets of similar size, weight, and cost. Therefore, this paper proposes the use of a permanent magnet to produce the magnetic force necessary for levitation, and the use of a linear servomotor to control the magnitude of this force by adjusting the distance between the magnet and the levitating object. To demonstrate this idea in practice, an experimental setup is designed, prototyped, and successfully stabilized using a computer-based feedback control loop. 

This paper presents experimental results to verify a novel concept of magnetic manipulation in which arrays of permanent magnets and electromechanical actuators generate and effectively control magnetic fields, through which, magnetic objects can be manipulated from a distance without any direct contact. This concept is realized by an experimental setup that consists of six diametrically magnetized permanent magnets actuated by rotary servomotors to control their directions, by which, the aggregate magnetic field is controlled in a planar circular workspace. To leverage this magnetic field for control of magnetic objects inside the workspace, a feedback loop must be established to command the servomotors based on the positions of these objects measured in real time. A suitable control law is developed for this feedback loop, and is verified by experiments, which demonstrate successful results. The experimental results are compared with those generated by computer simulations under similar conditions. 

This paper presents the concept, implementation, feedback control, and experimental verification of a noncontact magnetic manipulator that relies on a controllable array of permanent magnets to manipulate magnetized objects inside a workspace encircled by the magnets. To gain control over the aggregate magnetic field inside the workspace, the position of each magnet is independently controlled by a linear servomotor that dynamically changes the distance between that magnet and the workspace. By feedback control of the array of servomotors, the magnetic force applied to a magnetized object inside the workspace is dynamically adjusted to steer it along a desired reference trajectory. The successful steering of a small magnetic bead is demonstrated by experiments performed on a planar magnetic manipulator, designed and prototyped with six linear servomotors and six permanent magnets. 

A nonlinear estimation technique is proposed to combine a precise but inaccurate sensor with an accurate but imprecise one in such a manner that their fusion enables both precise and accurate measurement of a physical quantity. This estimation technique solely relies on certain bounds on the measurement noise, rather than a detailed statistical description of the noise and the measured quantity. The estimation strategy is to estimate the slowly-varying offset of the inaccurate sensor based on a dynamic model for its temporal evolution, and the observations of the imprecise sensor. This measurement offset is estimated by recursively generating some tight upper and lower bounds for it, and then, taking the midpoint of these~bounds as its midrange estimation. This estimation technique is verified effective both analytically and by Monte Carlo simulations. 

Closed-loop stability of uncertain linear systems is studied under the state feedback realized by a linear quadratic regulator (LQR). Sufficient conditions are presented that ensure the closed-loop stability in the presence of uncertainty, initially for the case of a non-robust LQR designed for a nominal model not reflecting the system uncertainty. Since these conditions are usually violated for a large uncertainty, a procedure is offered to redesign such a non-robust LQR into a robust one that ensures closed-loop stability under a predefined level of uncertainty. The analysis of this paper largely relies on the concept of inverse optimal control to construct suitable performance measures for uncertain linear systems, which are non-quadratic in structure but yield optimal controls in the form of LQR. The relationship between robust LQR and zero-sum linear quadratic dynamic games is established. 

This paper investigates a control strategy in which the state of a dynamical system is driven slowly along a trajectory of stable equilibria. This trajectory is a continuum set of points in the state space, each one representing a stable equilibrium of the system under some constant control input. Along the continuous trajectory of such constant control inputs, a slowly varying control is then applied to the system, aimed to create a stable quasistatic equilibrium that slowly moves along the trajectory of equilibria. As a stable equilibrium attracts the state of system within its vicinity, by moving the equilibrium slowly along the trajectory of equilibria, the state of system travels near this trajectory alongside the equilibrium. Despite the disadvantage of being slow, this control strategy is attractive for certain applications, as it can be implemented based only on partial knowledge of the system dynamics. This feature is in particular important for the complex systems for which detailed dynamical models are not available. 

This article investigates a stochastic optimal control problem with linear Gaussian dynamics, quadratic performance measure, but non-Gaussian observations. The linear Gaussian dynamics characterizes a large number of interacting agents evolving under a centralized control and external disturbances. The aggregate state of the agents is only partially known to the centralized controller by means of the samples taken randomly in time and from anonymous randomly selected agents. Due to removal of the agent identity from the samples, the observation set has a non-Gaussian structure, and as a consequence, the optimal control law that minimizes a quadratic cost is essentially nonlinear and infinite-dimensional, for any finite number of agents. For infinitely many agents, however, this paper shows that the optimal control law is the solution to a reduced order, finite-dimensional linear quadratic Gaussian problem with Gaussian observations sampled only in time. For this problem, the separation principle holds and is used to develop an explicit optimal control law by combining a linear quadratic regulator with a separately designed finite-dimensional minimum mean square error state estimator. Conditions are presented under which this simple optimal control law can be adopted as a suboptimal control law for finitely many agents. 

A magnetic levitation system consists of a magnet facing groundward to attract a magnetic object against gravity and levitate it at a distance from the face of magnet. Due to the unstable nature of this system, it must be stabilized by means of feedback control, which adjusts the magnetic force applied to the levitating object depending on its measured position and possibly velocity. Conventionally, electromagnets have been used for magnetic levitation, as they can be simply controlled via their terminal voltages. This paper, however, studies a levitation system relying on a permanent magnet and a linear servomotor to control the applied magnetic force by changing the distance between the magnet and the levitating object. For the proposed system, which is highly nonlinear, a stabilizing feedback control law is developed using feedback linearization and other control design tools. Then, the closed-loop stability is examined against system parameters such as the size of the levitating object, the viscosity of the medium it moves in, and certain characteristics of the magnet in use. The emphasis here is on understanding the impact of intrinsic servomotor limitations, particularly its finite slew rate (cap on its maximum velocity), on the ability of feedback control to stabilize the closed-loop system. This particular limitation seems to be a major concern in utilizing permanent magnets for noncontact actuation and control. 

A system of multiple agents is considered which at random times change their discrete states on an Ising lattice as a results of their internal interactions and possibly some external control. For certain applications such as directed self-assembly of charged particles, the stochastic dynamics of such interacting agents is represented by a master equation, or equivalently, by a continuous-time Markov chain. The dimension of this master equation is typically large and numerically intractable, since it grows combinatorially with the lattice size. This paper presents two alternative models at significantly lower complexity growing polynomially with the size of Ising lattice. These models describe the interactive dynamics of the agents by two different classes of coupled stochastic differential equations driven by doubly stochastic Poisson processes (Cox processes).