A geometric approach to structural model matching by output feedback in linear impulsive systems

AbstractThis paper provides a complete characterization of solvability of the problem of structural model matching by output feedback in linear impulsive systems with nonuniformly spaced state jumps. Namely, given a linear impulsive plant and a linear impulsive model, both subject to sequences of state jumps which are assumed to be simultaneous and measurable, the problem consists in finding a linear impulsive compensator that achieves exact matching between the respective forced responses of the linear impulsive plant and of the linear impulsive model, by means of a dynamic feedback of the plant output, for all the admissible input functions and for all the admissible sequences of jump times. The solution of the stated problem is achieved by reducing it to an equivalent problem of structural disturbance decoupling by dynamic feedforward. Indeed, this latter problem is formulated for the so-called extended linear impulsive system, which consists of a suitable connection between the given plant and a modified model. A necessary and sufficient condition for the solution of the structural disturbance decoupling problem is first shown. The proof of sufficiency is constructive, since it is based on the synthesis of the compensator that solves the problem. The proof of necessity is based on the definition and the geometric properties of the unobservable subspace of a linear impulsive system subject to unequally spaced state jumps. Finally, the equivalence between the two structural problems is formally established and proven

Approximate Nonlinear Regulation via Identification-Based Adaptive Internal Models

This article concerns the problem of adaptive output regulation for multivariable nonlinear systems in normal form. We present a regulator employing an adaptive internal model of the exogenous signals based on the theory of nonlinear Luenberger observers. Adaptation is performed by means of discrete-time system identification schemes, in which every algorithm fulfilling some optimality and stability conditions can be used. Practical and approximate regulation results are given relating the prediction capabilities of the identified model to the asymptotic bound on the regulated variables, which become asymptotic whenever a “right” internal model exists in the identifier's model set. The proposed approach, moreover, does not require “high-gain” stabilization actions

Stochastic Event-Based Control and Estimation

Digital controllers are traditionally implemented using periodic sampling, computation, and actuation events. As more control systems are implemented to share limited network and CPU bandwidth with other tasks, it is becoming increasingly attractive to use some form of event-based control instead, where precious events are used only when needed. Forms of event-based control have been used in practice for a very long time, but mostly in an ad-hoc way. Though optimal solutions to most event-based control problems are unknown, it should still be viable to compare performance between suggested approaches in a reasonable manner. This thesis investigates an event-based variation on the stochastic linear-quadratic (LQ) control problem, with a fixed cost per control event. The sporadic constraint of an enforced minimum inter-event time is introduced, yielding a mixed continuous-/discrete-time formulation. The quantitative trade-off between event rate and control performance is compared between periodic and sporadic control. Example problems for first-order plants are investigated, for a single control loop and for multiple loops closed over a shared medium. Path constraints are introduced to model and analyze higher-order event-based control systems. This component-based approach to stochastic hybrid systems allows to express continuous- and discrete-time dynamics, state and switching constraints, control laws, and stochastic disturbances in the same model. Sum-of-squares techniques are then used to find bounds on control objectives using convex semidefinite programming. The thesis also considers state estimation for discrete time linear stochastic systems from measurements with convex set uncertainty. The Bayesian observer is considered given log-concave process disturbances and measurement likelihoods. Strong log-concavity is introduced, and it is shown that the observer preserves log-concavity, and propagates strong log-concavity like inverse covariance in a Kalman filter. A recursive state estimator is developed for systems with both stochastic and set-bounded process and measurement noise terms. A time-varying linear filter gain is optimized using convex semidefinite programming and ellipsoidal over-approximation, given a relative weight on the two kinds of error

Developing Design and Analysis Framework for Hybrid Mechanical-Digital Control of Soft Robots: from Mechanics-Based Motion Sequencing to Physical Reservoir Computing

The recent advances in the field of soft robotics have made autonomous soft robots working in unstructured dynamic environments a close reality. These soft robots can potentially collaborate with humans without causing any harm, they can handle fragile objects safely, perform delicate surgeries inside body, etc. In our research we focus on origami based compliant mechanisms, that can be used as soft robotic skeleton. Origami mechanisms are inherently compliant, lightweight, compact, and possess unique mechanical properties such as– multi-stability, nonlinear dynamics, etc. Researchers have shown that multi-stable mechanisms have applications in motion-sequencing applications. Additionally, the nonlinear dynamic properties of origami and other soft, compliant mechanisms are shown to be useful for ‘morphological computation’ in which the body of the robot itself takes part in performing complex computations required for its control. In our research we demonstrate the motion-sequencing capability of multi-stable mechanisms through the example of bistable Kresling origami robot that is capable of peristaltic locomotion. Through careful theoretical analysis and thorough experiments, we show that we can harness multistability embedded in the origami robotic skeleton for generating actuation cycle of a peristaltic-like locomotion gait. The salient feature of this compliant robot is that we need only a single linear actuator to control the total length of the robot, and the snap-through actions generated during this motion autonomously change the individual segment lengths that lead to earthworm-like peristaltic locomotion gait. In effect, the motion-sequencing is hard-coded or embedded in the origami robot skeleton. This approach is expected to reduce the control requirement drastically as the robotic skeleton itself takes part in performing low-level control tasks. The soft robots that work in dynamic environments should be able to sense their surrounding and adapt their behavior autonomously to perform given tasks successfully. Thus, hard-coding a certain behavior as in motion-sequencing is not a viable option anymore. This led us to explore Physical Reservoir Computing (PRC), a computational framework that uses a physical body with nonlinear properties as a ‘dynamic reservoir’ for performing complex computations. The compliant robot ‘trained’ using this framework should be able to sense its surroundings and respond to them autonomously via an extensive network of sensor-actuator network embedded in robotic skeleton. We show for the first time through extensive numerical analysis that origami mechanisms can work as physical reservoirs. We also successfully demonstrate the emulation task using a Miura-ori based reservoir. The results of this work will pave the way for intelligently designed origami-based robots with embodied intelligence. These next generation of soft robots will be able to coordinate and modulate their activities autonomously such as switching locomotion gait and resisting external disturbances while navigating through unstructured environments

Uniform finite time stabilisation of non-smooth and variable structure systems with resets

This thesis studies uniform finite time stabilisation of uncertain variable structure and non-smooth systems with resets. Control of unilaterally constrained systems is a challenging area that requires an understanding of the underlying mechanics that give rise to reset or jumps while synthesizing stabilizing controllers. Discontinuous systems with resets are studied in various disciplines. Resets in states are hard nonlinearities. This thesis bridges non-smooth Lyapunov analysis, the quasi-homogeneity of differential inclusions and uniform finite time stability for a class of impact mechanical systems. Robust control synthesis based on second order sliding mode is undertaken in the presence of both impacts with finite accumulation time and persisting disturbances. Unlike existing work described in the literature, the Lyapunov analysis does not depend on the jumps in the state while also establishing proofs of uniform finite time stability. Orbital stabilization of fully actuated mechanical systems is established in the case of persisting impacts with an a priori guarantee of finite time convergence between t he periodic impacts. The distinguishing features of second order sliding mode controllers are their simplicity and robustness. Increasing research interest in the area has been complemented by recent advances in Lyapullov based frameworks which highlight the finite time Convergence property. This thesis computes the upper bound on the finite settling time of a second order sliding mode controller. Different to the latest advances in the area, a key contribution of this thesis is the theoretical proof of the fact that finite settling time of a second order sliding mode controller tends to zero when gains tend to infinity. This insight of the limiting behaviour forms the basis for solving the converse problem of finding an explicit a priori tuning formula for the gain parameters of the controller when and arbitrary finite settling time is given. These results play a central role ill the analysis of impact mechanical systems. Another key contribution of the thesis is that it extends the above results on variable structure systems with and without resets to non-smooth systems arising from continuous finite time controllers while proving uniform finite time stability. Finally, two applications are presented. The first application applies the above theoretical developments to the problem of orbital stabilization of a fully actuated seven link biped robot which is a nonlinear system with periodic impacts. The tuning of the controller gains leads to finite time convergence of the tracking errors between impacts while being robust to disturbances. The second application reports the outcome of an experiment with a continuous finite time controller

Development of a ground testing facility and attitude control for magnetically actuated nanosatellites

Growing popularity of the highly capable small- and nano-satellites, driven by components miniaturization, face new technological challenges and at the same time provides new opportunities for the whole space sector. Low cost of nanosatellites launches make them accessible. Reliability is an exigency: especially challenging is design and testing of Attitude and Determination Control Systems (ADCS). Demand for nanosatellitesdedicated attitude control algorithms and careful performance assessment of the spacecrafts motivates the research work presented in this thesis. In the first part of the manuscript, development and assessment of the three degreesoffreedom ADCS testbed for nanosatellites testing is described. The facility was developed within the Microsatellites and Space Microsystems Lab at University of Bologna, and designed to meet strict low-cost requirements. The facility includes several integrated subsystems to simulate the on-orbit environment: i) an air-bearing based, three degree of freedom platform with automatic balancing system, ii) a Helmholtz , iii) a Sun simulator, and iv) a metrology vision system . Experimental assessment of the subsystems guarantee necessary level of performance. Control law design for smallsats is addressed in the second part. Limited power availability and reliability makes magnetic actuation particularly suited for ADCS design, but, the control system faces inherent underactuation. To overcome the intrinsic limits of existing control designs, a novel approach to the three-axis attitude control of a magnetically actuated spacecrafts is proposed, based on hybrid systems theory. A local H-inf regulator with guaranteed performance and a global nonlinear controller used for ensuring global stability and robustness, are combined. Hybrid control theory is employed to develop a mixed continuous-discrete controller able to switch between different feedbacks. Analytical results are verified by means of realistic numerical simulations: errors on the state comply with the computed bounds and stability is guaranteed

OBSERVED NONLINEAR RESPONSES IN PATTERNED SUPERCONDUCTING, FERROMAGNETIC, AND INTERACTING THIN FILMS

Many advances in technology ranging from biology and medicine through engineering and computer science to fundamental physics and chemistry depend upon the capability to control the fabrication of materials and devices at the submicron scale. Quantum mechanical effects become increasingly important to atomic and molecular interactions as the distances between neighbors decrease. These effects will provide materials and device designers with additional flexibility to establish properties of the designers choice, but the cost of this additional flexibility must be paid in the complexity of nonlinearities entering the interactions and the design process. The work presented here has provided several early results on three such interactions among closely-spaced submicron material structures: 1) the properties of superconductivity have been studied, 2) the properties of ferromagnetism have been studied, and 3) the interactions between superconductivity and ferromagnetism have been studied. Since our work was published, there has been considerable interest in all three of these wide-open areas and hundreds or thousands of additional results are now in the literature. We have used standard methods from the semiconductor industry as well as innovative methods to fabricate micron and submicron devices for observation. Standard optical lithography and standard electron beam lithography have been implemented to shape micron and submicron structures, respectively. Additionally, a laser interferometric lithography method has been invented and used to shape submicron structures. The materials used were vanadium, niobium, nickel, and/or permalloy. We have utilized SQUID magnetometry and Hall effect magnetometry to observe the properties of superconductor structures and superconductorferromagnetic mixed systems. We have used SQUID magnetometry and ferromagnetic resonance to observe the physical properties of ferromagnetic structures and the interactions between adjacent structures. Using these materials and methods we have discovered an unusual paramagnetic Meissner effect in thin Nb films that exists at igh-applied magnetic fields. We have discovered fluxoid matching anomalies at low sample temperature. And we have discovered interactions between electron exchange and magnetic dipole forces. Additionally, we have found clear evidence to support several past hypotheses advanced by other authors